CN109726417B

CN109726417B - Method for determining calculation step length and envelope curve of cylindrical array wave force amplitude curve

Info

Publication number: CN109726417B
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: 2020-08-04
Anticipated expiration: 2038-07-17
Also published as: CN109726417A

Abstract

The invention provides a method for determining a calculation step length and an envelope curve of a wave force amplitude curve of a cylindrical array, which comprises the steps of establishing a coordinate system for the cylindrical array consisting of a limited number of sitting cylinders which are arranged in a straight line, determining related parameters, analyzing interference effects of diffraction waves of any cylinder and cylinders upstream and downstream of the cylinder based on a constructive elimination theory, obtaining a description model of wave intervals when the wave incidence angles are equal to zero and not equal to zero, expressions of wave intervals and horizontal coordinates of peak points and valley points, and determining the calculation step length of each area and the vertical coordinates of the peak points and the valley points; and connecting the peak points/valley points to obtain the upper/lower envelope curve of the wave force curve in the non-capture area. The invention proves that the fluctuation distance is only related to the total number of the columns in the column array, the column number for marking the position of the column and the wave incidence angle, the workload can be reduced on the premise of ensuring the precision, and the design and evaluation period can be shortened.

Description

Method for determining calculation step length and envelope curve of cylindrical array wave force amplitude curve

Technical Field

The invention relates to the field of ocean engineering, in particular to a description model for establishing a wave force amplitude of wave force borne by any cylinder in a non-capture area under the action of waves by a cylinder array consisting of a large number of cylinders penetrating through a water surface based on a constructive cancellation theory, a method for determining a wave force amplitude curve calculation step length and a method for determining a wave force amplitude curve envelope curve in the non-capture area.

Background

The ocean which accounts for 71 percent of the surface area of the earth contains abundant renewable energy sources such as recoverable resources such as petroleum, natural gas and the like and wind energy, wave energy and the like which can be used by human for a long time. With the increasing demand for energy and resources in economic development, it has become a clear trend to expand living space and seek various materials and energy supplies in the ocean.

Offshore structures as carriers need to be developed no matter marine resource exploitation, offshore space development or actual utilization of marine renewable energy. There is an important class of structures, although the upper structures are different, whose floats/support structures are composed of a plurality of cylinders (i.e., an array of cylinders) that penetrate the water surface. Such as offshore oil platforms, sea-crossing bridges, ultra-large floats, wave-power arrays, and the like. With the continuous expansion of the demand of the economic society for ocean development, the overall size of the ocean structure becomes larger and larger, and the size of the cylindrical array as the floating body/supporting structure of the ocean structure is also increased. The number of cylinders in a cylinder array increases from the first ones to tens, hundreds, and even thousands. A single row of bottomed cylindrical arrays is one of the typical versions of cylindrical arrays. The single row bottomed cylinder array here refers to: the circle center of the circular cross section obtained by the intersection of the horizontal plane and each cylinder is on a straight line, and the circular cross section is continuously communicated with the water surface from the water bottom and penetrates through the water surface to extend upwards to form a cylinder array. The wave force applied to the underwater cylindrical array is a key factor for determining the design scheme of the cylindrical array and ensuring the structural safety, and therefore, the rule that the amplitude of the wave force changes along with the dimensionless wave number needs to be mastered.

The amplitude of the wave force applied to any cylinder in the single-row seated cylinder array shown in fig. 1 fluctuates and fluctuates with the dimensionless wave number. Generally, the amplitude of the wave force experienced by a single column in a single row of a large number (e.g., a number greater than 9) finite array of columns varies with the number of waves with three distinct characteristics: 1) the wave force curve formed by the wave force amplitude changing with the dimensionless wave number has several high peak, the area where these high peak is located is called area I (RegionI) in the invention; 2) near the region I, the curve has a plurality of gradually-reduced secondary peaks and valleys, the heights of the secondary peaks are all lower than the peaks of the region I, and the fluctuation distance of the wave force curve changes along with the change of dimensionless wave numbers, and the region is called as a region II (region II); 3) outside the two regions mentioned above, there are very regular fluctuations in many places, which are referred to herein as region iii (region iii). The schematic diagram of the three regions is shown in fig. 2.

Region I and region II are related to near-trapping, and these two regions are referred to herein as "trapping-related regions". And region III, which is referred to herein as the "non-capture region". There are a number of studies published internationally and well understood for region I and region II involved in capture. For the non-capture area, the fluctuation rule of the non-capture area is not deeply researched, and a description model for describing the fluctuation distance of the non-capture area is further lacked. The fluctuation distance of the invention refers to: and the distance between the abscissas of two adjacent maximum values (or minimum values) on a wave force curve formed by the wave force amplitude along with the change of the dimensionless wave number. In the present invention, the maximum value point or the minimum value point is also referred to by "peak" or "valley". The non-capture zone fluctuation pitch is described to increase the design level to help extend the fatigue life of the structure at a lower cost. This is because, after a large number of calculations, it is found that the relative difference between the values of adjacent peaks and valleys in the region III of the wave force curve is sometimes large, and can be found only from a limited number of calculations, and can reach a maximum of about 20% in the region III.

Therefore, in the actual calculation of the hydrodynamic force, if the step size of the abscissa is not small enough, the error of the wave force calculation result in the region III may reach 20% or even more. For the "one-time" strength failure problem caused by extreme loads, this may not be much affected because the amplitude of the wave force at the peak of the trapping region is much higher than that of the non-trapping region, and the relatively small error of about 20% of the amplitude of the wave force in the non-trapping region does not affect the "one-time" failure of the structure. However, for fatigue failure due to cyclic loading, the above-mentioned wave force calculation error may have a significant negative impact, since the calculation of fatigue life requires accounting for the combined contribution of the wave force in a certain frequency range (rather than just considering the corresponding maximum value at the near-trapping frequency of the trapping region, as in the case of intensity analysis). This is because, when analyzing the linear time invariant system fatigue life, the spectral density function of the alternating stress response is equal to the input ocean wave spectral density multiplied by the square of the system transfer function digital-to-analog. The natural frequency of the elastic mode of the conventional marine structure is far higher than the wave frequency, so that the transfer function of the amplitude of the alternating stress amplitude can be obtained by multiplying the transfer function of the amplitude of the wave force shown in fig. 2 by a certain coefficient. If the wave force transfer function is calculated with a large error due to an improper step selection, the alternating stress magnitude transfer function also has a large error, and the squared error becomes larger (e.g., if the transfer function has a modulus error of 10%, the squared error increases to 20%, and if the transfer function has a modulus error of 20%, the squared error increases to 36%). Therefore, inaccurate alternating stress response results can be obtained, and the accuracy of fatigue life evaluation is further influenced. Considering that the design of the cylindrical array can make the near-tracking frequency of the system avoid the frequency band with larger energy of the sea waves, the alternating stress of the non-capture area can occupy a large part in the contribution to the fatigue damage. Thus, accurate calculation of the wave force in the non-capture zone as shown in fig. 2 is of great significance for accurate assessment of fatigue life.

In summary, the precondition for efficiently and accurately acquiring the wave force of the non-capture area is to grasp the wave force curve fluctuation characteristics of the non-capture area and obtain a description model capable of accurately predicting the wave force curve fluctuation distance of the non-capture area in advance. For a non-capture area occupying most of the wave force curve, namely an area III (the area has practical significance for evaluating the fatigue life of a structure), the fluctuation characteristics of the non-capture area are still lack of deep knowledge, and a description model of the fluctuation distance of the wave force curve formed by the wave force amplitude along with the dimensionless wave number change in the non-capture area is not used as a basis for efficient evaluation and design.

In addition, although the regions I and II are studied more frequently, as described above, since the fluctuation characteristics of the region III are not deeply known, it is common to perform trial and error calculation by changing the calculation step size in order to obtain an accurate wave force curve. How the calculation step is chosen cannot be quantitatively estimated before the calculation starts, and the initial calculation step and further the correction of the calculation step are basically determined by guessing and trying. This process is cumbersome and time consuming and laborious, even for highly experienced experts. For inexperienced or totally inexperienced people, this process is very burdensome and costly.

Another problem is that, at present, when designing and evaluating an actual engineering structure based on a wave force curve, in order to avoid missing peak-valley points of the wave force curve, a large number of complex calculations on the wave force curve are usually required, which causes problems of excessive time cost, high calculation cost, and the like. When the scheme is evaluated, selected or initially designed, the method causes low efficiency, greatly increases cost and consumes time, and is very uneconomical. At this time, if the upper and lower limits of the wave force curve fluctuation can be accurately and quickly mastered, a reasonable preliminary solution can be provided under the condition of avoiding complicated calculation, so that a method for quickly and accurately obtaining the peak point and the valley point of the wave force curve is urgently needed, and the problems are solved.

Disclosure of Invention

The invention aims to provide a description model of wave force amplitude of wave force borne by any cylinder in a non-capture area, a determination method of wave force amplitude curve calculation step length and a determination method of wave force amplitude curve envelope curve in the non-capture area, wherein the description model is established by a cylinder array formed by a large number of cylinders penetrating through a water surface based on a constructive-subtractive theory under the action of waves.

Particularly, the method for determining the calculation step size and the envelope curve of the cylindrical array wave force amplitude curve provided by the invention comprises the following steps:

step 100, taking a region where a plurality of high-rise peaks in a wave force curve formed by wave force amplitude values changing along with dimensionless wave numbers as a region I, taking a region where secondary peaks and valleys which are lower than the high-rise peaks and have curve fluctuation distances changing along with dimensionless wave numbers near the high-rise peaks are as a region II, and taking a wave force curve excluding the region I and the region II as a region III;

step 200, establishing a cylinder array coordinate system consisting of a plurality of same seated cylinders arranged in a straight line, determining related parameters, and converting a dimensionless wave number into a ratio of a distance between two adjacent cylinders to a wavelength, so that a wave force curve of each cylinder has a peak point when the diffracted waves of the cylinders generate constructive interference and a wave force curve has a valley point when the diffracted waves of the cylinders generate destructive interference; for the condition that the wave incident angle is equal to zero, analyzing the wave path difference of two paths that the incident wave is transmitted to any cylinder to be diffracted and the incident wave is transmitted to the last cylinder at the downstream of the cylinder to be diffracted, solving a preliminary expression of the abscissa of any peak point in a wave force curve area III and a preliminary expression of the difference between the abscissas of adjacent peak points, and a preliminary expression of the abscissa of any valley point and a preliminary expression of the difference between the abscissas of adjacent valley points, knowing that the differences between the abscissas of the adjacent two peak points or the adjacent two valley points are equal, and finally obtaining a preliminary wave spacing expression of any cylinder wave force curve in the area III;

step 300, at the upstream of any cylinder, summing the upstream-propagated left propagation diffraction waves generated by the cylinder and the downstream-propagated left propagation diffraction waves generated by each cylinder, simplifying the sum by using a hankel function to obtain two specific positions of equivalent cylinders which are equivalent to the current cylinder array and different from the current cylinder position for the fluctuation distance problem, and substituting the positions of equivalent cylinders farther away from the cylinder into a preliminary fluctuation distance expression, a preliminary expression of the abscissa of any peak point and a preliminary expression of the abscissa of any valley point for correction, so as to obtain a final expression of the fluctuation distance, a final expression of the abscissa of any peak point and a final expression of the abscissa of any valley point in the wave force curve area III when the wave incident angle is equal to zero;

step 400, for the case that the wave incident angle is not equal to zero, using the same method as above, first analyzing the wave path difference between the two paths of the incident wave transmitted to any one of the cylinders and diffracted by the incident wave transmitted to the first cylinder at the end of the array upstream of the cylinder, then analyzing the wave path difference of two paths of the incident wave transmitted to any cylinder to be diffracted and the incident wave transmitted to the last cylinder downstream of the cylinder to be diffracted, the preliminary expression I of the abscissa of any peak point, the preliminary expression I of the abscissa of any valley point and the preliminary fluctuation interval expression I of any valley point caused by the action of the cylindrical diffracted wave at the upstream of the cylinder in the region III of any cylindrical wave force curve can be respectively obtained, a second preliminary expression of the abscissa of any peak point, a second preliminary expression of the abscissa of any valley point and a second preliminary fluctuation interval expression, which are caused by the action of the cylindrical downstream diffracted wave;

step 500, firstly, at the downstream of any one cylinder, summing the downstream-transmitted diffraction wave generated by the cylinder and the downstream-transmitted diffraction wave generated by each cylinder at the upstream of the cylinder, and correcting by using the same method to obtain a final expression I of an arbitrary peak point abscissa, a final expression I of an arbitrary valley point abscissa and a final fluctuation interval expression I when the wave incidence angle is not equal to zero; then, at the upstream of any cylinder, summing the upstream-transmitted diffraction waves generated by the cylinder and the downstream-transmitted diffraction waves generated by each cylinder, and correcting by the same method to obtain a final expression II of the abscissa of any peak point, a final expression II of the abscissa of any valley point and a final fluctuation interval expression II; adopting the smaller of the fluctuation intervals given by the final fluctuation interval expression I and the final fluctuation interval expression II as a final expression of the fluctuation interval when the wave incidence angle is not equal to zero;

step 600, calculating the minimum fluctuation distance in the area III according to the final expression of the fluctuation distance with the incidence angle equal to zero and not equal to zero, taking the minimum fluctuation distance as the upper limit of the calculation step length of the wave force curve in the area III, and dividing the minimum fluctuation distance by the corresponding natural number according to different precision requirements as the lower limit of the calculation step length in the area III, thereby obtaining the calculation step length of the area III;

dividing the minimum fluctuation distance of the area III by a natural number corresponding to the corresponding precision requirement according to the required precision requirement to obtain a calculation step length in the area II; dividing the minimum fluctuation distance of the area III by a natural number corresponding to the corresponding precision requirement according to the required precision requirement to obtain a calculation step length in the area I;

step 700, taking the smaller of the abscissa in the final expression I and the final expression II as the final expression of the abscissa of the arbitrary peak point and the final expression of the abscissa of the arbitrary valley point when the wave incident angle is not equal to zero, and synthesizing the final expressions of the wave incident angle when the wave incident angle is equal to zero and not equal to zero to obtain the final expression of the abscissa of the arbitrary peak point and the final expression of the abscissa of the arbitrary valley point in the region III of the arbitrary cylindrical wave force curve; obtaining the abscissa of any peak point and valley point according to the final expression of the abscissa, thereby obtaining the corresponding wave number, solving a linear equation set to obtain an unknown diffraction coefficient in the velocity potential expression, further obtaining the wave force borne by any cylinder, carrying out dimensionless transformation on the wave force and carrying out modulus extraction, and obtaining the ordinate of the wave force curve at any peak point and valley point in the region III;

determining the position of each peak point and valley point according to the obtained abscissa of any peak point and valley point and the obtained ordinate of any peak point and valley point, and connecting the peak points to obtain an upper envelope line of the wave force curve in the region III; by connecting these valleys, the lower envelope of the wave force curve in region III is obtained.

In one embodiment of the invention, in the cylindrical array coordinate system, an included angle between a plane incident wave propagation direction and a positive direction of an x-axis in the cylindrical array global coordinate system is called a wave incident angle, and the global coordinate system is established so that the wave incident angle is less than or equal to 90 degrees; k is the serial number of any cylinder in the cylinder array, and the increasing direction of the serial number k is consistent with the positive direction of the x axis in the whole coordinate system of the cylinder array.

In one embodiment of the present invention, the preliminary expression of the preliminary fluctuation pitch, the preliminary expression of the abscissa of the arbitrary peak point, and the preliminary expression of the abscissa of the arbitrary valley point are obtained as follows:

the dimensionless wave number Kd/π can be rewritten as: kd/pi ═ R/λ;

first peak point R in wave force curve_p(1)And valley point R_v(1)The corresponding pillar spacing is represented by the following formula:

2(N-k)R_p(1)＝λ

where K is the wavenumber, R ═ 2d is the column spacing of adjacent cylinders, λ is the wavelength, in the subscripts, p represents the peak point, v represents the valley point, (1) represents the first peak or valley;

let the column pitch corresponding to any s-th and s + 1-th peak points in the region III be R_p(s)And R_p(s+1)，R_p(s+1)＝R_p(s)+R_pIf the peak occurs under the condition that constructive interference occurs, the wave path difference corresponding to the adjacent s-th and s + 1-th peak should be the wavelength which is s times and s +1 times respectively, and thus the preliminary expression of the difference between the abscissas of the adjacent peaks is obtained as follows:

the valley points occur under the condition that destructive interference occurs, and the column pitch R corresponds to the s-th and s + 1-th valley points_v(s)And R_v(s+1)＝R_v(s)+R_vThe corresponding path differences are equal to 2s-1 times and 2s +1 times the wavelength, respectively, from which a preliminary expression for the difference between the abscissas of adjacent valleys is derived:

from the above derivation, if the differences between the abscissa of the adjacent peak points and the abscissa of the adjacent valley points are equal, the preliminary fluctuation distance expression is:

n is the total number of cylinders in the cylinder array; at this time, the preliminary expression of the abscissa of any peak point and the preliminary expression of the abscissa of any valley point in the wave force curve region III are:

in one embodiment of the present invention, the process of obtaining the final expression of the wave pitch when the wave incident angle is equal to zero, the final expression of the abscissa of the arbitrary peak point, and the final expression of the abscissa of the arbitrary valley point is as follows:

at any k column upstream | x_kL position (x)_k<0) Summing the diffraction potentials of the k-pillar and the left propagating diffracted waves propagating upstream from the pillars downstream from the k-pillar to obtain:

wherein the content of the first and second substances,

A_nis the coefficient on column 1, i is an imaginary unit, ω is the wave circular frequency, t is time, n is an integer, Z_n＝J′_n(Ka)/H′_n(Ka), K is the wave number, J_nIs a Bessel function of the first kind, H_nIs a first type of hankel function, a is the cylinder radius;

the method for simplifying the Hankel function by using an asymptotic expression comprises the following steps:

wherein the content of the first and second substances,

the second term and the third term of the above formula are equivalent to the superposition effect of two equivalent cylindrical left waves with the wave path difference of 2(R/2) and 2(N +1/2-k) R with the k-pillar left wave, and the two equivalent cylinders are positioned at R/2 and (N +1/2-k) R at the downstream of the k-pillar;

and correcting the preliminary fluctuation distance expression by using the position of the equivalent cylinder farther away from the k column to obtain a final expression of the fluctuation distance in the wave force curve area III:

similarly, the final expression of the modified abscissa of the arbitrary peak point and the final expression of the abscissa of the arbitrary valley point are:

in one embodiment of the present invention, for the case that the wave incident angle is not equal to zero, the first preliminary expression of the abscissa of any peak point, the first preliminary expression of the abscissa of any valley point, and the first preliminary fluctuation interval expression are obtained as follows:

wherein, the k column is any one column in the column array, β is the wave incident angle, and when β ≠ 0, the column spacing corresponding to the random s-th and s + 1-th peak points and valley points in the region III is

After the symbols representing the column spacing are increased by the upper corner mark u, corresponding quantities caused by the right-turn wave action of each column at the upstream are represented;

obtaining a primary fluctuation interval expression I, a primary expression I of the abscissa of any peak point and a primary expression I of the abscissa of any valley point:

and correcting the three formulas to obtain a final fluctuation distance expression I, a final expression I of the abscissa of any peak point and a final expression I of the abscissa of any valley point:

in one embodiment of the invention, for the condition that the wave incident angle is not equal to zero, the preliminary expression two of the abscissa of any peak point, the preliminary expression two of the abscissa of any valley point and the preliminary fluctuation interval expression two are obtained as follows:

wherein the content of the first and second substances,

the sign of equal representing the column spacing is increased and the superscript l represents the corresponding quantity caused by the left wave propagation effect of each column downstream; then, a preliminary expression two of the fluctuation pitch, a preliminary expression two of the abscissa of an arbitrary peak point, and a preliminary expression two of the abscissa of an arbitrary valley point can be obtained:

and correcting the three formulas to obtain a final fluctuation distance expression II, a final expression II of the abscissa of any peak point and a final expression II of the abscissa of any valley point:

in one embodiment of the present invention, at a wave incidence angle equal to zero, the wave spacing of any cylindrical wave force curve in region III is:

when the wave incident angle is not equal to zero, the wave distance of any cylindrical wave force curve in the region III is as follows:

in one embodiment of the invention, the natural number of the area III ranges from 2 to 10, the natural number of the area II ranges from 5 to 10, and the natural number of the area I ranges from 40 to 50; and when the calculation step length of the area III is the minimum fluctuation distance of the area III which is one fifth, the calculation step length of the area II is the minimum fluctuation distance of the area III which is one tenth, and the calculation step length of the area I is the minimum fluctuation distance of the area III which is one fiftieth, the calculation accuracy of the wave force curve is within 1 percent of the relative error.

In one embodiment of the present invention, the process of obtaining the abscissa of each of the peak points is as follows:

for the case of a wave incident angle equal to zero, the final expression in terms of the column pitch-wavelength ratio for the abscissa of any peak in the wave force curve region III is:

for the case where the wave incidence angle is not equal to zero, combining the final expression one for the abscissa of the arbitrary peak point and the final expression two for the abscissa of the arbitrary peak point can obtain the final expression for the abscissa of the arbitrary peak point expressed in terms of the column pitch-wavelength ratio:

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

for the case of a wave incident angle equal to zero, the final expression in the column pitch-wavelength ratio for the abscissa of any valley point in the wave force curve region III is:

for the case where the wave incidence angle is not equal to zero, combining the final expression one for the abscissa of any valley point and the final expression two for the abscissa of any valley point yields the final expression for the abscissa of any valley point in terms of the ratio of the column pitch to the wavelength:

in one embodiment of the present invention, the ordinate of each of the peak point and the valley point is obtained as follows:

according to the space factor phi (r) of the velocity potential near any k column in the water wave diffraction problem of the bottomed cylinder array_k,θ_k) The formula:

wherein the content of the first and second substances,

for the diffraction coefficient, k is the number of any column in the column array, and the increasing direction of the number k is consistent with the positive direction of the x axis, (r)_k,θ_k) Polar coordinate of a local cylindrical coordinate system passing through the k-pillar axis for the vertical axis Z-axis, Z_n＝J′_n(Ka)/H′_n(Ka), K is the wave number, a is the radius of the cylinder, J_nIs a Bessel function of the first kind, H_nIs a first type of hank function, n being an integer.

Solving a linear equation system of the diffraction coefficient in the velocity potential expression as follows:

wherein β is the angle between the plane incident wave propagation direction and the positive direction of the x axis in the cylindrical array global coordinate system (wave incident angle), and the global coordinate system is established to make the wave incident angle β not more than pi/2, R_jkIs the distance from the kth pillar to the jth pillar, i is in imaginary units, m is an integer α_jkFrom the kth column to the jth columnAngle of direction of the column, I_kThe phase factor of the incident wave at the kth pillar;

substituting the wave number K corresponding to the peak point and the valley point into the equation to obtain the diffraction coefficients of the peak point and the valley point under the wave number

Value of (2) is the diffraction coefficient

Substituting the following formula

The wave force F along the connection line of the centers of circles in the horizontal section of the cylindrical array on any cylinder k under the wave number corresponding to any peak point and valley point in the region III of the wave force curve can be obtained^k(ii) a Wherein rho is the density of water, g is the acceleration of gravity, A is the amplitude of incident waves, and h is the water depth;

carrying out non-dimensionalization on the wave force shown by the formula by using the wave force borne by the cylinders with the same geometric dimension under the same environmental condition, and obtaining the dimensionless wave force of any kth column in the cylinder array under the wave numbers corresponding to any peak point and valley point in the region III of a wave force curve as follows:

the dimensionless wave force amplitude is obtained by taking the mode, and the dimensionless wave force amplitude is the ordinate of the wave force curve at any peak point and valley point in the area III.

The present invention provides such recognition and understanding: the wave distance of a non-capture area (area III) in a wave force curve formed by the wave force amplitude value changing along with the dimensionless wave number does not change along with the dimensionless wave number, the wave distance is only related to the total number of cylinders in the cylinder array, the number of columns for marking the positions of the cylinders and the wave incidence angle, and the formula provided by the invention can be used for accurately predicting.

The invention can deepen the understanding and the cognition of the wave characteristic of the non-capture area (area III) in the wave force curve formed by the wave force amplitude changing along with the dimensionless wave number, and provides a prediction formula of the wave distance in the non-capture area. Based on the invention, when the design and evaluation of the related engineering structure are carried out, the workload can be reduced on the premise of ensuring the precision, the design and evaluation period can be shortened, and the technical support can be provided for improving the design and evaluation level of the engineering structure.

By adopting the method for determining the wave force curve calculation step length provided by the invention, the accurate wave force curve can be obtained by accurately predicting the value of the calculation step length before the calculation of any cylindrical wave force curve is started as long as the total number of cylinders in the cylindrical array, the cylinder number for identifying the position of the cylinder and the wave incident angle are known. Therefore, an accurate wave force curve can be obtained on the premise of not increasing the unnecessary calculation time blindly, the workload can be reduced on the premise of ensuring the precision, the design and evaluation period is shortened, and the technical support is provided for improving the design and evaluation level of the engineering structure.

The invention provides a method for determining upper and lower envelope lines in a cylindrical array wave force curve area III, and the positions of peak points and valley points in the wave force curve area III can be directly predetermined by adopting the method for calculating the horizontal and vertical coordinates of the peak points and the valley points in the cylindrical array wave force curve area III, so that the upper and lower envelope lines in the wave force curve area III are obtained. Therefore, when the scheme is evaluated, selected or initially designed, the peak-valley points of the wave force curve can be prevented from being missed, and a large number of other data points which are not important for the stages of the actual engineering can be avoided, so that the calculation amount can be greatly reduced, the cost is saved, the efficiency is improved, and the technical support is provided for finally improving the evaluation and design level.

Drawings

FIG. 1 is a schematic view of a cylindrical array of cylinders of the same diameter aligned in a line in accordance with one embodiment of the present invention;

fig. 2 is a schematic diagram of three regions, i.e., a wave force curve formed by the amplitude of the wave force of a single-row seated-bottom column group with a total number N of columns being 17, column number k being 9, wave incidence angle β being 0, and diameter-column spacing ratio a/d being 1/4, as a function of dimensionless wave numbers, and a capture-related Region (Region i and Region II) and a non-capture Region (Region III);

fig. 3 is an image of the amplitude of the wave force at dimensionless wavenumbers corresponding to near-drawing peaks for a single-row array of bottomed cylinders with total number of cylinders N301, column number k 151, wave incidence angle β 0, and diameter-to-column spacing ratio a/d 1/2 as a function of column number;

fig. 4 is an image of the amplitude of the wave force at a dimensionless wave number corresponding to the first valley point to the left of the near-drawing peak for a single-row bottomed cylinder array having a total number of cylinders N301, a column number k 151, a wave incidence angle β 0, and a diameter-column pitch ratio a/d 1/2, as a function of the column number;

fig. 5 is an image of the amplitude of the wave force at a dimensionless wave number corresponding to the first peak point to the left of the near-drawing peak for a single-row seated-bottom cylinder array with a total number of cylinders N301, a column number k 151, a wave incidence angle β 0, and a diameter-column pitch ratio a/d 1/2, as a function of the column number;

FIG. 6 is a schematic diagram of constructive/destructive interference of waves, wherein the wave force amplitude of a single-row seated-bottom cylindrical array is varied with dimensionless wave numbers, the wave incidence angle β is 0, and the diameter-to-column spacing ratio a/d is 1/4, with the wave curve being N being 21, the column number k being 1;

fig. 7 is a graph of the variation of the wave force amplitude fluctuation distance measurements with dimensionless wavenumbers for different column numbers k, for a total number of columns N of 101, a wave incidence angle β of 0, a diameter-column distance ratio a/d of 1/4;

FIG. 8 shows the measured value of the wave pitch in region III for the amplitude of the wave force experienced by the kth column at the time when the number of columns N is 11,21,51,101, the wave incidence angle β is 0, and the diameter column pitch ratio a/d is 1/4

And theoretical calculated value

The image is changed with the column number.

Detailed Description

Before elaborating on the details of the present invention, a method for determining the location and extent of the regions (region I and region II) of interest captured by the wave force curve, which is a combination of the results of the prior art studies and our analysis, is described. (regions I and II are the previously described capture-related regions having significantly higher and deeper peaks and valleys than region III. in addition, these two regions are further characterized by a change in the undulation pitch with a change in dimensionless wave number)

1) Region I (Capture related region)

There is a lot of literature on the frequency of the tapped mode for an infinitely long array of cylinders or a single cylinder placed on the centerline of a water bath, and these results allow estimation of the near-tapping wavenumber for a finite number of arrays of bottomed cylinders, i.e. the location of region I can be obtained. Specifically, according to the ratio a/d of the cylinder diameter to the cylinder spacing (2a is the cylinder diameter, and 2d is the distance between the adjacent cylinder axes), the wave number corresponding to the trailing mode known in the literature is searched, and the region I in the capture relevant region of the finite-length cylinder array can be obtained by searching and calculating the peak in the vicinity of the wave number. For some cases where the a/d literature does not show the corresponding wavenumber of the traced mode, the region I in the region of interest for capture of a finite length cylinder array can be obtained by searching for peaks near an integer multiple of Kd/π of 0.5 using 1/[20(N-K) +10] as an initial calculation step (N being the total number of cylinders in the cylinder array and K being the number of the pillars identifying the pillar positions) to find peaks. For a finite long single row cylindrical array, as the diameter-to-cylinder spacing ratio a/d decreases, the peak of region I also moves to the right. By comparing the result with the result corresponding to the close a/d, the calculation range of the region I can be further narrowed. For the wave number value corresponding to the obtained peak, a relation graph of the wave force amplitude and the column number is drawn, if a complete half-wave form can be presented, as shown in fig. 3, the maximum hydrodynamic force acts on the middle column, and the peak position is accurate enough. If not, the encryption step size can be continued to find a more accurate peak point.

2) Region II (Another Capture related region)

The secondary peaks and valleys in the vicinity of the wave force curve region I constitute a region II in which the wave pitch of the curve changes with the dimensionless wave number. At present, the literature researches on some secondary peaks and valleys on the left side of the peak of the region I in the limited long cylindrical array wave force curve. Studies have shown that these secondary peaks, troughs are related to the infinite length cylinder array Rayleigh-Bloch wave problem and the tracked modes with multiple cylinders laterally arranged in the water bath. In particular, for the middle column of the column array composed of N single-row seated columns, the abscissa (dimensionless wave number) of the positions of the secondary peak and the secondary valley left to the peak point of the wave force curve strictly corresponds to the abscissa (dimensionless wave number) of the peak position of the middle column wave force curve in the column array with the number of columns being N/2, N/3, N/4 …, and is specifically as follows:

the abscissa of the peak position of the middle column wave force curve of the single-row bottom-sitting cylindrical array with the number of cylinders being N/2 corresponds to the abscissa of the first valley point position on the left side of the peak of the middle column wave force curve of the single-row bottom-sitting cylindrical array with the number of cylinders being N, the relation graph of the wave force amplitude value of the cylindrical array with the number of cylinders being N under the dimensionless wave number corresponding to the abscissa of the valley point position and the number of the cylinders presents a form of two half waves, as shown in fig. 4, the wave force amplitude value corresponding to the highest peak of the two half waves is equal to the wave force amplitude value of the middle column of the cylindrical array with the number of cylinders being N/2 under the same wave number.

The abscissa of the peak position of the middle column wave force curve in the single-row seated bottom cylinder array with the number of cylinders being N/3 corresponds to the abscissa of the first peak position on the left side of the peak of the middle column wave force curve in the cylinder array with the number of cylinders being N, the relation graph of the wave force amplitude of the cylinder array with the number of cylinders being N under the dimensionless wave number corresponding to the abscissa of the peak position and the number of the cylinders presents a form of three half-waves, as shown in fig. 5, the wave force amplitude corresponding to the highest peak of the three half-waves is equal to the wave force amplitude of the middle column in the cylinder array with the number of cylinders being N/3 under the same wave number.

The number of cylinders is N/4, N/5 …, etc. is similar to that described above, and so on. Generally, when N/N _i10 hours (n)_iNatural number), the effect of near-drawing is already rather weak, and the number of cylinders can be (at this time)N/n_iThat is) 10 as the left boundary of the region II of the cylindrical array wave force curve composed of N cylinders.

We found by computational analysis that region II is affected differently by near-bridging for different diameter-to-column spacing ratios a/d. The larger a/d, the larger the range of influence of near-tracking. For example, for a/d equal to 0.25, the number of cylinders N/N_iThe dimensionless wavenumber corresponding to the peak position of the wave force of 20 arrays can be used as the left limit of region II, and for a/d equal to 0.5, this left limit will last until the number of cylinders N/N _i5 dimensionless wavenumbers corresponding to the peak positions of the wave force of the array. For the case of any kth column in a single row of the seated cylinder cluster array, this can be determined with reference to the ranges of the above-mentioned middle columns.

The cylindrical array in the present invention refers to a cylindrical array in which a large number of cylinders of the same diameter penetrating the water surface are arranged in a straight line (i.e., the centers of the respective circles in the horizontal section of the cylindrical array are on a straight line). The wave force in the invention refers to the wave force applied to any cylinder along the direction of the connection line of the centers of circles in the horizontal section of the cylinder array. The fluctuation distance in the invention refers to the distance between the abscissa of two adjacent maximum value points (or minimum value points) on a wave force curve formed by the wave force amplitude changing along with dimensionless wave numbers. In the present invention, the maximum point or minimum point is also described by "peak" or "valley".

As shown in fig. 2 and fig. 6, the present invention provides a method for determining a step size and an envelope curve of a cylindrical array wave force amplitude curve, including the following steps:

region III (region III) is called the non-capture region, region i (region i) and region ii (region ii) are called capture-related regions, and in the non-capture region (region III), the wave force curve has a very regular wave phenomenon.

the wave path difference is in direct proportion to the distance between two adjacent cylinders, the wave path difference is respectively equal to the wavelength (s is any natural number) which is s times and s +1 times, a preliminary expression of the abscissa of any peak point in a wave force curve area III and a preliminary expression of the difference between the abscissas of adjacent peak points can be obtained, the wave path difference is respectively equal to 2s-1 times and 2s +1 half wave length, and a preliminary expression of the abscissa of any valley point in the wave force curve area III and a preliminary expression of the difference between the abscissas of adjacent valley points can be obtained;

here the number of cylinders in the cylindrical array is usually greater than 9, and the abscissa spacing of the adjacent maxima or adjacent minima of the wave force amplitude curve is constant in region III, does not vary with dimensionless wave frequency, is only related to the total number of cylinders N in the array, the number of columns k identifying the cylinder position, the wave incidence angle β, and can be predicted very accurately with simple formulas.

In the cylindrical array coordinate system, an included angle between a plane incident wave propagation direction and the positive direction of an x axis in the cylindrical array global coordinate system is called a wave incident angle, and the building of the global coordinate system enables the wave incident angle to be smaller than or equal to 90 degrees; k is the serial number of any cylinder in the cylinder array, and the increasing direction of the serial number k is consistent with the positive direction of the x axis in the whole coordinate system of the cylinder array.

The preliminary expression obtaining process is as follows:

the dimensionless wavenumber (i.e. the wave force curve abscissa) Kd/π can be rewritten as: kd/pi ═ R/λ; thus, a change in the amplitude of the wave force with dimensionless wavenumber can also be considered as a change in the amplitude of the wave force with the column pitch-to-wavelength ratio. When the diffracted wave of j column is transmitted to the vicinity of k column and makes constructive (destructive) interference with the diffracted wave of k column, the amplitude of wave force on k column will obtain a peak (valley) value. R_p(1)And R_v(1)Respectively, the first peak point R in the wave force curve for the case where the wave incident angle β is 0_p(1)And valley point R_v(1)The corresponding pillar spacing is represented by the following formula:

2(N-k)R_p(1)＝λ

where K is the wavenumber, R ═ 2d is the column pitch of adjacent cylinders, λ is the wavelength, and in the subscripts, p represents the peak point, v represents the valley point, and (1) represents the first peak or valley.

Let the column pitch corresponding to any s-th and s + 1-th peak points in the region III be R_p(s)And R_p(s+1)，R_p(s+1)＝R_p(s)+R_pIf the peak occurs under the condition of constructive interference, the wave path difference corresponding to the adjacent s-th and s + 1-th peak should be s times and s +1 times of wavelength, respectively, so that the wave path difference between the N-column and the k-column left-transmitted diffracted wave (hereinafter referred to as "left-transmitted wave") should satisfy:

2(N-k)R_p(s)＝sλ

2(N-k)(R_p(s)+R_p)＝(s+1)λ

the above two subtraction equations obtain the initial expression of the difference between the abscissas of adjacent peaks:

the valley points occur under the condition that destructive interference occurs, and the column pitch R corresponds to the s-th and s + 1-th valley points_v(s)And R_v(s+1)＝R_v(s)+R_vThe corresponding path differences are equal to 2s-1 times and 2s +1 times the wavelength, respectively, and therefore:

the preliminary expression for obtaining the difference between the abscissas of adjacent valley points is:

n is the total number of cylinders in the cylinder array; at this time, the preliminary expression of the abscissa of any peak point and the preliminary expression of the abscissa of any valley point in the wave force curve region III are as follows:

the process of obtaining the final expression for the wave spacing in the wave force curve region III when the wave incidence angle is equal to zero is as follows:

at any k column upstream | x_kL position (x)_k<0) Summing the diffraction potentials of the k-pillars and the pillars downstream of the k-pillars (which is equivalent to the left wave summation described above) yields:

wherein for a long row of columns, the columns in the middle area far away from the two ends are provided with

the method for simplifying the formula by taking an asymptotic expression from the Hankel function comprises the following steps:

the constants + -pi/2 of the second and third terms in the equation do not contribute to the problem of the undulation pitch discussed below; wherein the content of the first and second substances,

the above formula is actually the superposition of three left-transmitted plane waves, the first term is k-column left-transmitted wave, the second term and the third term are the sum of the left-transmitted waves of N-k columns from k +1 column to N column, the second term and the third term are equivalent to the superposition effect of two equivalent cylindrical left-transmitted waves with the wave path difference of 2(R/2) and 2(N +1/2-k) R with the k-column left-transmitted wave, and the two equivalent cylinders are positioned at R/2 and (N +1/2-k) R at the downstream of the k-column;

namely:

similarly, when the incident angle is equal to zero, the final expression of the abscissa of any peak point and the final expression of the abscissa of any valley point in the corrected wave force curve region III are as follows:

the case where the incident angle is not zero (β ≠ 0) is more complicated than the case where the incident angle is zero, and at this time, the difference in the path length between the right diffracted wave of each column upstream of the k column and the right diffracted wave of the k column (hereinafter simply referred to as "right transmitted wave") is different from the case where β ═ 0 is observed, and when β ≠ 0, the column pitch corresponding to the s-th and s + 1-th peaks and valleys in Region III is assumed to be equal to

Since it is necessary to consider the cases related to the upstream and downstream column right and left waves, respectively, hereinafter, the above-mentioned symbol indicating the column pitch indicates the corresponding quantity caused by the upstream column right wave action when the upper corner mark "u" is added, and indicates the corresponding quantity caused by the downstream column left wave action when the upper corner mark "l" is added.

For the condition that the wave incident angle is not equal to zero, firstly, analyzing the wave path difference between the right propagation diffracted wave propagating downstream from the first cylinder at the end part of the array positioned at the upstream of the k column and the right propagation diffracted wave of the k column to ensure that the wave path difference meets the condition of generating constructive or destructive interference, and obtaining a preliminary wave pitch expression one, wherein the process is as follows:

wherein, the k column is any one cylinder in the cylinder array, β is the wave incident angle, obtains preliminary fluctuation interval expression one:

β ≠ 0, the first preliminary expression of the abscissa of any s-th peak point and the first preliminary expression of the abscissa of any s-th valley point in Region III are as follows:

and then analyzing the wave path difference between the left transmitted diffracted wave which is propagated upstream by the last cylinder positioned at the downstream of the k column and the left transmitted diffracted wave of the k column to ensure that the wave path difference meets the condition of generating constructive or destructive interference, and obtaining a second preliminary wave pitch expression, wherein the process comprises the following steps:

wherein l represents a quantity related to the left wave propagation of each column downstream; the preliminary undulation pitch expression two was obtained as follows:

the second preliminary expression of the abscissa of any s-th peak point and the second preliminary expression of the abscissa of any s-th valley point in Region III are as follows:

similar to the β ═ 0 process, downstream | x of the k column_kL position (x)_k>0) The sum of the diffraction potentials of the k column and the columns upstream of the k column is

Wherein the content of the first and second substances,

in this equation, the second term and the third term represent the sum of the right waves of the k-1 columns from the 1 st column to the k-1 column. The effect of these two terms can be seen as the effect of two columns located upstream of the kth column at R/2 and (k-1/2) R, so that the preliminary undulation pitch expresses one

The final fluctuation interval expression one with the incidence angle not equal to zero is obtained after correction

And the final expression I of the abscissa of any peak point and the final expression I of the abscissa of any valley point in the state are shown as follows;

at k column upstream | x_kL position (x)_k<0) The sum of the diffraction potentials of the k column and the columns downstream of the k column is:

wherein the content of the first and second substances,

in the formula, the second term and the third term represent the sum of the left waves of the N-k columns from the (k + 1) th column to the N column, and the effects of the two terms can be regarded as the effects of the left waves of the two columns at R/2 and (N +1/2-k) R which are positioned downstream of the k column, so that the wave incident angles are not equalPreliminary pitch expression at zero

And obtaining a final fluctuation distance expression II after correction:

and the final expression II of the abscissa of any peak point and the final expression II of the abscissa of any valley point in the state are;

adopting the smaller fluctuation space given by the final fluctuation space expression I and the final fluctuation space expression II to obtain the final expression of the minimum fluctuation space of any cylindrical wave force curve in the area III when the wave incidence angle is not equal to zero; synthesizing final expressions of the wave intervals when the wave incidence angle is equal to zero and is not equal to zero, and obtaining a final expression of a wave interval description model of any cylindrical wave force curve in the region III;

when the final expression is that the wave incidence angle is equal to zero, the wave distance of any cylindrical wave force curve in the region III is as follows:

FIG. 7 isWave pitch measurement of wave force amplitude for a total number of columns N of 101, a wave incidence angle β of 0, and a diametric column pitch ratio a/d of 1/4

Curve as a function of dimensionless wavenumber. It can be seen that the fluctuation pitch is constant over a large range of wave numbers, this region is region III, the regions where the fluctuation pitch rapidly decreases are regions I and II, the asymptotes and the values in the graph are theoretical predicted values calculated using the final expression of the present invention, and the results are very consistent.

Fig. 8 shows measured values of the wave pitch in the region III of the wave force received by the kth column of the single-row bottomed cylinder cluster array when N is 11, N is 21, N is 51, N is 101, the wave incident angle β is 0, and the diameter column pitch ratio a/d is 1/4

And describing model expression calculations

Comparison of (1). Through comparison, the predicted value of the description model expression is well matched with the actual calculated value.

final expression of the undulation spacing at an angle of incidence equal to zero

And

final expression for the pitch of the undulations with angles of incidence unequal to zero

After the wave force curve is substituted into N, k and β, the minimum fluctuation distance of any cylindrical wave force curve in the region III can be calculated

Or

In the following, for the sake of brevity, the symbols are used uniformly

Representing the minimum wave pitch for both a wave incident angle equal to zero and not equal to zero, it is noted that the wave incident angle β is 0

Calculating the minimum fluctuation pitch; minimum fluctuation pitch at this time

As the upper limit of the calculation step length of the region III, and the lower limit of the calculation step length, selecting a natural number within the range of 2-10 as the minimum fluctuation distance according to the precision requirement during calculation

The higher the value of the natural number is, the higher the precision is, and the longer the calculation time is correspondingly spent. And obtaining the calculation step length of the region III through the determined upper limit and the lower limit.

Since the range of region II is much smaller than the range of region III and the fluctuation pitch becomes small, a range can be selected according to the accuracy requirementA natural number between 5 and 10 as the minimum fluctuation pitch of the region III

The divisor of (2) can obtain the calculation step length of the area II, and here, the larger the natural number value is, the higher the precision is, and the longer the calculation time is correspondingly spent.

Since the range of the region I is much smaller than that of the region II and has separated high-rise peaks, a natural number ranging from 40 to 50 can be taken as the minimum fluctuation interval of the region III according to the precision requirement

The divisor of (2) can obtain the calculation step length of the area I, and here, the larger the natural number value is, the higher the precision is, and the longer the calculation time is correspondingly spent.

Specifically, when the calculation step size of the region III is one fifth, the minimum fluctuation distance of the region III is taken

Zone III minimum fluctuation interval with calculation step length of zone II one tenth

Zone III minimum fluctuation interval with calculation step length of zone I one fiftieth

And meanwhile, the calculation accuracy of the wave force curve reaches the relative error within 1 percent.

Step 700, taking the smaller of the abscissa in the final expression I and the final expression II as the final expression of the abscissa of the arbitrary peak point and the final expression of the abscissa of the arbitrary valley point when the wave incident angle is not equal to zero, and synthesizing the final expressions of the wave incident angle when the wave incident angle is equal to zero and not equal to zero, so as to obtain the final expression of the abscissa of the arbitrary peak point and the final expression of the abscissa of the arbitrary valley point; obtaining the abscissa of any peak point and valley point according to the final expression of the abscissa, thereby obtaining the corresponding wave number, solving a linear equation set to obtain an unknown diffraction coefficient in the velocity potential expression, further obtaining the wave force borne by any cylinder, carrying out dimensionless transformation on the wave force and carrying out modulus extraction, and obtaining the ordinate of the wave force curve at any peak point and valley point in the region III;

The final expression one and the final expression two of the abscissa of any valley point respectively reflect the influence of the upstream pillar and the downstream pillar on the abscissa of the valley point,

combining these two equations yields the final expression for the abscissa of any valley point expressed as the ratio of the column spacing to the wavelength:

the final expression I and the final expression II of the abscissa of any peak point respectively reflect the influence of the upstream pillar and the downstream pillar on the abscissa of the peak point,

combining these two equations yields the final expression for the abscissa of any peak in terms of the ratio of column spacing to wavelength:

the vertical coordinate in each peak point coordinate and valley point coordinate is obtained as follows:

calculating the space factor phi (r) of the velocity potential near any k column in the water wave diffraction problem of the bottomed cylinder array_k,θ_k) The formula of (1) is:

wherein the content of the first and second substances,

Coefficient of diffraction

The (unknown coefficients) are determined by the following linear equation of diffraction coefficients:

wherein β is the angle (wave incidence angle) between the plane incident wave propagation direction and the positive direction of the x axis in the cylindrical array global coordinate system, and the global coordinate system is established to make the wave incidence angle β not more than pi/2, the increasing direction of the cylindrical number k is consistent with the positive direction of the x axis, (r)_k,θ_k) Polar coordinate of a local cylindrical coordinate system passing through the center of the k-pillar for the vertical axis Z-axis, Z_n＝J′_n(Ka)/H′_n(Ka)，J_nIs of the first kindBessel function, H_nIs a Hankel function of the first kind, R_jkIs the distance from the kth column to the jth column, i is an imaginary unit, n, m is a Fourier mode truncation term, α_jkIs the angle of orientation from the kth post to the jth post, I_kIs the phase factor of the incident wave at the kth column.

Since the abscissa R/λ is equal to the dimensionless wave number Kd/π, it can be known that the final expression of the abscissa of an arbitrary valley point and the final expression of the abscissa of an arbitrary peak point are, that is, the abscissas of the peak point and the valley point expressed in dimensionless wave numbers, and thus the wave numbers K corresponding to the peak point and the valley point can be obtained.

The wave number K corresponding to the peak point and the valley point is substituted into the linear equation of the diffraction coefficient to obtain the diffraction coefficient under the condition of the wave number corresponding to the peak point and the valley point

Will have a value of

Substituting the following formula

The wave force F along the connection line of the centers of circles in the horizontal section of the cylindrical array on any cylinder k under the wave number corresponding to any peak point and valley point in the region III of the wave force curve can be obtained^k(ii) a Wherein rho is the density of water, g is the acceleration of gravity, A is the amplitude of the incident wave, K is the wave number, h is the water depth, and a is the radius of the cylinder.

The wave force F shown by the formula is subjected to the wave force by cylinders with the same geometric dimension under the same environmental condition^kPerforming dimensionless transformation to obtain the dimensionless wave force of any kth column in the cylinder group array under the wave numbers corresponding to any peak point and valley point in the region III of the wave force curve:

the dimensionless wave force amplitude is obtained by taking the mode, which is the ordinate of the wave force curve at any peak and valley point in the region III.

So far, the abscissa and the ordinate of the wave force curve at any peak point and valley point in the region III are obtained, and the valley points are connected to obtain a lower envelope curve of the wave force curve in the region III; by connecting these peaks, the upper envelope of the wave force curve in region III is obtained.

Thus, it should be appreciated by those skilled in the art that while a number of exemplary embodiments of the invention have been illustrated and described in detail herein, many other variations or modifications consistent with the principles of the invention may be directly determined or derived from the disclosure of the present invention without departing from the spirit and scope of the invention. Accordingly, the scope of the invention should be understood and interpreted to cover all such other variations or modifications.

Claims

1. The method for determining the step length and the envelope curve of the cylindrical array wave force amplitude curve is characterized by comprising the following steps of:

2. The determination method according to claim 1,

3. The determination method according to claim 1,

the preliminary fluctuation distance expression, the preliminary expression of the abscissa of any peak point and the preliminary expression of the abscissa of any valley point are obtained as follows:

the dimensionless wave number Kd/π can be rewritten as: kd/pi ═ R/λ;

the column spacing for the first peak and valley in the wave force curve is represented by the following equation:

2(N-k)R_p(1)＝λ

4. the determination method according to claim 3,

the process of obtaining the final expression of the wave incident angle equal to the zero time fluctuation distance, the final expression of the abscissa of any peak point and the final expression of the abscissa of any valley point is as follows:

at any k column upstream | x_kI where x_k<0, summing the diffraction potentials of the k-pillar and the left propagating diffracted waves propagating upstream from the pillars downstream from the k-pillar to obtain:

wherein the content of the first and second substances,

wherein the content of the first and second substances,

5. the determination method according to claim 3,

for the condition that the wave incidence angle is not equal to zero, the first preliminary expression of the abscissa of any peak point, the first preliminary expression of the abscissa of any valley point and the first preliminary expression of the fluctuation interval are obtained as follows:

6. the determination method according to claim 5,

for the condition that the wave incident angle is not equal to zero, the preliminary expression II of the abscissa of any peak point, the preliminary expression II of the abscissa of any valley point and the preliminary fluctuation interval expression II are obtained as follows:

wherein the content of the first and second substances,

7. the determination method according to claim 6,

when the wave incident angle is equal to zero, the wave distance of any cylindrical wave force curve in the region III is as follows:

8. the determination method according to claim 1,

the natural number range of the area III is between 2 and 10, the natural number range of the area II is between 5 and 10, and the natural number range of the area I is between 40 and 50; and when the calculation step length of the area III is the minimum fluctuation distance of the area III which is one fifth, the calculation step length of the area II is the minimum fluctuation distance of the area III which is one tenth, and the calculation step length of the area I is the minimum fluctuation distance of the area III which is one fiftieth, the calculation accuracy of the wave force curve is within 1 percent of the relative error.

9. The determination method according to claim 6,

the process of obtaining the abscissa of each peak point is as follows:

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

10. the determination method according to claim 9,

the vertical coordinate of each peak point and each valley point is obtained in the following manner:

wherein the content of the first and second substances,

for the diffraction coefficient, k is the number of any column in the column array, and the increasing direction of the number k is consistent with the positive direction of the x axis, (r)_k,θ_k) Polar coordinate of a local cylindrical coordinate system passing through the k-pillar axis for the vertical axis Z-axis, Z_n＝J′_n(Ka)/H′_n(Ka), K is the wave number, a is the radius of the cylinder, J_nIs a Bessel function of the first kind, H_nIs a first type of hank function, n is an integer;

wherein β is the angle between the plane incident wave propagation direction and the positive direction of the x axis in the cylindrical array global coordinate system (wave incident angle), and the global coordinate system is established to make the wave incident angle β not more than pi/2, R_jkIs the distance from the kth pillar to the jth pillar, i is in imaginary units, m is an integer α_jkIs the angle of orientation from the kth post to the jth post, I_kThe phase factor of the incident wave at the kth pillar;

Value of (2) is the diffraction coefficient

Substituting the following formula