CN109726417A

CN109726417A - The determination method of cylindrical-array wave force amplitude curve material calculation and envelope

Info

Publication number: CN109726417A
Application number: CN201810782937.7A
Authority: CN
Inventors: 曾晓辉; 孙哲; 于法军
Original assignee: Institute of Mechanics of CAS
Current assignee: Institute of Mechanics of CAS
Priority date: 2018-07-17
Filing date: 2018-07-17
Publication date: 2019-05-07
Anticipated expiration: 2038-07-17
Also published as: CN109726417B

Abstract

The present invention provides the determination methods of cylindrical-array wave force amplitude curve material calculation and envelope, coordinate system is established to cylindrical-array composed by the limited seat bottom cylinder arranged in a line and determines relevant parameter, interference effect based on any cylinder of mutually long cancellation theory analysis and its upstream and downstream cylinder diffracted wave, the descriptive model of spacing is fluctuated when obtaining wave incidence angle equal to zero and not equal to zero, fluctuates the expression formula of spacing and peak dot valley point abscissa, the material calculation in each region and the ordinate of peak dot and valley point are determined again；Each peak dot/each valley point line is obtained into up/down envelope of the wave force curve in non-trapping region.Present invention demonstrates that fluctuation spacing is only related with cylinder sum, the numbered cylinders of mark column position and wave incidence angle in cylindrical-array, workload can be reduced under the premise of guaranteeing precision, shortens design and assessment cycle.

Description

The determination method of cylindrical-array wave force amplitude curve material calculation and envelope

Technical field

The present invention relates to ocean engineering fields, in particular to penetrate cylindrical-array that water surface cylinder forms in wave by big quantity Under wave effect, the wave force amplitude for establishing wave force suffered by any cylinder based on mutually long cancellation theory fluctuates spacing in non-trapping region Descriptive model and wave force amplitude curve material calculation determination method and in non-trapping region wave force amplitude curve envelope Determination method.

Background technique

Be richly stored with the mining resources such as petroleum, natural gas and wind energy, wave in the ocean of land occupation ball surface product 71% The renewable energy that equal can be used for a long time for the mankind.As economic development is continuously increased the energy and resource requirement, in sea Midocean explores more opportunity for survival and seeks various substances and energy resource supply has become visible trend.

It either carries out marine resources exploitation, air space above sea exploitation, or reality and utilizes regenerable marine energy, require Develop the offshore structures as carrier.There is critically important a kind of works among these, although upper part building is different, Their floating body/support construction is made of multiple cylinders (that is, cylindrical-array) for penetrating the water surface.For example, offshore oil is flat Platform, bridge spanning the sea, super large floating body, wave-activated power generation array etc..Continuous expansion with socio-economic development to ocean development demand, Marine structure overall dimension becomes increasing, the rule of the cylindrical-array as above-mentioned marine structure floating body/support construction Mould also increases with it.In cylindrical-array the number of cylinder from initial units increase to more than ten, tens, it is hundreds of, very It is thousands of a to can reach.Single seat bottom cylindrical-array is one of typical pattern of cylindrical-array.Single seat bottom cylindrical-array herein Refer to: the center of circle that horizontal plane intersects gained circular cross section with each cylinder point-blank, from the bottom is led directly to incessantly The water surface and the cylindrical-array for penetrating the cylinder composition that the water surface extends up.Wave force suffered by cylindrical-array is to determine circle in water Column Array Design scheme, a key element for guaranteeing safety of structure, for this reason, it may be necessary to grasp wave force amplitude with dimensionless wave The rule of number variation.

The amplitude of suffered wave force is with dimensionless wave number on any cylinder in single seat bottom cylindrical-array as shown in Figure 1 Dipping and heaving, fluctuating change.In general, single column in the limited cylindrical-array of single larger amt (for example, quantity is greater than 9) There are three obvious features with wave number variation tool for the amplitude of wave force suffered by son: 1) wave force amplitude changes with dimensionless wave number The wave force curve of formation has several towering spikes, these towering spike region present invention are known as region I (RegionI)；2) near the I of region, which has several gradually smaller secondary peak and valleys, and the height at these secondary peaks is equal Spike and wave force curve fluctuation spacing lower than region I change with the change of dimensionless wave number, the region present invention Referred to as region II (Region II)；3) except above-mentioned two region, many places have fairly regular fluctuation, the area The domain present invention is known as region III (Region III).Above three area schematic is as shown in Figure 2.

Region I and region II are related with near-trapping, the two regions of the present invention are referred to as " capturing related region ". And region III, the present invention are called " non-trapping region ".The related region I and region II with capture has many in the world The research of near-trapping is delivered, and is understood it more deep.For non-trapping region, there is presently no to its fluctuation pattern There is further investigation, more lacks a kind of descriptive model for describing non-trapping region fluctuation spacing.Fluctuation spacing of the present invention refers to: wave Unrestrained power amplitude changes with dimensionless wave number on the wave force curve to be formed, two neighboring maximum point (or minimum point) abscissa The distance between.In the present invention, also with " peak " or " paddy " Lai Zhidai maximum point or minimum point.Between the fluctuation of non-trapping region Design level can be improved to facilitate with the fatigue life of lesser cost extending structure away from being described.This is because Found after investigating a large amount of calculated results, the relative mistake of adjacent peak and valley numerical value is sometimes larger in wave force curve regions III, only from It can be found in the calculated result of limited quantity, this relative mistake maximum is up to 20% or so in the III of region.

Therefore during actually calculating hydrodynamic, if the acquirement of abscissa step-length is not small enough, in region III wave The error of unrestrained power calculated result is possible to reach 20% even more greatly." disposable " strength failure caused by for ultimate load Problem, this may be influenced less, because the wave force amplitude at trapping region spike is much higher than non-capture region, non-capture region phase 20% or so error of lesser wave force amplitude will not have an impact " disposable to destroy " of structure.But for following For fatigue rupture caused by ring load, since the calculating of fatigue life needs to be included in the comprehensive of the wave force within the scope of certain frequency Contribution (and not only only needing to consider corresponding maximum value under trapping region near-trapping frequency as intensive analysis) is closed, Therefore there may be apparent negative effects for above-mentioned wave force calculation error.This is because tired in analysis linear time invariant system When the labor service life, the spectral density function of alternate stress response is equal to the wave spectrum density of input multiplied by the flat of ssystem transfer function mould Side.Conventional marine structure Elastic mode intrinsic frequency is much higher than wave frequencies, therefore by wave force amplitude as shown in Figure 2 Transmission function can obtain the transmission function of alternate stress amplitude multiplied by some coefficient.If wave force transmission function is calculating When inappropriate generation large error selected due to step-length, then alternate stress amplitude transmission function equally can also generate large error, This error will become much larger (for example, if the mould error 10% of transmission function, error just will increase after square after so square To 20%, if the mould error 20% of transmission function, after square 36%) error will increase to.To which the friendship of inaccuracy can be obtained Varying stress response results, and then influence the accuracy of Fatigue Life Assessment.It is considered that cylindrical-array is in design under normal circumstances The near-trapping frequency of system can be made to avoid the biggish frequency range of Wave energy, this can make the alternate stress of non-trapping region exist To occupying very big share in the contribution of fatigue damage.Thus, the accurate calculating of non-trapping region wave force as shown in Figure 2 is for tired The accurate evaluation in labor service life is significant.

In summary, it is desirable to which the premise for efficiently and accurately obtaining non-trapping region wave force is to grasp non-trapping region wave force Curve wave characteristic, and obtain the descriptive model for capableing of the prior non-trapping region wave force curve fluctuation spacing of Accurate Prediction.It is right In the non-trapping region for accounting for wave force curve major part region, i.e. (there is reality in the region to the fatigue life of evaluation structure to region III Meaning), also lack deep understanding to its wave characteristic at present, still changes being formed with dimensionless wave number without wave force amplitude Wave force curve fluctuates the descriptive model of spacing in non-trapping region as the basis efficiently assessed and designed.

Although in addition, more to the research of region I and region II at present, as previously described, because being fluctuated to region III special Property also lack heightened awareness, so to obtain accurate wave force curve, generally use the side for changing material calculation tentative calculation repeatedly Method carries out.How material calculation is chosen, before calculating starts can not quantitative estimation, substantially determined by guessing and attempting Initial calculation step-length and in turn corrected Calculation step-length.Even if this process is numerous for sophisticated expert, and very It is trivial and time-consuming and laborious.Insufficient for experience or absolutely not experience people, this process is then very heavy, of a high price 's.

Another question is, currently, carrying out related engineering structure design and assessment based on wave force curve When, for the peak valley point for avoiding missing wave force curve, it usually needs carry out complicated a large amount of calculating to wave force curve, this can draw Play the problems such as time cost is excessive and calculating is of a high price.And in scheme evaluation, type selecting or Preliminary design, this way can be led Inefficiency is caused, cost, lost time is significantly increased, it is very uneconomical.At this time, if it is possible to accurate quickly to grasp wave force song The boundary up and down of line fluctuation, so that it may reasonable preliminary solution is provided in the case where avoiding complicated calculating, therefore urgent A kind of method that can quick and precisely obtain wave force high and valley point is needed, to solve the above problems.

Summary of the invention

The invention aims to provide a kind of to penetrate cylindrical-array that water surface cylinder forms in wave action by big quantity Under, description of the wave force amplitude in non-trapping region fluctuation spacing of wave force suffered by any cylinder is established based on mutually long cancellation theory The determination method of model and wave force amplitude curve material calculation and determination in non-trapping region wave force amplitude curve envelope Method.

Particularly, the determination method of cylindrical-array wave force amplitude curve material calculation and envelope provided by the invention, Include the following steps:

Step 100, wave force amplitude is changed to multiple towering spikes in the wave force curve to be formed with dimensionless wave number Region is nearby lower than the towering spike as region I, by towering spike and curve fluctuation spacing changes with dimensionless wave number Become and the secondary peak and valley region that changes is as region II, using the wave force curve after exclusionary zone I and region II as Region III；

Step 200, the cylindrical-array coordinate system as composed by the limited identical seat bottom cylinder arranged in a line is established And determine relevant parameter, convert dimensionless wave number to the ratio of adjacent two circles intercolumnar distance and wavelength, then the diffraction of each cylinder There is peak dot in wave force curve when constructive interference occurs for wave, and valley point occurs in wave force curve when destructive interference occurs；For wave The null situation of incidence angle, analysis incidence wave passes to any some cylinder generation diffraction and incidence wave passes to the cylinder downstream most The wave path-difference in the two paths of diffraction occurs for the latter cylinder, finds out any peak dot abscissa in wave force curve regions III The preliminary expression formula of preliminary expression formula and the difference of adjacent peak dot abscissa, and the preliminary expression formula and phase of any valley point abscissa The preliminary expression formula of the difference of adjacent valley point abscissa, and then know the difference phase of the abscissa of two neighboring peak dot or two neighboring valley point Deng finally obtaining preliminary fluctuation spacing expression formula of any cylinder wave force curve in the III of region；

Step 300, in some any cylinder upstream end, the left biography diffracted wave upstream propagated which is generated and should The left biography diffracted wave summation that each cylinder in cylinder downstream generates, takes Asymptotic Expression to be simplified, obtains using Hankel function And position and existing column position of equal value with current cylindrical-array are all different for fluctuation pitch problems two are located at should The specific location of the cylinder of equal value in cylinder downstream substitutes into the position from that farther cylinder of equal value of the cylinder between preliminary fluctuation Preliminary expression formula away from expression formula, the preliminary expression formula of any peak dot abscissa and any valley point abscissa is modified The final expression formula of spacing, any peak dot abscissa are fluctuated when obtaining wave incidence angle equal to zero in wave force curve regions III Final expression formula and any valley point abscissa final expression formula；

Step 400, zero situation is not equal to for wave incidence angle, utilizes aforementioned same method, first analysis incidence wave Pass to some any cylinder occur diffraction and incidence wave pass to the cylinder upstream the cylinder of array end first occur diffraction this The wave path-difference in two paths, then analysis incidence wave passes to any some cylinder generation diffraction and incidence wave passes to the cylinder downstream The last one cylinder occur the two paths of diffraction wave path-difference, any cylinder wave force curve can be respectively obtained in region The preliminary expression formula one of any peak dot abscissa, any paddy as caused by the effect of the cylinder upstream cylinder diffracted wave in III The preliminary expression formula one of point abscissa and preliminary fluctuation spacing expression formula one, and the work due to the cylinder downstream cylinder diffracted wave With between the preliminary expression formula two of caused any peak dot abscissa, the preliminary expression formula two of any valley point abscissa and preliminary fluctuation Away from expression formula two；

Step 500, first at the downstream of some any cylinder, to the right biography diffraction of cylinder generation downstream propagated The right biography diffracted wave summation that each cylinder of wave and the cylinder upstream generates, is corrected using aforementioned same method, obtains wave and enter When firing angle is not equal to zero, the final expression formula one of any peak dot abscissa, the final expression formula one of any valley point abscissa and most Fluctuation spacing expression formula one eventually；Then, in the upstream end of some any cylinder, the left biography upstream propagated generated to the cylinder The left biography diffracted wave summation that each cylinder of diffracted wave and the cylinder downstream generates, obtains the horizontal seat of any peak dot after same method amendment The final expression formula two of target, the final expression formula two of any valley point abscissa and final fluctuation spacing expression formula two；Using final The smaller person for the fluctuation spacing that fluctuation spacing expression formula one and final fluctuation spacing expression formula two provide as wave incidence angle not The final expression formula of spacing is fluctuated when equal to zero；

Step 600, the final expression formula of fluctuation spacing calculates region III when according to incidence angle equal to zero and not equal to zero In minimal ripple spacing, using the minimal ripple spacing as the upper limit of wave force curve material calculation in the III of region, according to Different accuracy is required minimal ripple spacing divided by corresponding natural number as the lower limit of material calculation in the III of region, thus To the material calculation of region III；

It is required the minimal ripple spacing of region III according to the required accuracy divided by the corresponding natural number of corresponding required precision, Obtain the material calculation in the II of region；It requires to want the minimal ripple spacing of region III divided by corresponding precision according to the required accuracy Corresponding natural number is sought, the material calculation in the I of region is obtained；

Step 700, using the smaller person of abscissa in final expression formula one and final expression formula two as wave incidence angle The final expression formula of the final expression formula of any peak dot abscissa and any valley point abscissa when not equal to zero, comprehensive wave are incident It is any in the III of region that any cylinder wave force curve can be obtained in final expression formula when angle is equal to zero and not equal to zero The final expression formula of the final expression formula of peak dot abscissa and any valley point abscissa；It is obtained according to the final expression formula of abscissa Abscissa at any peak dot and valley point solves system of linear equations so as to obtain corresponding wave number to obtain velocity potential expression formula In unknown diffraction coefficient, and then wave force suffered by any cylinder can be obtained, the wave force nondimensionalization and modulus just obtains Ordinate of the wave force curve in the III of region at any peak dot and valley point；

According to the abscissa at any peak dot of above-mentioned acquisition and valley point and the ordinate at any peak dot and valley point, determine These peak dot lines are just obtained coenvelope of the wave force curve in the III of region by the position of each peak dot and valley point out Line；By these valley point lines, lower envelope line of the wave force curve in the III of region is just obtained.

In an embodiment of the invention, in the cylindrical-array coordinate system, plane incidence direction of wave travel with The angle of positive direction of the x-axis is known as wave incidence angle in cylindrical-array global coordinate system, and the foundation of global coordinate system enters wave Firing angle is less than or equal to 90 degree；K is the number of any one cylinder in cylindrical-array, and number k augment direction and cylindrical-array are whole Positive direction of the x-axis is consistent in body coordinate system.

In an embodiment of the invention, it is described it is preliminary fluctuation spacing expression formula, any peak dot abscissa it is preliminary The acquisition process of expression formula and the preliminary expression formula of any valley point abscissa is as follows:

Dimensionless wave number Kd/ π can rewrite are as follows: Kd/ π=R/ λ；

First peak dot R in wave force curve_p(1)With valley point R_v(1)Corresponding intercolumniation is indicated with following formula:

2(N-k)R_p(1)=λ

Wherein, K is wave number, and R=2d is the intercolumniation of adjacent column, and λ is wavelength, and in footnote, p represents peak dot, and v represents paddy Point, (1) represent first peaks or valleys；

Enabling any s and the corresponding intercolumniation of the s+1 peak dot in the III of region is R_p(s)And R_p(s+1), R_p(s+1)=R_p(s) +δR_p, the condition that peak dot occurs is that constructive interference occurs, then adjacent s and the corresponding wave path-difference of the s+1 peak dot should divide It is not the wavelength of s times He s+1 times, it can thus be concluded that the preliminary expression formula of the difference of adjacent peak dot abscissa are as follows:

The condition that valley point occurs is that destructive interference occurs, for s and the corresponding intercolumniation R in the s+1 valley point_v(s)With R_v(s+1)=R_v(s)+δR_v, corresponding wave path-difference is respectively equal to 2s-1 times and 2s+1 times of half-wavelength, it can thus be concluded that the horizontal seat in adjacent valley point The preliminary expression formula of the difference of mark are as follows:

By above-mentioned derivation it is found that the difference of adjacent peak dot and the abscissa of adjacent valley point is equal, then tentatively fluctuation spacing expression Formula are as follows:

N is the cylinder sum in cylindrical-array；At this time in wave force curve regions III any peak dot abscissa preliminary table Up to the preliminary expression formula of formula and any valley point abscissa are as follows:

In an embodiment of the invention, obtain wave incidence angle be equal to zero when fluctuation spacing final expression formula, The process of the final expression formula of the final expression formula and any valley point abscissa of any peak dot abscissa is as follows:

In any k column upstream | x_k| place (x_k< 0) the left propagation diffracted wave that, each column of k column and k column downstream is upstream propagated Diffraction gesture sum to obtain:

Wherein,A_nFor the coefficient on the 1st column, i is imaginary unit, and ω is wave circular frequency, and t is the time, N is integer, Z_n=J '_n(Ka)/H′_n(Ka), K is wave number, J_nIt is Bessel function of the first kind, H_nIt is Hankel function of the first kind, a It is cylindrical radius；

Asymptotic Expression is taken have after simplifying Hankel function:

Wherein,Above formula Section 2 and Section 3 are equivalent to two and the left biography of k column Wave wave path-difference is the Overlay of the cylinder Zuo Chuanbo of equal value of 2 (R/2) and 2 (N+1/2-k) R, the two cylinders of equal value are located at k column At downstream R/2 and (N+1/2-k) R；

Wave can be obtained after being modified using the position from the farther cylinder of equal value of k column to preliminary fluctuation spacing expression formula The final expression formula of spacing is fluctuated in unrestrained force curve region III:

Likewise, the final expression formula of revised any peak dot abscissa and the final expression formula of any valley point abscissa Are as follows:

In an embodiment of the invention, the case where zero being not equal to for wave incidence angle, any peak dot abscissa Preliminary expression formula one, the preliminary expression formula one of any valley point abscissa and the acquisition process of preliminary fluctuation spacing expression one such as Under:

Wherein, k column is any one cylinder in cylindrical-array, and β is wave incidence angle, when enabling β ≠ 0, in the III of region Any s and the s+1 peak dot, the corresponding intercolumniation in valley point are After these are indicated that the symbol of intercolumniation is further added by superscript u, indicate to be acted on by each column right-hand rotation wave in upstream Caused corresponding amount；

It obtains tentatively fluctuating spacing expression one, the preliminary expression formula one of any peak dot abscissa and any valley point abscissa Preliminary expression formula one:

Above-mentioned three formula is modified to get the final table of final fluctuation spacing expression formula one, any peak dot abscissa is arrived Up to the final expression formula one of formula one and any valley point abscissa:

In an embodiment of the invention, the case where zero being not equal to for wave incidence angle, any peak dot abscissa Preliminary expression formula two, the preliminary expression formula two of any valley point abscissa and the acquisition process of preliminary fluctuation spacing expression two such as Under:

Wherein,Deng expression intercolumniation Away from symbol be further added by superscript l indicate by each column in downstream it is left pass wave effect caused by corresponding amount；Then available first Step fluctuation spacing expression formula two, the preliminary expression formula of the preliminary expression formula two of any peak dot abscissa and any valley point abscissa Two:

Above-mentioned three formula is modified to get the final table of final fluctuation spacing expression formula two, any peak dot abscissa is arrived Up to the final expression formula two of formula two and any valley point abscissa:

In an embodiment of the invention, when wave incidence angle is equal to zero, any cylinder wave force curve is in area Spacing is fluctuated in the III of domain are as follows:

When wave incidence angle is not equal to zero, any cylinder wave force curve fluctuates spacing in the III of region are as follows:

In an embodiment of the invention, the natural number value range of the region III is described between 2~10 The natural number value range of region II is between 5~10, and the natural number value range of the region I is between 40~50；Work as institute The material calculation for stating region III takes 1/5th region III minimal ripple spacing, and the material calculation of the region II takes very One of region III minimal ripple spacing, the material calculation of the region I takes between 1/50th region III minimal ripple Away from when, the computational accuracy of wave force curve reaches relative error within 1%.

In an embodiment of the invention, the process for obtaining the abscissa of each peak dot is as follows:

Situation null for wave incidence angle, any peak dot abscissa with intercolumniation in wave force curve regions III Final expression formula away from-wavelength than expression are as follows:

The case where zero is not equal to for wave incidence angle, final expression formula one and any peak in conjunction with any peak dot abscissa The available final expression with intercolumniation-wavelength than any peak dot abscissa indicated of final expression formula two of point abscissa Formula:

The process for obtaining the abscissa of each valley point is as follows:

Situation null for wave incidence angle, any valley point abscissa with intercolumniation in wave force curve regions III Final expression formula away from-wavelength than expression are as follows:

The case where zero is not equal to for wave incidence angle, final expression formula one and any paddy in conjunction with any valley point abscissa The available final expression formula with intercolumniation-wavelength than any valley point abscissa indicated of the final expression formula two of point abscissa:

In an embodiment of the invention, the ordinate acquisition modes of each described peak dot and the valley point are such as Under:

According to the steric factor φ (r for sitting velocity potential near any k column in bottom cylindrical-array Modelling Water Wave Diffraction Problems_k,θ_k) public Formula:

Wherein,For diffraction coefficient, k is the number of any one cylinder in cylindrical-array, number k augment direction and x-axis Positive direction is consistent, (r_k,θ_k) it is polar coordinates of the vertical axis z-axis by the partial cylindrical coordinate system of k mast axis, Z_n=J '_n (Ka)/H′_n(Ka), K is wave number, and a is cylindrical radius, J_nFor Bessel function of the first kind, H_nIt is Hankel function of the first kind, n is Integer.

The system of linear equations for solving diffraction coefficient in the velocity potential expression formula is as follows:

Wherein, β is the angle (wave of positive direction of the x-axis in plane incidence direction of wave travel and cylindrical-array global coordinate system Incidence angle), and the foundation of global coordinate system makes wave incident angle β≤pi/2, R_jkFor k-th of pillar to the distance of j-th of pillar, i For imaginary unit, m is integer, α_jkFor k-th of pillar to the deflection of j-th of pillar, I_kFor incidence wave k-th of pillar phase Location factor；

The corresponding wave number K substitution equation of the peak dot and the valley point can be acquired into the peak dot and the valley point is corresponding Diffraction coefficient under wave numberValue, by diffraction coefficientSubstitute into following formula

Wave force curve any peak dot and valley point in the III of region just can be obtained to correspond under wave number, edge suffered by any cylinder k The wave force F in each circle center line connecting direction in cylindrical-array horizontal cross-section^k；Wherein, ρ is the density of water, and g is acceleration of gravity, and A is The wave amplitude of incidence wave, h are the depth of water；

With the cylinder of identical geometric dimension, suffered wave force carries out wave force shown in preceding formula under same environmental conditions Nondimensionalization can be obtained wave force curve any peak dot and valley point in the III of region and correspond under wave number any kth in cylindrical-array The dimensionless wave force of column are as follows:

Dimensionless wave force amplitude i.e. is obtained to the formula modulus, this namely wave force curve any peak in the III of region Ordinate at point and valley point.

The present invention provides such understanding and understanding: it is bent that wave force amplitude changes the wave force to be formed with dimensionless wave number The fluctuation spacing of non-trapping region (region III) does not change with the variation of dimensionless wave number in line, the fluctuation spacing and cylinder Cylinder sum, the numbered cylinders of mark column position are related with wave incidence angle in array, the formula that can be provided with the present invention Accurate Prediction.

The present invention can deepen to change wave force amplitude with dimensionless wave number non-trapping region in the wave force curve to be formed The understanding and cognition of (region III) wave characteristic, the present invention provides the predictor formulas that spacing is fluctuated in non-trapping region.Based on this Invention can reduce workload when carrying out related Structural Design and assessment under the premise of guaranteeing precision, shorten design And assessment cycle, technical support is provided to improve design and the appreciable levels of engineering structure.

Method is determined using the wave force curve material calculation that the present invention provides, as long as cylinder is total in known cylindrical-array The cylinder number and wave incidence angle of number, mark column position, so that it may before the calculating of any cylindrical wave wave force curve starts, Accurate Prediction goes out that material calculation value is much to can be obtained accurate wave force curve.So as to do not increase blindly it is unnecessary Under the premise of calculating the time, accurate wave force curve is obtained, also can reduce workload under the premise of guaranteeing precision, contracted Short design and assessment cycle provide technical support to improve design and the appreciable levels of engineering structure.

The present invention gives the determination methods of envelope upper and lower in cylindrical-array wave force curve regions III, using this hair The calculation method of the bright peak dot valley point transverse and longitudinal coordinate provided can directly predefine peak dot in wave force curve regions III out With the position of valley point, the envelope up and down in wave force curve regions III is obtained.Thus set in scheme evaluation, type selecting or tentatively Timing can avoid calculating for these stages of Practical Project not while not missing wave force curve peak valley point Other too important a large amount of data points, so as to which calculation amount is greatly decreased, save the cost is improved efficiency, and is commented for final raising Estimate and provides technical support with design level.

Detailed description of the invention

Fig. 1 be one embodiment of the present invention in same diameter cylinder arrange in a line composed by cylindrical-array signal Figure；

Fig. 2 is cylinder sum N=17, numbered cylinders k=9, wave incident angle β=0, diameter-intercolumniation ratio a/d=1/4 Single seat foundation group's wave force amplitude change the wave force curve to be formed region (Region related with capture with dimensionless wave number I and Region II) and the trizonal schematic diagram such as non-trapping region (Region III)；

Fig. 3 is cylinder sum N=301, numbered cylinders k=151, wave incident angle β=0, diameter-intercolumniation ratio a/d= 1/2 single seat bottom cylindrical-array wave force amplitude under the corresponding dimensionless wave number of near-trapping spike is compiled with pillar Number modified-image；

Fig. 4 is cylinder sum N=301, numbered cylinders k=151, wave incident angle β=0, diameter-intercolumniation ratio a/d= Wave of the 1/2 single seat bottom cylindrical-array under the corresponding dimensionless wave number in near-trapping spike first left valley point Unrestrained power amplitude is with numbered cylinders modified-image；

Fig. 5 is cylinder sum N=301, numbered cylinders k=151, wave incident angle β=0, diameter-intercolumniation ratio a/d= Wave of the 1/2 single seat bottom cylindrical-array under the corresponding dimensionless wave number of near-trapping spike first left peak dot Unrestrained power amplitude is with numbered cylinders modified-image；

Fig. 6 is wave constructive interference/destructive interference schematic diagram；Wherein, curve of cyclical fluctuations N=21, numbered cylinders k=1, Wave incident angle β=0, the single seat bottom cylindrical-array wave force amplitude of diameter-intercolumniation ratio a/d=1/4 is with dimensionless wave number Change curve；

Fig. 7 is cylinder sum N=101, and wave incident angle β=0, diameter-intercolumniation ratio a/d=1/4, numbered cylinders k is not The figure that same wave force amplitude fluctuations pitch measurements change with dimensionless wave number；

It is N=11 that Fig. 8, which is cylinder number, 21,51,101, wave incident angle β=0, and when diameter intercolumniation ratio a/d=1/4, Fluctuation pitch measurements of the wave force amplitude that kth column is subject in region IIIAnd calculated valueBecome with numbered cylinders Change image.

Specific embodiment

Before elaborating particular content of the present invention, first introduces comprehensive existing research achievement and our analysis result obtains The method in relation to region (region I and region II) location and range is captured to standing wave wave force curve really.(region I and region II As the related region of capture described previously, the two regions have obviously deeper peak valley higher than region III, in addition, this two Another of a region is characterized in: fluctuation spacing changes with dimensionless wave number and is changed)

1) region I (capturing related region)

Have at present and arranges single cylinder on many literature research endless cylindrical-array or sink center's line Trapped mode frequency issues, these results can be evaluated whether that finite population sits the near-trapping wave number of bottom cylindrical-array, It can obtain the position of region I.Specific practice is that (2a is body diameter, and 2d is according to the ratio between body diameter-intercolumniation a/d The distance between adjacent column axis), the corresponding wave number of known in the literature trapped mode is searched, is searched near the wave number Spike is found in rope calculating can obtain the capture of limited cylinder array in relation to the region I in region.For certain a/d documents In the case where not providing corresponding trapped mode wave number, an initial calculation step-length can be used as using 1/ [20 (N-k)+10] (N is cylinder sum in cylindrical-array, and k is the numbered cylinders for identifying pillar position), searches near the integral multiple that Kd/ π is 0.5 Spike is found in calculating (K is wave number) can obtain the capture of limited cylinder array in relation to the region I in region.For limited Long single cylindrical-array, as diameter-intercolumniation ratio a/d reduces, the spike point of region I also moves right.By with it is close Comparative result corresponding to a/d can further reduce the computer capacity of region I.Wave number value corresponding for acquired spike, The relational graph of wave force amplitude and numbered cylinders is drawn out, as can complete half waveshape is presented, as shown in figure 3, maximum Hydrodynamism on intermediolateral column, then illustrate that the peak location is accurate enough.If it is not, can also continue to encryption step Length finds more accurate spike point.

2) region II (another captures related region)

Secondary peak valley near wave force curve regions I constitutes region II, in the II of region the fluctuation spacing of curve with Dimensionless wave number changes and changes.Existing document is left to region I spike in limited cylinder array wave force curve at present Some secondary peaks on side, Gu Jinhang research.Studies have shown that these secondary peak, paddy and endless cylindrical-array Rayleigh- The Trapped modes for cylinders of laterally arranging in Bloch wave problem and sink is related.Particularly, for by N number of single seat The intermediolateral column of the cylindrical-array of bottom cylinder composition, the secondary peak on the wave force curve spike point left side, secondary paddy position abscissa (nothing Dimension wave number) with cylinder number be N/2, the horizontal seat of the intermediolateral column wave force curve peak location of the cylindrical-array of N/3, N/4 ... (dimensionless wave number) is marked strictly to correspond to, specific as follows:

Cylinder number is that the intermediolateral column wave force curve peak location abscissa of the single seat bottom cylindrical-array of N/2 corresponds to Cylinder number is the abscissa of the intermediolateral column wave force curve spike first left valley point position of the cylindrical-array of N, this valley point Cylinder number is the wave force amplitude and cylinder number relational graph of the cylindrical-array of N under the corresponding dimensionless wave number of position abscissa The form of two half-waves is showed, as shown in figure 4, under the corresponding wave force amplitude in the top of the two half-waves and same wave number Cylinder number is that the wave force amplitude of the intermediolateral column of the cylindrical-array of N/2 is equal in magnitude.

Cylinder number is that the intermediolateral column wave force curve peak location abscissa of the single seat bottom cylindrical-array of N/3 corresponds to Cylinder number is the abscissa of the intermediolateral column wave force curve spike first left peak dot position of the cylindrical-array of N, this peak dot Cylinder number is the wave force amplitude and cylinder number relational graph of the cylindrical-array of N under the corresponding dimensionless wave number of position abscissa The form of three half-waves is showed, as shown in figure 5, under the corresponding wave force amplitude in the top of these three half-waves and same wave number Cylinder number is that the wave force amplitude of the intermediolateral column of the cylindrical-array of N/3 is equal in magnitude.

Cylinder number is N/4, and the situation that N/5 ... is waited is similar to the above, can the rest may be inferred.Usually, work as N/n_i~10 When (n_iFor natural number), the influence of near-trapping is quite faint, can will cylinder number be at this time (N/n_i=) 10 The corresponding dimensionless wave number of cylindrical-array wave force curve peak location forms cylindrical-array wave force curve area as N number of cylinder The left side boundary of domain II.

We have found that, for different diameters-intercolumniation ratio a/d, region II is by near- by calculating analysis The coverage of trapping is different.A/d is bigger, and the coverage of near-trapping is also bigger.For example, for a/d= 0.25 the case where, cylinder number N/n_iThe corresponding dimensionless wave number of wave force peak location of~20 arrays can be used as region II's Left boundary, and for the situation of a/d=0.5, this left boundary can continue to cylinder number N/n_iThe wave force spike of~5 arrays The corresponding dimensionless wave number in position.For the case where any kth column, being referred to above-mentioned centre in single seat bottom cylinder group's array The range of column determines.

Cylindrical-array in the present invention refers to, the same diameter cylinder that larger amt penetrates the water surface arrange in a line group At cylindrical-array (that is, in the horizontal cross-section of the cylindrical-array each center of circle point-blank).Wave force in the present invention Refer to, the wave force in circle center line connecting direction each along cylindrical-array horizontal cross-section suffered by any cylinder.Between fluctuation in the present invention Away from referring to, wave force amplitude changes with dimensionless wave number on the wave force curve to be formed, two neighboring maximum point (or minimum The distance between point) abscissa.In the present invention, maximum point or minimum point are also described with " peak " or " paddy ".

As shown in Figure 2 and Figure 6, the present invention provides a kind of cylindrical-array wave force amplitude curve material calculation and envelope It determines method, includes the following steps:

Region III (Region III) is known as non-trapping region, and region I (Region I) and region II (Region II) claim To capture related region, in non-trapping region (region III), wave force curve has very regular wave phenomenon.

Wave path-difference is directly proportional to adjacent two circle intercolumnar distances, and enabling the wave path-difference be respectively equal to s times, (s is with s+1 times of wavelength Random natural number), the preliminary expression formula and the horizontal seat of adjacent peak dot of any peak dot abscissa in wave force curve regions III can be acquired The preliminary expression formula of the difference of mark, enables the wave path-difference be respectively equal to 2s-1 times and 2s+1 times of half-wavelength, can acquire wave force curve area The preliminary expression formula of the difference of the preliminary expression formula and adjacent valley point abscissa of any valley point abscissa in the III of domain；

Here the quantity of cylinder is typically larger than 9 in cylindrical-array, the adjacent very big or consecutive roots of wave force amplitude curve The abscissa spacing of small value point is definite value in the III of region, is not changed with dimensionless wave frequencies, only total with cylinder in array N, numbered cylinders k, the wave incident angle β for identifying column position are related, and can extremely accurate be predicted with simple formula.

X-axis is being just in the cylindrical-array coordinate system, in plane incidence direction of wave travel and cylindrical-array global coordinate system The angle in direction is known as wave incidence angle, and the foundation of global coordinate system makes wave incidence angle be less than or equal to 90 degree；K is cylindrical array Positive direction of the x-axis keeps one in the number of any one cylinder in column, number k augment direction and cylindrical-array global coordinate system It causes.

Preliminary expression formula acquisition process therein is as follows:

Dimensionless wave number (i.e. wave force curvilinear abscissa) Kd/ π can rewrite are as follows: Kd/ π=R/ λ；Then, wave force width Value changes with dimensionless wave number it is also assumed that being that wave force amplitude changes with intercolumniation-wavelength ratio.When the diffraction of j column When wave passes to k column mutually long (cancellation) interference nearby occurs with k column diffracted wave, the wave force amplitude on k column can obtain a peak (paddy) value.R_p(1)And R_v(1)The corresponding intercolumniation of first peak dot and valley point in wave force curve is respectively indicated, wave is entered The case where firing angle β=0, first peak dot R in wave force curve_p(1)With valley point R_v(1)Corresponding intercolumniation is indicated with following formula:

2(N-k)R_p(1)=λ

Wherein, K is wave number, and R=2d is the intercolumniation of adjacent column, and λ is wavelength, and in footnote, p represents peak dot, and v represents paddy Point, (1) represent first peaks or valleys.

Enabling any s and the corresponding intercolumniation of the s+1 peak dot in the III of region is R_p(s)And R_p(s+1), R_p(s+1)=R_p(s) +δR_p, the condition that peak dot occurs is that constructive interference occurs, then adjacent s and the corresponding wave path-difference of the s+1 peak dot should divide It is not the wavelength of s times He s+1 times, then N column should meet with the left wave path-difference for passing diffracted wave (hereinafter referred to as " Zuo Chuanbo ") of k column:

2(N-k)R_p(s)=s λ

2(N-k)(R_p(s)+δR_p)=(s+1) λ

Above-mentioned two formula subtracts each other to obtain the preliminary expression formula of the difference of adjacent peak dot abscissa are as follows:

The condition that valley point occurs is that destructive interference occurs, for s and the corresponding intercolumniation R in the s+1 valley point_v(s)With R_v(s+1)=R_v(s)+δR_v, corresponding wave path-difference is respectively equal to 2s-1 times and 2s+1 times of half-wavelength, so that

Obtain the preliminary expression formula of the difference of adjacent valley point abscissa are as follows:

N is the cylinder sum in cylindrical-array；At this time in wave force curve regions III any peak dot abscissa preliminary table Up to the preliminary expression of formula and any valley point abscissa are as follows:

Obtain the process for the final expression formula for fluctuating spacing when wave incidence angle is equal to zero in wave force curve regions III such as Under:

In any k column upstream | x_k| place (x_k< 0), the diffraction gesture of each column of k column and k column downstream is summed (before being equivalent to Left biography wave summation described in face) it obtains:

Wherein, intermediate region pillar of organ timbering far from both ends long for one, hasA_nFor on the 1st column Coefficient, i are imaginary units, and ω is wave circular frequency, and t is the time, and n is integer, Z_n=J '_n(Ka)/H′_n(Ka), K is wave number, J_n It is Bessel function of the first kind, H_nIt is Hankel function of the first kind, a is cylindrical radius；

Have after taking Asymptotic Expression to simplify preceding formula Hankel function:

Constant ± the pi/2 of second and third in the formula does not contribute fluctuation pitch problems discussed below；Wherein,

Above formula is actually three left superpositions for passing plane wave, and first item is k column Zuo Chuanbo, and Section 2 and Section 3 are To the sum of the Zuo Chuanbo of this N-k pillar of N column, Section 2 and Section 3 are equivalent to two and are with k column Zuo Chuanbo wave path-difference k+1 column The Overlay of the cylinder Zuo Chuanbo of equal value of 2 (R/2) and 2 (N+1/2-k) R, the two cylinders of equal value be located at k column downstream R/2 with (N+1/2-k) at R；

That is:

Likewise, when incidence angle is equal to zero, in revised wave force curve regions III, any peak dot abscissa is most The final expression formula of whole expression formula and any valley point abscissa are as follows:

Incidence angle be not zero (β ≠ 0) the case where situation more null than incidence angle it is complicated, each column in k column upstream is right at this time Passing diffracted wave and the right biography diffracted wave of k column (hereinafter referred to as " right biography wave ") has the case where wave path-difference, this point is from β=0 different.It enables When β ≠ 0, any s and the s+1 peak, the corresponding intercolumniation in valley point are in Region III It is each with the right biography wave of the consideration each column in upstream and downstream respectively due to needing Column is left to pass the related situation of wave, and hereinafter, the symbol of above-mentioned expression intercolumniation indicates each by upstream when increasing superscript " u " Column is right to pass corresponding amount caused by wave effect, caused by being indicated when increasing superscript " l " by the left biography wave effect of each column in downstream Corresponding amount.

The cylinder of array end first that the case where being not equal to zero for wave incidence angle, first analysis are located at k column upstream The right wave path-difference for passing diffracted wave of the right biography diffracted wave and k column downstream propagated, makes it meet the item that constructive or destructive interferences occur Preliminary fluctuation spacing expression one can be obtained in part, and process is as follows:

Wherein, k column is any one cylinder in cylinder display, and β is wave incidence angle, obtains tentatively fluctuating spacing expression Formula one:

When β ≠ 0, the preliminary expression formula one of any s-th of peak dot abscissa and any s-th of valley point are horizontal in Region III The preliminary expression formula one of coordinate are as follows:

The left biography diffracted wave and the left biography diffracted wave of k column that the last one cylinder positioned at k column downstream is upstream propagated are analyzed again Wave path-difference, so that it is met the condition that constructive or destructive interferences occur, preliminary fluctuation spacing expression two can be obtained, process is as follows:

Wherein, l indicates amount related with the left biography wave of each column in downstream；It is as follows to obtain tentatively fluctuating spacing expression two:

The preliminary expression formula two of any s-th of peak dot abscissa and any s-th of valley point abscissa in Region III Preliminary expression formula two are as follows:

It is similar with the process of β=0, in k column downstream | x_k| place (x_k> 0), the sum of the diffraction gesture of each column of k column and k column upstream is

Wherein,

In the formula, Section 2 and Section 3 indicate the 1st column to this k- of k-1 column The sum of the right biography wave of 1 pillar.This two effect can be regarded as being located at two at kth column upstream R/2 and (k-1/2) R The effect of pillar, it is then, preliminary to fluctuate spacing expression one

Spacing expression one is finally fluctuated when obtaining incidence angle after amendment not equal to zero

And any peak dot abscissa under this state final expression formula one and any valley point abscissa final expression formula One is；

In k column upstream | x_k| place (x_k< 0), the sum of the diffraction gesture of each column of k column and k column downstream are as follows:

Wherein,

In the formula, Section 2 and Section 3 indicate+1 column of kth to this N- of N column The sum of the Zuo Chuanbo of k pillar, this two effect can be regarded as being located at two at k column downstream R/2 and (N+1/2-k) R The effect of the Zuo Chuanbo of cylinder, the preliminary spacing expression formula two when then wave incidence angle is not equal to zero

It obtains finally fluctuating spacing expression formula two after amendment:

And any peak dot abscissa under this state final expression formula two and any valley point abscissa final expression formula Two are；

Spacing expression formula one and the final smaller person for fluctuating the fluctuation spacing that spacing expression formula two provides are fluctuated using final, The final expression of any cylindrical wave wave force curve minimal ripple spacing in the III of region when just obtaining wave incidence angle not equal to zero Formula；The final expression formula of fluctuation spacing when comprehensive wave incidence angle is equal to zero and not equal to zero, can be obtained any cylinder Wave force curve fluctuates the final expression formula of spacing descriptive model in the III of region；

For final expression formula when wave incidence angle is equal to zero, any cylinder wave force curve fluctuates spacing in the III of region Are as follows:

Fig. 7 is pillar sum N=101, wave incident angle β=0, when diameter intercolumniation ratio a/d=1/4, wave force amplitude Fluctuation pitch measurementsThe curve changed with dimensionless wave number.It can be seen that fluctuation spacing is under very big wave-number range Be it is constant, this region is exactly region III, and fluctuating the region that declines rapidly of spacing later is exactly region I and II, asymptotic in figure Line and numerical value are the theoretical expectation values being calculated using final expression formula of the invention, are as a result coincide very much.

Fig. 8 is N=11, N=21, N=51 respectively, in the case of N=101, wave incident angle β=0, and diameter intercolumniation ratio a/ When d=1/4, the single wave force that is subject to of bottom cylinder group array kth column of sitting is in the fluctuation pitch measurements of region IIIWith retouch State model expression calculated valueComparison.By comparison, it was found that description of the invention model expression predicted value and reality It is very good that calculated value coincide.

The final expression formula of spacing is fluctuated when incidence angle is equal to zero

With

Incidence angle fluctuates the final expression formula of spacing when being not equal to zero

Minimal ripple spacing of any cylinder wave force curve in the III of region can be calculated after middle substitution N, k and βOrBelow for brevity, symbol is uniformly usedExpression wave incidence angle is equal to zero and not Equal to the minimal ripple spacing in the case of 0 two kinds, it should be noted that used when wave incident angle β=0Expression formula calculate Minimal ripple spacing；Minimal ripple spacing at this timeAs the upper limit of region III material calculation, and the lower limit of material calculation, Natural number of the range between 2~10 is then chosen according to required precision when calculating, as minimal ripple spacingRemove Number, that is, can determine the lower limit, the value of natural number is bigger here, then precision is higher, and the calculating time accordingly spent is also longer.It is logical The upper and lower bound after determining is crossed, the material calculation of region III can be obtained.

Since region II range is more much smaller than region III range and fluctuation spacing becomes smaller, it can be taken according to required precision Minimal ripple spacing of natural number of one range between 5~10 as region IIIDivisor, region II can be obtained Material calculation, be equally that the value of natural number is bigger here, then precision is higher, and the calculating time accordingly spent is also longer.

Since region I range is more much smaller than region II and has the towering spike separated, it can be taken according to required precision Minimal ripple spacing of natural number of one range between 40~50 as region IIIDivisor, region I can be obtained Material calculation, be equally that the value of natural number is bigger here, then precision is higher, and the calculating time accordingly spent is also longer.

Specifically, when the material calculation of region III takes 1/5th region III minimal ripple spacingArea The material calculation of domain II takes 1/10th region III minimal ripple spacingThe material calculation of region I takes 50 / mono- region III minimal ripple spacingWhen, the computational accuracy of wave force curve reaches relative error 1% Within.

Step 700, using the smaller person of abscissa in final expression formula one and final expression formula two as wave incidence angle The final expression formula of the final expression formula of any peak dot abscissa and any valley point abscissa when not equal to zero, comprehensive wave are incident When angle is equal to zero and final expression formula when not equal to zero, can obtain any peak dot abscissa final expression formula and any valley point The final expression formula of abscissa；The abscissa at any peak dot and valley point is obtained according to the final expression formula of abscissa, so as to Corresponding wave number is obtained, solves system of linear equations to obtain the unknown diffraction coefficient in velocity potential expression formula, and then can be obtained any Wave force suffered by cylinder, by the wave force nondimensionalization and modulus, just obtain wave force curve in the III of region any peak dot with Ordinate at valley point；

It is determined according to the abscissa at any peak dot of above-mentioned acquisition and valley point and the ordinate at any peak dot and valley point These peak dot lines are just obtained coenvelope of the wave force curve in the III of region by the position of each peak dot and valley point out Line；By these valley point lines, lower envelope line of the wave force curve in the III of region is just obtained.

The final expression formula one and final expression formula two of any valley point abscissa embody upstream pillar and downstream column respectively Influence of the son to valley point abscissa,

In conjunction with the available final expression formula with intercolumniation-wavelength than any valley point abscissa indicated of this two formula:

The final expression formula one and final expression formula two of any peak dot abscissa embody upstream pillar and downstream column respectively Influence of the son to peak dot abscissa,

In conjunction with the available final expression formula with intercolumniation-wavelength than any peak dot abscissa indicated of this two formula:

Ordinate acquisition modes in each peak dot coordinate and valley point coordinate are as follows:

Calculate the steric factor φ (r for sitting velocity potential near any k column in bottom cylindrical-array Modelling Water Wave Diffraction Problems_k,θ_k) public affairs Formula are as follows:

Diffraction coefficient(unknowm coefficient) is determined by following diffraction coefficient linear equation:

Wherein, β is the angle (wave of positive direction of the x-axis in plane incidence direction of wave travel and cylindrical-array global coordinate system Incidence angle), and the foundation of global coordinate system makes wave incident angle β≤pi/2, cylinder number k augment direction and positive direction of the x-axis are kept Unanimously, (r_k,θ_k) it is polar coordinates of the vertical axis z-axis by the partial cylindrical coordinate system of the k axis of a cylinder heart, Z_n=J '_n(Ka)/H′_n(Ka), J_nFor Bessel function of the first kind, H_nIt is Hankel function of the first kind, R_jkFor k-th of pillar to the distance of j-th of pillar, i is Imaginary unit, n, m are Fourier's mode truncation item, α_jkFor k-th of pillar to the deflection of j-th of pillar, I_kExist for incidence wave The phase factor of k-th of pillar.

Since abscissa R/ λ is equal to dimensionless wave number Kd/ π, it is known that the final expression formula of any valley point abscissa and any The abscissa of peak dot and valley point that the final expression formula of peak dot abscissa is namely indicated with dimensionless wave number, thus it is available Peak dot and the corresponding wave number K in valley point.

The aforementioned diffraction coefficient linear equation of the corresponding wave number K substitution of peak dot and valley point can be acquired into peak dot and valley point corresponds to wave Under several, diffraction coefficientValue, willSubstitute into following formula

Wave force curve any peak dot and valley point in the III of region just can be obtained to correspond under wave number, edge suffered by any cylinder k The wave force F in each circle center line connecting direction in cylindrical-array horizontal cross-section^k；Wherein, ρ is the density of water, and g is acceleration of gravity, and A is The wave amplitude of incidence wave, K are wave number, and h is the depth of water, and a is cylindrical radius.

With the cylinder of identical geometric dimension under same environmental conditions suffered wave force to wave force shown in aforementioned formula F^kNondimensionalization is carried out, wave force curve any peak dot and valley point in the III of region can be obtained and correspond under wave number, cylinder group's array In any kth column dimensionless wave force are as follows:

Dimensionless wave force amplitude is just obtained to the formula modulus, this namely wave force curve any peak in the III of region Ordinate at point and valley point.

So far, abscissa and ordinate of the wave force curve in the III of region at any peak dot and valley point have obtained, will These valley point lines just obtain lower envelope line of the wave force curve in the III of region；By these peak dot lines, wave is just obtained Coenvelope line of the force curve in the III of region.

So far, although those skilled in the art will appreciate that present invention has been shown and described in detail herein multiple shows Example property embodiment still without departing from the spirit and scope of the present invention, still can according to the present disclosure directly Determine or deduce out many other variations or modifications consistent with the principles of the invention.Therefore, the scope of the present invention is understood that and recognizes It is set to and covers all such other variations or modifications.

Claims

1. the determination method of cylindrical-array wave force amplitude curve material calculation and envelope, which is characterized in that including walking as follows It is rapid:

Step 100, wave force amplitude is changed with dimensionless wave number where multiple towering spikes in the wave force curve to be formed Region as region I, will towering spike be nearby lower than the towering spike and curve fluctuation spacing changes with dimensionless wave number and The secondary peak and valley region of variation is as region II, using the wave force curve after exclusionary zone I and region II as region III；

Step 200, the cylindrical-array coordinate system as composed by the limited identical seat bottom cylinder arranged in a line and true is established Determine relevant parameter, convert dimensionless wave number to the ratio of adjacent two circles intercolumnar distance and wavelength, then the diffracted wave hair of each cylinder There is peak dot in wave force curve when raw constructive interference, and valley point occurs in wave force curve when destructive interference occurs；For wave incidence The null situation in angle, analysis incidence wave pass to some any cylinder occur diffraction and incidence wave pass to the cylinder downstream last The wave path-difference in the two paths of diffraction occurs for a cylinder, finds out the preliminary of any peak dot abscissa in wave force curve regions III The preliminary expression formula of expression formula and the difference of adjacent peak dot abscissa, and the preliminary expression formula and adjacent valleys of any valley point abscissa The preliminary expression formula of the difference of point abscissa, and then know that the difference of the abscissa of two neighboring peak dot or two neighboring valley point is equal, Finally obtain preliminary fluctuation spacing expression formula of any cylinder wave force curve in the III of region；

Step 300, in some any cylinder upstream end, the left biography diffracted wave upstream propagated which is generated and the cylinder The left biography diffracted wave summation that each cylinder in downstream generates, takes Asymptotic Expression to be simplified, obtains to wave using Hankel function And position and existing column position of equal value with current cylindrical-array are all different for dynamic pitch problems two are located at the cylinder Position from that farther cylinder of equal value of the cylinder is substituted into preliminary fluctuation spacing table by the specific location of the cylinder of equal value in downstream Preliminary expression formula up to formula, the preliminary expression formula of any peak dot abscissa and any valley point abscissa is modified, and can be obtained Spacing is fluctuated in wave force curve regions III when wave incidence angle is equal to zero final expression formula, any peak dot abscissa are most The final expression formula of whole expression formula and any valley point abscissa；

Step 400, zero situation is not equal to for wave incidence angle, using aforementioned same method, analysis incidence wave first is passed to Diffraction occurs for some any cylinder and incidence wave pass to the cylinder upstream the cylinder of array end first occur diffraction the two The wave path-difference in path, then analysis incidence wave passes to any some cylinder generation diffraction and incidence wave passes to the cylinder downstream most The wave path-difference in the two paths of diffraction occurs for the latter cylinder, can respectively obtain any cylinder wave force curve in region III In the preliminary expression formula one of any peak dot abscissa as caused by the effect of the cylinder upstream cylinder diffracted wave, any valley point it is horizontal The preliminary expression formula one of coordinate and preliminary fluctuation spacing expression formula one, and since the effect of the cylinder downstream cylinder diffracted wave is led The preliminary expression formula two of any peak dot abscissa, the preliminary expression formula two of any valley point abscissa and the preliminary fluctuation spacing table caused Up to formula two；

Step 500, first at the downstream of some any cylinder, the right biography diffracted wave downstream propagated that generated to the cylinder and The right biography diffracted wave summation that each cylinder in the cylinder upstream generates, is corrected using aforementioned same method, obtains wave incidence angle When not equal to zero, the final expression formula one of any peak dot abscissa, the final expression formula one of any valley point abscissa and final wave Dynamic spacing expression formula one；Then, in the upstream end of some any cylinder, the left biography diffraction upstream propagated generated to the cylinder The left biography diffracted wave summation that each cylinder of wave and the cylinder downstream generates, obtains any peak dot abscissa after same method amendment Final expression formula two, the final expression formula two of any valley point abscissa and final fluctuation spacing expression formula two；Using final fluctuation The smaller person for the fluctuation spacing that spacing expression formula one and final fluctuation spacing expression formula two provide is not equal to as wave incidence angle The final expression formula of spacing is fluctuated when zero；

Step 600, the final expression formula of fluctuation spacing calculates in the III of region when according to incidence angle equal to zero and not equal to zero Minimal ripple spacing, using the minimal ripple spacing as the upper limit of wave force curve material calculation in the III of region, according to difference Required precision using minimal ripple spacing divided by corresponding natural number as the lower limit of material calculation in the III of region, to obtain area The material calculation of domain III；

It requires to obtain the minimal ripple spacing of region III divided by the corresponding natural number of corresponding required precision according to the required accuracy Material calculation in the II of region；It is required the minimal ripple spacing of region III according to the required accuracy divided by corresponding required precision pair The natural number answered obtains the material calculation in the I of region；

Step 700, it is differed using the smaller person of abscissa in final expression formula one and final expression formula two as wave incidence angle The final expression formula of the final expression formula of any peak dot abscissa and any valley point abscissa when zero, comprehensive wave incidence angle etc. Any cylinder wave force curve any peak dot in the III of region can be obtained in final expression formula when zero and when not equal to zero The final expression formula of the final expression formula of abscissa and any valley point abscissa；It is obtained arbitrarily according to the final expression formula of abscissa Abscissa at peak dot and valley point solves system of linear equations so as to obtain corresponding wave number to obtain in velocity potential expression formula Unknown diffraction coefficient, and then wave force suffered by any cylinder can be obtained, by the wave force nondimensionalization and modulus, just obtain wave Ordinate of the force curve in the III of region at any peak dot and valley point；

According to the abscissa at any peak dot of above-mentioned acquisition and valley point and the ordinate at any peak dot and valley point, determine every These peak dot lines are just obtained coenvelope line of the wave force curve in the III of region by the position of one peak dot and valley point；It will These valley point lines just obtain lower envelope line of the wave force curve in the III of region.

2. determining method according to claim 1, which is characterized in that

In the cylindrical-array coordinate system, positive direction of the x-axis in plane incidence direction of wave travel and cylindrical-array global coordinate system Angle be known as wave incidence angle, and the foundation of global coordinate system makes wave incidence angle be less than or equal to 90 degree；K is in cylindrical-array Any one cylinder number, number k augment direction is consistent with positive direction of the x-axis in cylindrical-array global coordinate system.

3. determining method according to claim 1, which is characterized in that

The preliminary table of the preliminary fluctuation spacing expression formula, the preliminary expression formula of any peak dot abscissa and any valley point abscissa Acquisition process up to formula is as follows:

Dimensionless wave number Kd/ π can rewrite are as follows: Kd/ π=R/ λ；

2(N-k)R_p(1)=λ

Wherein, K is wave number, and R=2d is the intercolumniation of adjacent column, and λ is wavelength, and in footnote, p represents peak dot, and v represents valley point, (1) first peaks or valleys is represented；

Enabling any s and the corresponding intercolumniation of the s+1 peak dot in the III of region is R_p(s)And R_p(s+1), R_p(s+1)=R_p(s)+δ R_p, the condition that peak dot occurs is that constructive interference occurs, then adjacent s and the corresponding wave path-difference of the s+1 peak dot should be distinguished It is the wavelength of s times He s+1 times, it can thus be concluded that the preliminary expression formula of the difference of adjacent peak dot abscissa are as follows:

The condition that valley point occurs is that destructive interference occurs, for s and the corresponding intercolumniation R in the s+1 valley point_v(s)And R_v(s+1)= R_v(s)+δR_v, corresponding wave path-difference is respectively equal to 2s-1 times and 2s+1 times of half-wavelength, it can thus be concluded that the difference of adjacent valley point abscissa Preliminary expression formula are as follows:

By above-mentioned derivation it is found that the difference of adjacent peak dot and the abscissa of adjacent valley point is equal, then spacing expression formula is tentatively fluctuated are as follows:

N is the cylinder sum in cylindrical-array；At this time in wave force curve regions III any peak dot abscissa preliminary expression formula With the preliminary expression formula of any valley point abscissa are as follows:

4. determining method according to claim 3, which is characterized in that

It obtains the final expression formula of fluctuation spacing, the final expression formula of any peak dot abscissa when wave incidence angle is equal to zero and appoints The process of the final expression formula of meaning valley point abscissa is as follows:

In any k column upstream | x_k| place (x_k< 0) the left propagation diffracted wave that, each column of k column and k column downstream is upstream propagated around Gesture is penetrated to sum to obtain:

Wherein,A_nFor the coefficient on the 1st column, i is imaginary unit, and ω is wave circular frequency, and t is the time, and n is Integer, Z_n=J_n′(Ka)/H_n' (Ka), K are wave number, J_nIt is Bessel function of the first kind, H_nIt is Hankel function of the first kind, a is Cylindrical radius；

Asymptotic Expression is taken have after simplifying Hankel function:

Wherein,Above formula Section 2 and Section 3 are equivalent to two and k column Zuo Chuanbo wave Path difference is the Overlay of the cylinder Zuo Chuanbo of equal value of 2 (R/2) and 2 (N+1/2-k) R, the two cylinders of equal value are located at k column downstream At R/2 and (N+1/2-k) R；

Wave force can be obtained after being modified using the position from the farther cylinder of equal value of k column to preliminary fluctuation spacing expression formula The final expression formula of spacing is fluctuated in curve regions III:

5. determining method according to claim 1, which is characterized in that

The case where zero is not equal to for wave incidence angle, the preliminary expression formula one of any peak dot abscissa, any valley point abscissa Preliminary expression formula one and preliminary fluctuation spacing expression one acquisition process it is as follows:

Wherein, k column is any one cylinder in cylindrical-array, and β is wave incidence angle, any in the III of region when enabling β ≠ 0 S and the s+1 peak dot, the corresponding intercolumniation in valley point are After these are indicated that the symbol of intercolumniation is further added by superscript u, indicate to be acted on by each column right-hand rotation wave in upstream Caused corresponding amount；

It obtains tentatively fluctuating the preliminary of spacing expression one, the preliminary expression formula one of any peak dot abscissa and any valley point abscissa Expression formula one:

Above-mentioned three formula is modified and fluctuates spacing expression formula one, the final expression formula of any peak dot abscissa to get to final One and any valley point abscissa final expression formula one:

6. determining method according to claim 5, which is characterized in that

The case where zero is not equal to for wave incidence angle, the preliminary expression formula two of any peak dot abscissa, any valley point abscissa Preliminary expression formula two and preliminary fluctuation spacing expression two acquisition process it is as follows:

Wherein, Deng the symbol for indicating intercolumniation Number being further added by superscript l indicates by the left corresponding amount passed caused by wave effect of each column in downstream；Then available preliminary fluctuation The preliminary expression formula two of spacing expression formula two, the preliminary expression formula two of any peak dot abscissa and any valley point abscissa:

Above-mentioned three formula is modified and fluctuates spacing expression formula two, the final expression formula of any peak dot abscissa to get to final Two and any valley point abscissa final expression formula two:

7. determining method according to claim 6, which is characterized in that

When wave incidence angle is equal to zero, any cylinder wave force curve fluctuates spacing in the III of region are as follows:

8. determining method according to claim 1, which is characterized in that

The natural number value range of the region III is between 2~10, and the natural number value range of the region II is 5~10 Between, the natural number value range of the region I is between 40~50；When the material calculation of the region III takes 1/5th Region III minimal ripple spacing, the material calculation of the region II takes 1/10th region III minimal ripple spacing, institute When stating the material calculation of region I and taking 1/50th region III minimal ripple spacing, the computational accuracy of wave force curve reaches Relative error is within 1%.

9. determining method according to claim 6, which is characterized in that

The process for obtaining the abscissa of each peak dot is as follows:

Situation null for wave incidence angle, any peak dot abscissa with intercolumniation-wave in wave force curve regions III The long final expression formula than expression are as follows:

It is the case where zero is not equal to for wave incidence angle, horizontal in conjunction with the final expression formula one of any peak dot abscissa and any peak dot The available final expression formula with intercolumniation-wavelength than any peak dot abscissa indicated of the final expression formula two of coordinate:

The process for obtaining the abscissa of each valley point is as follows:

Situation null for wave incidence angle, any valley point abscissa with intercolumniation-wave in wave force curve regions III The long final expression formula than expression are as follows:

It is the case where zero is not equal to for wave incidence angle, horizontal in conjunction with the final expression formula one of any valley point abscissa and any valley point The available final expression formula with intercolumniation-wavelength than any valley point abscissa indicated of the final expression formula two of coordinate:

10. determining method according to claim 9, which is characterized in that

The ordinate acquisition modes of each described peak dot and the valley point are as follows:

According to the steric factor φ (r for sitting velocity potential near any k column in bottom cylindrical-array Modelling Water Wave Diffraction Problems_k,θ_k) formula:

Wherein,For diffraction coefficient, k is the number of any one cylinder in cylindrical-array, and number k augment direction and x-axis are square To being consistent, (r_k,θ_k) it is polar coordinates of the vertical axis z-axis by the partial cylindrical coordinate system of k mast axis, Z_n=J_n′(Ka)/ H_n' (Ka), K are wave number, and a is cylindrical radius, J_nFor Bessel function of the first kind, H_nIt is Hankel function of the first kind, n is integer.

Wherein, β is angle (the wave incidence of positive direction of the x-axis in plane incidence direction of wave travel and cylindrical-array global coordinate system Angle), and the foundation of global coordinate system makes wave incident angle β≤pi/2, R_jkFor k-th of pillar to the distance of j-th of pillar, i is void Number unit, m is integer, α_jkFor k-th of pillar to the deflection of j-th of pillar, I_kFor incidence wave k-th of pillar phase because Son；

The corresponding wave number K substitution equation of the peak dot and the valley point can be acquired into the peak dot and the valley point corresponds to wave number Lower diffraction coefficientValue, by diffraction coefficientSubstitute into following formula

Wave force curve any peak dot and valley point in the III of region just can be obtained to correspond under wave number, any cylinder k is suffered along cylinder The wave force F in each circle center line connecting direction in array horizontal cross-section^k；Wherein, ρ is the density of water, and g is acceleration of gravity, and A is incidence The wave amplitude of wave, h are the depth of water；

With the cylinder of identical geometric dimension under same environmental conditions suffered wave force wave force shown in preceding formula is carried out it is immeasurable Guiding principle can be obtained wave force curve any peak dot and valley point in the III of region and correspond under wave number any kth column in cylindrical-array Dimensionless wave force are as follows:

To the formula modulus i.e. obtain dimensionless wave force amplitude, this namely wave force curve in the III of region any peak dot with Ordinate at valley point.