CN106503472A - A kind of consideration soil and the equivalent time domain model building method of blower fan system dynamic interaction - Google Patents

Abstract

The present invention relates to a kind of consider that the native equivalent time domain model building method with blower fan system dynamic interaction, this equivalent time domain model building method comprise the steps：Step S1, the vibration impedance of normalization soil and blower foundation dynamic interaction are simultaneously expressed as dynamic flexibility；Step S2, is fitted dynamic flexibility using Chebyshev's complex polynomails and is expressed as recursive function form, set up the recurrence physical model for characterizing soil and blower foundation dynamic interaction, determine the undetermined coefficient of each spring and antivibrator in the recurrence physical model with this；And step S3, set up the equivalent time domain model of consideration soil and blower fan system dynamic interaction.The present invention is for when under calculated level exciting, consideration soil is responded with the blower fan system that baseline power interacts, as recurrence physical model does not contain mass-element, therefore without the need for being modified to the horizontal power load on input basis so that the model more direct convenience of the application in Practical Project.Additionally, recursive nature causes blower fan system motor control equation that there is regularity, solver there is more preferable versatility.

Description

A kind of consideration soil and the equivalent time domain model construction of blower fan system dynamic interaction Method

Technical field

The present invention relates to a kind of consideration soil ruins (Soil-Structure Dynamic Interaction, abbreviation SSDI) effect modeling method, more particularly to a kind of based on vibration impedance consideration soil and blower fan Equivalent time domain model and system that system dynamic interacts.

Background technology

Wind energy has been increasingly becoming replacement because having pollution-free, reproducible feature to receive the attention of international energy circle The principal mode that traditional energy generates electricity, the foundation stone that has constructed needed for low-carbon (LC) industrial strategy.China coastline is very long, and coastal waters wind energy is provided Source is enriched, and power load center is gathered in the coastal region in east China, and therefore offshore wind farm has vast potential for future development at home. Blower foundation is the key component for ensureing stable operation of unit, the horizontal exciting lotus being mainly subject under the effect such as wind, wave, earthquake Carry.Current China related specifications (《Building foundation specification (GB5007-2011)》、《Wind turbines Base foundation design specifies (FD003-2007)》) in basis be mainly designed to from bear ground dead load basic engineering theory in promote and come simultaneously Revised using empirical coefficient.Additionally, frequently with rigid foundation it is assumed that i.e. vacation in the analysis to blower fan system dynamic trait The motion on fixed basis is consistent with neighbouring free field, have ignored the SSDI effects between foundation soil and blower foundation.But above letter Change certain error can be brought to blower fan system characteristic frequency, natural mode of vibration and dynamic response and stability analyses.

Consideration SSDI (Soil-Structure-Dynamic-Interaction) effect is to blower fan system dynamic trait shadow Loud theoretical study method mainly has with the numerical method based on finite element and boundary element as representative and based on vibration of foundation impedance Semi analytical method.Although the former can become more meticulous modeling analysis to soil and blower fan system, because infinite domain ground brought huge The modeling process of intensive and complexity brings significant limitation to the application of Practical Project.The latter can then use and retouch State vibration of foundation displacement and the vibration impedance of external force relation goes to consider that blower fan is mutual between soil and basis under dynamic load function Action effect, clear physics conception amount of calculation are little.Vibration of foundation impedance is to rely on the complex function of dynamic excitation Loading frequency, Its real part represents that stiffness coefficient, imaginary part represent damped coefficient.When vibrating impedance frequency dependency and being weak, its dependency negligible, Take the vibration impedance fixed value under a certain characteristic frequency and be directly used in the time-histories reaction for solving blower fan system.But when vibration impedance frequency The time-histories reaction of blower fan system when rate dependence is strong, then directly cannot be solved in time domain, can only be asked by Fourier conversion Solution, and cannot the nonlinear dynamic response problem of processing system, thus limit vibration application of the impedance in Practical Project.I Coastal ground of the sea bed top based on weak soil of state and the dynamic interaction between blower foundation are engineers in design and construction In the Consideration that can not be ignored.Therefore, set up a clear concept, be easy to consideration soil and blower fan that engineering staff grasps utilization The equivalent time domain model of dynamic interaction effect is very necessary.

Content of the invention

Present invention aims to the blower fan system vibration problem under horizontal exciting, there is provided computational efficiency height, Application consideration soil and the equivalent time domain model of blower fan system dynamic interaction convenient and that can meet required precision, are solved with this Vibration impedance cannot be used directly for the blower fan dynamic trait for considering SSDI effects under the horizontal exciting of solution because of its frequency dependence And time-histories data.

For reaching above-mentioned purpose, the invention provides a kind of equivalent time domain model, comprises the steps：

Step S1, the vibration impedance of normalization soil and blower foundation dynamic interaction are simultaneously expressed as dynamic flexibility；

Step S2, is fitted the dynamic flexibility using Chebyshev's complex polynomails and is expressed as recursive function form, set up table The recurrence physical model of soil and blower foundation dynamic interaction is levied, each spring and damping in the recurrence physical model is determined with this The undetermined coefficient of device；And

Step S3, sets up the equivalent time domain model of consideration soil and blower fan system dynamic interaction.

Further, soil of standardizing in step S1 with the vibration impedance of blower foundation dynamic interaction and is represented Method into dynamic flexibility form includes：

To vibrating impedanceNormalization, i.e.,

In formula (1), K_sBased on Static stiffness, K (a₀)、C(a₀) normalized rigidity, geometry damping is respectively,For imaginary number, and a₀=ω d/V_sFor dimensionless frequency, wherein excited frequency is ω, V_sFor soil body shear wave velocity, d is The characteristic length on basis；

It is dynamic flexibility F (a by vibration impedance transformation₀), and adopt quiet flexibility F_sWhich is standardized, i.e.,

In formula (2), F_sFor quiet flexibility, F_d(a₀) be normalized dynamic flexibility, dynamic flexibility F (a₀) it is corresponding vibration impedanceInverse.

Further, the recurrence physical model for characterizing soil and blower foundation dynamic interaction, profit are set up in step S2 Dynamic flexibility is fitted with Chebyshev's complex polynomails and is expressed as recursive function form determining each spring in the recurrence physical model Comprise the steps with the method for the undetermined coefficient of antivibrator：

Step S21, is fitted normalized dynamic flexibility function using Chebyshev's complex polynomails, is expressed as recurrence letter Number；And

Step S22, sets up the dynamic flexibility expression formula of recurrence Time domain physical model, by with passed again based on Chebyshev multinomial The expression formula contrast of the recursive function of formula, determines each spring and the corresponding undetermined coefficient of antivibrator in the recurrence physical model.

Further, normalized dynamic flexibility function is fitted using Chebyshev's complex polynomails in step S21, by its table The method for being shown as recursive function form includes：

By Chebyshev's complex polynomails T_iS () carries out Function Fitting and is expressed as to dynamic flexibility function：

In formula (3), s=ia₀/a_0max,a_0maxFor needing the peak frequency of fitting；Coefficient κ and coefficient C are by basis Tend to static and high frequency limit two maximum conditions, that is, work as a₀When → 0, F_d(a₀)→1；And work as a₀→a_0maxWhen,

Coefficient κ and coefficient C are corresponding respectively：

And

Undetermined coefficient φ of each rank Chebyshev complex polynomails in formula (3)_nWithAnd be suitable to intend by method of least square Conjunction is obtained, and the coefficient for obtaining is substituted into after formula (3) is rearranged and can be obtained：

In formulaWithFor elementary recursion coefficient.

According to recursive algorithm, formula (5) is expressed as N rank recursive functions, i.e.,

Wherein, each rank recursion coefficientWithRecurrence relation be：

Further, the dynamic flexibility expression formula of recurrence Time domain physical model is set up in step S22, by cutting ratio with being based on The expression formula contrast of the recursive function of snow husband's complex polynomails, determines that each spring and antivibrator are corresponding in the recurrence physical model The method of undetermined coefficient includes：

In order to characterize soil and blower foundation dynamic interaction effect, set up by a series of springs and antivibrator are constituted pass Return Model in Time Domain, the dynamic flexibility of the recurrence physical model is represented by：

By the contrast of formula (6) and formula (8), you can obtain the undetermined of each spring and antivibrator in the recurrence physical model Coefficient lambda_jAnd γ_j, i.e.,

In above formula (9), λ_jRepresent spring corresponding coefficient, γ_jRepresent antivibrator corresponding coefficient.

Further, the side of consideration soil and the equivalent time domain model of blower fan system dynamic interaction is set up in step S3 Method includes：

By discrete for blower fan superstructure for N_sSection mass concentrating in the elastic beam of equal section of lower end, in conjunction with the recurrence physics Model is adapted to set up the equivalent time domain model of soil and blower fan dynamic interaction；I.e.

The lumped mass and mass mement of inertia m that i-th section of blower fan top_iAnd I_iRepresent, i-th section of horizontal shearing rigidity and K is used in damping respectively_iAnd c_iRepresent, height h of i-th particle to basis_iExpression, the quality of blower foundation and the moment of inertia M_f And I_fRepresent, the horizontal resistivity on basis and wave impedance and be respectively adopted containing N_hAnd N_rThe recurrence physical model of individual degree of freedom carrys out table Show；

Horizontal relative displacement u in the presence of horizontal exciting { F }, between i-th particle and basis_siRepresent, recurrence thing In reason model, the abswolute level displacement of i-th degree of freedom and corner use u respectively_hiWithRepresent, the abswolute level position of blower foundation Move and corner u_fWithRepresent, motor control side of the blower fan system under horizontal loads is set up according to dAlembert principle Journey：

Mass matrix [M] expression formula in formula (10) is as follows：

Wherein submatrix [M_s] be：

In above formula, diag represents diagonal matrix；

Stiffness matrix [K] expression formula in formula (10) is as follows：

Wherein,

Damping matrix [C] expression formula in formula (10) is as follows：

Wherein

In formula (10) system generalized displacement vector { u } be：

{ F } is the outer exciting load of level on each particle of the system that acts on；

According to time domain step by step integration solution formula (10), you can obtain considering under horizontal exciting that soil is mutual with blower foundation power The system time domain dynamic response of action effect；And system is tried to achieve by entering line translation using complex modal theory to formula (10) simultaneously Characteristic frequency.

Present invention consideration soil is specific as follows with the advantage of the equivalent time domain model of blower fan dynamic interaction：

(1) characterize soil vibration of foundation impedance can be described well with the recurrence physical model of blower foundation dynamic interaction Frequency dependence, moreover it is possible to the requirement according to fitting precision is extended computing, it is possible to reflect in the wider frequency domain Change of the accurate solution with frequency.

(2) recurrence physical model avoids the numerical value in the complicated impedance of fitting due to causing using high-order ordinary polynomials Oscillation problem, while it also avoid that the numerical value that causes when Chebyshev's ratio fraction is expressed as partial fraction is unstable to ask Topic, therefore this model passes through increase degree of freedom can make which reach arbitrary accuracy when impedance versus frequency dependency is described.

(3) when being used for considering that soil is responded with the blower fan system that baseline power interacts under calculated level exciting, due to passing Return physical model without mass-element, therefore without the need for being modified to the horizontal power load on input basis so that the model is in reality Application in the engineering of border more direct convenience.Additionally, recursive nature causes blower fan system motor control equation that there is regularity, solve Program has more preferable versatility.

Description of the drawings

The present invention is further described with reference to the accompanying drawings and examples.

Fig. 1 is the method flow diagram of the construction method of the equivalent time domain model of the present invention；

Fig. 2 is the recurrence physical model for considering soil and blower foundation dynamic interaction；

Fig. 3 is the equivalent time domain model of soil and blower fan system dynamic interaction；

Fig. 4 (a) and Fig. 4 (b) are the recurrence physical model that soil is interacted with blower foundation level, swinging driving respectively Validation verification.

Specific embodiment

In conjunction with the accompanying drawings, the present invention is further detailed explanation.These accompanying drawings are simplified schematic diagram, only with The basic structure of the illustration explanation present invention, therefore which only shows the composition relevant with the present invention.

The present invention proposes the construction method of consideration soil and the equivalent time domain model of blower fan dynamic interaction, wherein emphasis To propose a recurrence physical model, in order under Representation Level exciting soil with blower foundation dynamic interaction effect, specifically Implementing procedure is as shown in Figure 1.

Step S1, the vibration impedance of normalization soil and blower foundation dynamic interaction are simultaneously expressed as dynamic flexibility.

Calculate consideration soil to be such as, but not limited to according to thin-layer method, Green with the vibration impedance methodologies that baseline power interacts Function method etc. can be calculated in Practical Project and characterize shaking for vibration of foundation displacement and outer exciting (excited frequency is ω) relation Impedance,motionalAnd it is as follows to be standardized：

Wherein, K_sBased on Static stiffness, K (a₀) and C (a₀) normalized rigidity and geometry damping is respectively, For imaginary number.a₀=ω d/V_sFor dimensionless frequency, wherein V_sFor soil body shear wave velocity, the characteristic length based on d.

In order to cause vibration impedance low-frequency range to prevail in calculating process, vibration impedance is write as dynamic by the present invention Flexibility F (a₀), and adopt quiet flexibility F_sWhich is standardized：

In formula, F_sFor quiet flexibility, F_d(a₀) be normalized dynamic flexibility, dynamic flexibility F (a₀) it is corresponding vibration impedance's Reciprocal.

Step S2, is fitted the dynamic flexibility using Chebyshev's complex polynomails and is expressed as recursive function form, set up table The recurrence physical model of soil and blower foundation dynamic interaction is levied, each spring and damping in the recurrence physical model is determined with this The undetermined coefficient of device.

In step S1 due to F_d(a₀) it is a complex function for depending on external load excited frequency, it is impossible to directly apply In soil and the time-domain analyses of blower fan system dynamic interaction, and cannot processing system nonlinear problem.Therefore, present invention profit Chebyshev's complex polynomails are used, a recurrence physical model being made up of the spring unrelated with frequency and antivibrator is set up, is used for Soil and blower foundation dynamic interaction effect is characterized, vibration impedance is solved with this and be cannot be used directly for because of its frequency dependence Solve blower fan dynamic trait and the time-histories data that SSDI effects are considered under horizontal exciting.

Compared with ordinary polynomials, the interpolation polynomial of Chebyshev's complex polynomails can reduce imperial lattice now to greatest extent As, there is provided best uniformity approximation of the multinomial in continuous function, therefore the present invention is using Chebyshev complex polynomails T_iS () is to dynamic Compliance function carries out Function Fitting, can be expressed as：

In formula, s=ia₀/a_0max,a_0maxFor needing the peak frequency of fitting；Coefficient κ and C can tend to static by basis (work as a with two maximum conditions of high frequency limit₀When → 0, F_d(a₀)→1；Work as a₀→a_0maxWhen,) limiting Fixed：

Additionally, in formula (3) each rank Chebyshev complex polynomails undetermined coefficient φ_nWithCan be intended by method of least square Conjunction is obtained, and is real number, and the coefficient for obtaining is substituted into after formula (3) is rearranged and can be obtained：

In formulaWithFor elementary recursion coefficient；

According to recursive algorithm, formula (5) can be written as form：

Wherein,

In order to characterize soil and blower foundation dynamic interaction effect, set up as shown in Figure 2 by a series of springs and resistance The recurrence Model in Time Domain of Buddhist nun's device composition, the dynamic flexibility of the model are represented by：

By the contrast of formula (6) and formula (8), you can obtain treating for each mechanical elements in the recurrence physical model shown in Fig. 2 Determine coefficient：

In above formula (9), λ_jRepresent spring corresponding coefficient, γ_jRepresent antivibrator corresponding coefficient.The corresponding coefficient includes：Water Flat coefficient and wave coefficient.

So far it can be seen that：In recurrence physical model, the value of each spring-dampers element is unrelated with frequency, therefore The model can be directly used for the time domain dynamic analyses for characterizing soil and blower foundation dynamic interaction effect.

Step S3, sets up the equivalent time domain model of consideration soil and blower fan system dynamic interaction.

By discrete for blower fan superstructure for N_sSection mass concentrating is set up in conjunction with step 2 in the elastic beam of equal section of lower end Recurrence physical model, you can set up the equivalent time domain model of as shown in Figure 3 consideration soil and blower fan dynamic interaction.On blower fan The lumped mass and mass mement of inertia m that i-th section of portion_iAnd I_iRepresent, k is used in i-th section of horizontal shearing rigidity and damping respectively_iWith c_iRepresent.Height h of i-th particle to basis_iRepresent.The quality of blower foundation and the moment of inertia M_fAnd I_fRepresent.Basis Level and wave impedance and be respectively adopted containing N_hAnd N_rThe recurrence physical model of individual degree of freedom is representing.

Horizontal relative displacement u in the presence of horizontal exciting { F }, between i-th particle and basis_siRepresent.Recurrence thing In reason model, the abswolute level displacement of i-th degree of freedom and corner use u respectively_hiWithRepresent.The abswolute level position of blower foundation Move and corner u_fWithRepresent.Motion control of the blower fan system under horizontal loads can be set up according to dAlembert principle Equation processed：

Mass matrix [M] expression formula in formula (10) is as follows：

Wherein submatrix [M_s] be：

In above formula, diag represents diagonal matrix；

Stiffness matrix [K] expression formula in formula (10) is as follows：

Wherein,

Damping matrix [C] expression formula in formula (10) is as follows：

Wherein,

In formula (10) system generalized displacement vector { u } be：

{ F } is the outer exciting load of level on each particle of the system that acts on.According to time domain step by step integration solution formula (10), i.e., It is obtained under horizontal exciting and considers the system time domain dynamic response of soil and blower foundation dynamic interaction effect.Meanwhile, utilize Complex modal theory tries to achieve the characteristic frequency of system by entering line translation to formula (10).

Below in conjunction with the accompanying drawings and concrete case is described in detail to embodiments of the invention, so that advantages of the present invention Can be easier to be readily appreciated by one skilled in the art with feature.

In present case, certain blower fan is built on the middle weak soil that shear wave velocity is 200m/s, can be with using existing literature method Calculate under corresponding site condition and basic condition, the horizontal Static stiffness K on basis_hsWith wave Static stiffness K_rs, and basis is not Vibration impedance under same frequency exciting

Step one：

With the horizontal Static stiffness on the basis and wave Static stiffness shaking standardize soil and blower foundation dynamic interaction Impedance,motional, by horizontal resistivity and waves impedance and is written as form respectively：

Wherein,For imaginary number.Dimensionless frequency a₀=ω d/V_s, V_sFor soil body shear wave velocity, the feature based on d Length, the corresponding vibration impedance of each frequency after standardizing in case are as shown in table 1.

, below will so that low-frequency range accounts for the ascendancy of fit procedure in order in the case where any weight function is not used The level of formatting and rocking vibration impedance are write as the dynamic flexibility form of formatting：

F_h(a₀)=F_hs×F_hd(a₀)

F_r(a₀)=F_rs×F_rd(a₀)

Wherein, F_hsAnd F_rsBased on level and the quiet flexibility waved, F_hd(a₀) and F_rd(a₀) it is dynamic soft after standardizing Degree, its coefficient are as shown in table 1.As vibration impedance, dynamic flexibility is also plural number, and real part uses Re (F respectively_hd(a₀)) and Re (F_rd (a₀)) represent, imaginary part uses Im (F respectively_hd(a₀)) and Im (F_rd(a₀)) represent.

Level and rocking vibration impedance and dynamic flexibility that table 1 is formatted

Step 2

Water by taking horizontal vibration impedance in present case as an example, by the use of Chebyshev's complex polynomails as basic function to formatting Translation compliance function F_hd(a₀) carry out data fitting.Work as N_hFront quadravalence Chebyshev complex polynomails when=4, as shown in Fig. 4 (a) Change of the horizontal vibration impedance with frequency can be reflected well：

In formula, s=ia₀/a_0max,a_0maxFor needing the peak frequency of fitting；Can be obtained according to content of the invention Chinese style (4), κ=σ a_0max/ 2,The unknowm coefficient of remaining every multiple Chebyshev polynomials can pass through least square Method fitting is obtained.The coefficient for obtaining is substituted into above formula, rearrangement can be obtained：

Each level number of above formula is substituted into the recurrence system that formula (7) in content of the invention is obtained each fraction in stepping type Each recursion coefficient is substituted into the recurrence physics that formula (9) in content of the invention is obtained horizontal vibration impedance by number on this basis Undetermined coefficient in model, as shown in table 2.

Impedance is waved in for present case, dynamic to waving of formatting as basic function by the use of Chebyshev's complex polynomails Compliance function carries out data fitting.Work as N_rWhen=3, first three rank Chebyshev's complex polynomails as shown in Fig. 4 (b) can be well Reflect change of the rocking vibration impedance with frequency.For same method is adopted, the recurrence of rocking vibration impedance can be obtained Model in Time Domain, in model, corresponding spring and antivibrator coefficient are as shown in table 2.

Spring and antivibrator undetermined coefficient in 2 recurrence physical model of table

Coefficient	λ0	λ1	λ2	λ3	λ4	γ0	γ1	γ2	γ3	γ4
											Level	1	-8.120	0.7821	-1.667	7.511	-0.18	1.689	-1.092	6.368	-5.960
Wave	1	-0.4763	46.31	-2.534	-	-0.19	-5.787	4.192	2.099	-

Step 3

Each spring-dampers element in recurrence physical model in step 2 is unrelated with frequency.Therefore, tied according to top Structure and level, the dynamic equilibrium condition for waving recurrence physical model, can set up soil with blower fan system dynamic interaction when Domain motor control equation is as follows：

In the formula, [M], [K], [C] are respectively general mass matrix, stiffness matrix and the damping matrix of system, by engineering Obtain in the parameter and step 2 of middle blower fan structure recurrence physical model parameter substitute into formula (11)-(21) be obtained with The value of upper three matrixes.The displacement column vector of { u } for each particle of system；{ F } is to act on the horizontal exciting load in system.

Above formula is solved according to time domain step by step integration, you can obtain under horizontal exciting, considering that soil is mutual with blower foundation power The system time domain dynamic response of action effect.Meanwhile, the characteristic frequency that system can be tried to achieve using complex modal theory.

With the above-mentioned desirable embodiment according to the present invention as enlightenment, by above-mentioned description, relevant staff is complete Various change and modification can be carried out entirely in the range of without departing from this invention technological thought.The technology of this invention Property scope is not limited to the content in description, it is necessary to determine its technical scope according to right.

Claims (6)

1. a kind of construction method of equivalent time domain model, it is characterised in that comprise the steps：

Step S1, the vibration impedance of normalization soil and blower foundation dynamic interaction are simultaneously expressed as dynamic flexibility；

Step S2, is fitted the dynamic flexibility using Chebyshev's complex polynomails and is expressed as recursive function form, set up and characterize soil With the recurrence physical model of blower foundation dynamic interaction, each spring and antivibrator in the recurrence physical model are determined with this Undetermined coefficient；And

Step S3, sets up the equivalent time domain model of consideration soil and blower fan system dynamic interaction.

2. the construction method of equivalent time domain model according to claim 1, it is characterised in that

Soil of standardizing in the step S1 impedance is expressed as dynamic flexibility with the vibration of blower foundation dynamic interaction Method includes：

To vibrating impedanceNormalization, i.e.,

In formula (1), K_sBased on Static stiffness, K (a₀)、C(a₀) normalized rigidity, geometry damping is respectively,For Imaginary number, and a₀=ω d/V_sFor dimensionless frequency, wherein excited frequency is ω, V_sFor soil body shear wave velocity, the spy based on d Levy length；

It is dynamic flexibility F (a by vibration impedance transformation₀), and adopt quiet flexibility F_sWhich is standardized, i.e.,

$F\left(a_0\right)=\frac{1}{K_s\×\[K\left(a_0\right)+{\mathrm{ia}}_{0}C\left(a_0\right)\]}=F_s\×F_d\left(a_0\right)---\left(2\right);$

In formula (2), F_sFor quiet flexibility, F_d(a₀) be normalized dynamic flexibility, dynamic flexibility F (a₀) it is corresponding vibration impedance's Reciprocal.

3. the construction method of equivalent time domain model according to claim 2, it is characterised in that

The dynamic flexibility is fitted using Chebyshev's complex polynomails in step S2 and is expressed as recursive function form, set up table The recurrence physical model of soil and blower foundation dynamic interaction is levied, each spring and damping in the recurrence physical model is determined with this The method of the undetermined coefficient of device comprises the steps：

Step S21, is fitted normalized dynamic flexibility function using Chebyshev's complex polynomails, is expressed as recursive function；With And

Step S22, sets up the dynamic flexibility expression formula of recurrence physical model, by with the recurrence letter based on Chebyshev's complex polynomails Number expression formula contrast, determines the undetermined coefficient of each spring and antivibrator in the recurrence physical model.

4. the construction method of equivalent time domain model according to claim 3, it is characterised in that

Normalized dynamic flexibility function is fitted using Chebyshev's complex polynomails in step S21, is expressed as recurrence letter The method of number form formula includes：

By Chebyshev's complex polynomails T_iS () carries out Function Fitting and is expressed as to dynamic flexibility function：

In formula (3), s=ia₀/a_0max,a_0maxFor needing the peak frequency of fitting；Coefficient κ and coefficient C are to tend to static by basis With two maximum conditions of high frequency limit, that is, work as a₀When → 0, F_d(a₀)→1；And work as a₀→a_0maxWhen,

Coefficient κ and coefficient C are corresponding respectively：

And

Undetermined coefficient φ of each rank Chebyshev complex polynomails in formula (3)_nWithAnd be suitable to obtain by least square fitting Arrive, and the coefficient for obtaining is substituted into after formula (3) is rearranged and can be obtained：

$F_d\left(a_0\right)=F_d\left(s\right)\≈\frac{1+q_1^{\left(0\right)}s+q_2^{\left(0\right)}{s}^2+...+q_N^{\left(0\right)}{s}^N}{1+p_1^{\left(0\right)}s+p_2^{\left(0\right)}{s}^2+...+p_N^{\left(0\right)}{s}^N+p_{N+1}^{\left(0\right)}{s}^{N+1}}---\left(5\right);$

In formulaWithFor elementary recursion coefficient；

According to recursive algorithm, formula (5) is expressed as N rank recursive functions, i.e.,

Wherein, each rank recursion coefficientWithRecurrence relation be：

$q_n^{\left(j\right)}=q_n^{(j-1)}-\frac{q_{N-j+1}^{(j-1)}}{p_{N-j+1}^{\left(j\right)}}{p}_n^{\left(n\right)},p_n^{(j+1)}=p_n^{\left(j\right)}-\frac{p_{N-j+1}^{\left(j\right)}}{q_{N-j}^{\left(j\right)}}{q}_{n-1}^{\left(j\right)},q_0^{\left(0\right)}=1;j=0,1,\mathrm{...},N;n=1,2,\mathrm{...},N-j---\left(7\right).$

5. the construction method of equivalent time domain model according to claim 4, it is characterised in that

Set up the dynamic flexibility expression formula of recurrence physical model in step S22, by with based on Chebyshev's complex polynomails Recursive function expression formula is contrasted, and determines the method bag of each spring and the corresponding undetermined coefficient of antivibrator in the recurrence physical model Include：

In order to characterize soil and blower foundation dynamic interaction effect, a series of recurrence thing being made up of springs and antivibrator is set up Model is managed, the dynamic flexibility expression formula of the recurrence physical model is：

By the contrast of formula (6) and formula (8), you can obtain the undetermined coefficient of each spring and antivibrator in the recurrence physical model λ_jAnd γ_j, i.e.,

${\mathrm{\λ}}_0=1,{\mathrm{\γ}}_0=\frac{p_{N+1}^{\left(0\right)}}{q_N^{\left(0\right)}{a}_{0\max }},{\mathrm{\λ}}_j=\frac{p_{N-j+1}^{\left(j\right)}}{q_{N-j+1}^{(j-1)}},{\mathrm{\γ}}_j=\frac{p_{N-j+1}^{\left(j\right)}}{q_{N-j}^{\left(j\right)}{a}_{0\max }},j=0,1,\mathrm{...},N---\left(9\right);$

In above formula (9), λ_jRepresent the undetermined coefficient in spring, γ_jRepresent the undetermined coefficient in antivibrator.

6. the construction method of equivalent time domain model according to claim 5, it is characterised in that

The method that consideration soil is set up in step S3 with the equivalent time domain model of blower fan system dynamic interaction includes：

By discrete for blower fan superstructure for N_sSection mass concentrating in the elastic beam of equal section of lower end, in conjunction with the recurrence physical model It is adapted to set up the equivalent time domain model of soil and blower fan dynamic interaction；I.e.

The lumped mass and mass mement of inertia m that i-th section of blower fan top_iAnd I_iExpression, i-th section of horizontal shearing rigidity and damping K is used respectively_iAnd c_iRepresent, height h of i-th particle to basis_iExpression, the quality of blower foundation and the moment of inertia M_fAnd I_fTable Show, the level on basis and wave impedance and be respectively adopted containing N_hAnd N_rThe recurrence physical model of individual degree of freedom is representing；

Horizontal relative displacement u in the presence of horizontal exciting { F }, between i-th particle and basis_siRepresent, recurrence physics mould In type, the abswolute level displacement of i-th degree of freedom and corner use u respectively_hiWithRepresent, the abswolute level displacement of blower foundation and Corner u_fWithRepresent, motor control equation of the blower fan system under horizontal loads is set up according to dAlembert principle：

$\[M\]\left\{\stackrel{\·\·}{u}\right\}+\[C\]\left\{\stackrel{\·}{u}\right\}+\[K\]\left\{u\right\}=\left\{F\right\}---\left(10\right);$

Mass matrix [M] expression formula in formula (10) is as follows：

Wherein submatrix [M_s] be：

In above formula, diag represents diagonal matrix；

Stiffness matrix [K] expression formula in formula (10) is as follows：

${\[K\]}_{(N_s+N_h+N_r+2)\×(N_s+N_h+N_r+2)}=\left[\begin{array}{ccc}{\[K_s\]}_{N_s\×N_s}& {\[0\]}_{N_s\×(N_h+1)}& {\[0\]}_{N_s\×(N_r+1)}\\ {\[0\]}_{(N_h+1)\×N_s}& {\[K_h\]}_{(N_h+1)\×(N_h+1)}& {\[0\]}_{(N_h+1)\×(N_r+1)}\\ {\[0\]}_{(N_r+1)\×N_s}& {\[0\]}_{(N_r+1)\×(N_h+1)}& {\[K_r\]}_{(N_r+1)\×(N_r+1)}\end{array}\right]---\left(13\right);$

Wherein,

Damping matrix [C] expression formula in formula (10) is as follows：

${\[C\]}_{(N_s+N_h+N_r+2)\×(N_s+N_h+N_r+2)}=\left[\begin{array}{ccc}{\[C_s\]}_{N_s\×N_s}& {\[0\]}_{N_s\×(N_h+1)}& {\[0\]}_{N_s\×(N_r+1)}\\ {\[0\]}_{(N_h+1)\×N_s}& {\[C_h\]}_{(N_h+1)\×(N_h+1)}& {\[0\]}_{(N_h+1)\×(N_r+1)}\\ {\[0\]}_{(N_r+1)\×N_s}& {\[0\]}_{(N_r+1)\×(N_h+1)}& {\[C_r\]}_{(N_r+1)\×(N_r+1)}\end{array}\right]---\left(17\right);$

Wherein

${\[C_h\]}_{(N_h+1)\×(N_h+1)}=diag\left(\begin{array}{cccc}{C}_{h0}& C_{h1}& ...& C_{N_h}\end{array}\right)---\left(18\right);$

${\[C_r\]}_{(N_r+1)\×(N_r+1)}=diag\left(\begin{array}{cccc}{C}_{r0}& C_{r1}& ...& C_{N_r}\end{array}\right)---\left(19\right);$

In formula (10) system generalized displacement vector { u } be：

{ F } is the outer exciting load of level on each particle of the system that acts on；

According to time domain step by step integration solution formula (10), you can obtain considering soil and blower foundation dynamic interaction under horizontal exciting The system time domain dynamic response of effect；And by entering line translation using complex modal theory to formula (10) simultaneously, try to achieve the spy of system Levy frequency.