CN109063305A - Defeated stream straight pipeline Vibration Absorption Designing method under random vibration environment - Google Patents

Defeated stream straight pipeline Vibration Absorption Designing method under random vibration environment Download PDF

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CN109063305A
CN109063305A CN201810829554.0A CN201810829554A CN109063305A CN 109063305 A CN109063305 A CN 109063305A CN 201810829554 A CN201810829554 A CN 201810829554A CN 109063305 A CN109063305 A CN 109063305A
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CN109063305B (en
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张怀亮
李卫
瞿维
赵丽娜
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Central South University
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Abstract

The invention discloses a kind of stream straight pipeline Vibration Absorption Designing method defeated under random vibration environment, include the following steps: to establish defeated stream straight pipeline vibration maths model under random vibration environment；Mathematical model is solved, the solving model of piping displacement response covariance and stress response covariance is obtained；The design variable for determining optimization, establishes constraint condition, is then based on required piping displacement response covariance and stress response covariance solving model and sets up objective function；Using genetic algorithm, the objective function of foundation is solved, obtains globally optimal solution, that is, solves send as an envoy to piping displacement response mean-square value and the smallest pipeline configuration parameter of stress response mean-square value.The present invention establishes pipe vibration model for defeated stream straight pipeline, and speed, stress and displacement response analysis are carried out to it, the structural parameters of pipeline after design are determined further according to multi-objective genetic algorithm, to reduce defeated stream straight pipeline vibration, improve the stability and safety of pipe-line system.

Description

Defeated stream straight pipeline Vibration Absorption Designing method under random vibration environment
Technical field
The invention belongs to stream straight pipeline vibration dampings defeated under pipe vibration-damping technical field more particularly to a kind of random vibration environment to set Meter method.
Background technique
Engineering machinery under work condition environment complicated and changeable, such as hard rock mole (TBM), mining machinery, it is worked Cheng Zhong, load abrupt potential and self-excited vibration must make equipment generate judder, and the pipeline in hydraulic system thereon is caused to produce Raw vibration, oscillatory type are generally random vibration.Vibration can not only be such that pipe stress aggravates, and cause pipeline to be easy to appear stress tired Strain wound, influences safety and construction progress, can also aggravate the unstable of fluid energy stream fluctuation and then influence downstream driving member The stability of part work.The influence or only of random vibration is not accounted for defeated stream straight pipeline construction design method both at home and abroad at present In view of simple sinusoidal is vibrated, and driving source suffered by pipeline is generally random vibration in reality, in addition, existing pipe design method Mostly single goal method, i.e., be only designed simple target, and the design of the hydraulic straight pipeline under random vibration effect is one A multiple target multiple constraint problems, easily sink into local extremum using conventional method, it is difficult to obtain globally optimal solution.Therefore, it is necessary to The design method of stream straight pipeline defeated under random vibration environment is studied.
Summary of the invention
The application aims to solve at least one of the technical problems existing in the prior art.For this purpose, an object of the present invention It is to provide defeated stream straight pipeline Vibration Absorption Designing method under the accurate and effective random vibration environment of one kind.
In order to solve the above technical problems, the present invention adopts the following technical scheme:
A kind of defeated stream straight pipeline Vibration Absorption Designing method under random vibration environment, includes the following steps:
S1: defeated stream straight pipeline vibration maths model under random vibration environment is established；
S2: solving pipe vibration mathematical model using DISCRETE ANALYSIS METHOD OF RANDOM VIBRATION, obtains piping displacement and rings Answer the solution formula of covariance and stress response covariance；
S3: determining the design variable of optimization, establish constraint condition, is then based on piping displacement response required in S2 step Covariance and stress response covariance solve formula and set up objective function；
S4: utilizing genetic algorithm, and the objective function established to S3 step solves, and obtains globally optimal solution, that is, solves Piping displacement of sening as an envoy to responds mean-square value and the smallest pipeline configuration parameter of stress response mean-square value.
Further, the vibration maths model are as follows:
Wherein: [M] is straight pipeline mass matrix, and [K] is straight pipeline stiffness matrix, and [C] is straight pipeline damping matrix, { y } For piping displacement response vector, { p } is density of load vector, indicates load active position and intensity,It is white for transverse acceleration Noise；AndPipeline acceleration and speed responsive vector are respectively indicated, that is, is respectively the second order and first derivative of displacement.
Further, straight pipeline mass matrix [M], stiffness matrix [C] and damping matrix [K] in the vibration maths model Assembled by corresponding element mass matrix, element stiffness matrix and unit damping matrix, in which:
The unit damping matrix [C] of entire pipe-line systemeAre as follows:
[C]e=[Cf]e
The element mass matrix [M] of entire pipe-line systemeAre as follows:
[M]e=[Mp]e+[Mf]e
The element stiffness matrix [K] of entire pipe-line systemeAre as follows:
[K]e=[Kp]e+[Kf]e
In above-mentioned formula:
Wherein, [Mf]eFor solid-liquid coupling element mass matrix, [Cf]eFor solid-liquid coupling unit damping matrix, [Kf]eIt is solid Liquid coupling unit stiffness matrix, A indicate piping unit cross-sectional area；P indicates tube fluid pressure, and v indicates fluid flow rate, mf Indicate fluid units linear mass, ρfIndicate fluid density, IfIndicate fluid cross-section the moment of inertia, x indicates that piping unit is longitudinally sat Mark, subscript x expression obtain partial derivative to corresponding Matrix Calculating x, and a indicates piping unit length, and [N] indicates lateral displacement shape function Matrix,Indicate that section rotated shape Jacobian matrix, [U] indicate length travel shape function matrix.
Further, the solution formula of piping displacement response covariance are as follows:
Wherein,[M] is straight pipeline mass matrix, and [C] is stiffness matrix, [K] is damping matrix；R for moment n Δ t, in above formula1(n-1), r2(n-1) and r3It (n-1) is known terms；
The solution formula of pipe stress response covariance are as follows:
Wherein, [Rσ(n)] stress response covariance matrix, [K] are indicatedeFor pipeline overall cell stiffness matrix；[Ryy(n)] For dynamic respond covariance matrix.
Further, the element in each shape function matrix is as follows:
Wherein, a indicates piping unit length, and E is pipeline elasticity modulus, and I is pipeline section the moment of inertia, and κ indicates shearing system Number, G indicate modulus of shearing, and A indicates that piping unit cross-sectional area, x indicate piping unit longitudinal coordinate.
Further, the objective function that S3 step is established are as follows:
Further, pipe vibration mathematical model is solved using DISCRETE ANALYSIS METHOD OF RANDOM VIBRATION in S2 step Detailed process are as follows:
S21: vibration maths model is converted into state equation form:
Wherein:
S22: it is theoretical according to random vibration discrete analysis, obtain the relational expression between { S (n) } and { S (n-1) } are as follows:
S23: taking β=0.5, and the recurrence method of the theory of random vibration discrete analysis at this time is unconditional stability, to above-mentioned Formula both sides take mathematic expectaion to obtain hydraulic straight pipeline mean value response formula:
S24: to the formula in S22 step, the right side multiplies respective transposition and takes mathematic expectaion respectively again, while considering white noise It is irrelevant for motivating with response, obtains hydraulic straight pipeline and just responds expression formula are as follows:
Wherein,For the mean-square value of actuation duration function；
S25: transformation solution is carried out to above formula and obtains dynamic respond covariance matrix [Ryy(n)] solution formula:
According to the relationship of element stress and displacement, pipeline configuration stress response covariance matrix is acquired are as follows:
Wherein, [Rσ(n)] stress response covariance matrix, [K] are indicatedeFor pipeline overall cell stiffness matrix.
Further, in S3 step, design variable are as follows: pipeline wall thickness, internal diameter of the pipeline and duct length, constraint condition Are as follows:
Wherein: z1For pipeline wall thickness；z2For internal diameter of the pipeline；z3For duct length.
Further, the operating parameter of genetic algorithm is provided that
The length of chromosome is 20；
Initial scale is 100；
Crossover probability is 0.7；
Mutation probability is 0.01.
Further, the genetic algorithm uses parallelism selection genetic algorithm.
Compared with prior art, the defeated design method for flowing straight pipeline under random vibration environment provided by the present invention, for Defeated stream straight pipeline establishes pipe vibration model, and carries out speed, stress and displacement response analysis to it, further according to multi-objective Genetic Algorithm determines the structural parameters of pipeline after design, to reduce defeated stream straight pipeline vibration, improves the stability and peace of pipe-line system Quan Xing.
Detailed description of the invention
Fig. 1 is defeated stream straight pipeline design method step schematic diagram under random vibration environment；
Fig. 2 is defeated stream straight pipeline design method flow diagram under random vibration environment；
Fig. 3 is defeated stream straight pipeline illustraton of model；
Fig. 4 is Timoshenko beam element model schematic diagram；
Fig. 5 is the mean value of first object function population objective function with the variation schematic diagram of the number of iterations；
Fig. 6 is that first object Function Optimization solution changes schematic diagram；
Fig. 7 is the mean value of the second objective function population objective function with the variation schematic diagram of the number of iterations；
Fig. 8 is that the second objective function optimal solution changes schematic diagram；
Fig. 9 is that optimization front and rear pipes are displaced mean-square value contrast schematic diagram；
Figure 10 is optimization front and rear pipes stress mean-square value contrast schematic diagram；
Figure 11 is optimization front and rear pipes speed mean-square value contrast schematic diagram.
Specific embodiment
Below in conjunction with the drawings and specific embodiments, the present invention is further illustrated.
The present invention is a kind of design method of defeated stream straight pipeline under random vibration environment, in conjunction with Fig. 1, Fig. 2 and Fig. 3, by with Lower step carries out:
Step 1 establishes defeated stream straight pipeline model of vibration under random vibration environment.
Defeated stream straight pipeline vibration maths mould under random vibration is established using Fluid structure interaction and finite element analysis theory Type:
In formula, [M] is straight pipeline mass matrix, and [K] is straight pipeline stiffness matrix, and [C] is straight pipeline damping matrix, { y } For piping displacement response vector, { p } is density of load vector, indicates load active position and intensity,It is white for transverse acceleration Noise,Pipeline acceleration and speed responsive vector are respectively indicated, that is, is respectively the second order and first derivative of displacement.
Firstly the need of mass matrix, stiffness matrix and the damping matrix in the formula of determination, hydraulic direct piping unit is used Timoshenko beam element model (as shown in Figure 4), and it is considered thin-wall long and thin pipeline.
Element displacement field indicates are as follows:
Wherein:
Wherein w indicates that the lateral displacement of beam model, θ indicate that cross section corner, u indicate length travel.Corresponding subscript i1 First node and second node of unit are respectively indicated with i2.
[N] indicates lateral displacement shape function matrix,Indicate that section rotated shape Jacobian matrix, [U] indicate longitudinal position Move shape function matrix, { y }eiIndicate that cell node freedom degree vector, the element in each shape function matrix are as follows:
In formula (4)-formula (7), a expression piping unit length, EI expression bending stiffness (E is pipeline elasticity modulus,For pipeline section the moment of inertia, wherein D indicates outer diameter tube, and d indicates internal diameter of the pipeline), κ indicates shearing factor, G indicates modulus of shearing, and A indicates that piping unit cross-sectional area, x indicate piping unit longitudinal coordinate.
Consider that shear strain effect, the piping unit strain energy that length is a indicate are as follows:
Shear strain in cross section is set as constant, the constant shear in cross section, which strains, to be indicated are as follows:
Character meaning and front analysis are identical in formula (8), and formula (1)-formula (7) is substituted into formula (8) can be in the hope of piping unit Stiffness matrix:
[Kp]e=[Kb]e+[Ka]e+[Ks]e (9)
Wherein, [Kb]eFor bending strain effect stiffness matrix:
[Ka]eFor axial strain effect stiffness matrix:
[Ks]eFor shearing strain effect stiffness matrix:
Subscript x indicates the partial derivative to corresponding Matrix Calculating x in formula (10)-formula (12).
Shape function before use in analysis considers the piping unit kinetic energy T of shearing effect and rotary inertiaeIt can be with table It is shown as:
In formula, mpIndicate linear mass, ρpIndicate piping unit density, I indicates piping unit cross sectional moment of inertia, a table Show piping unit length, t is the time.
As the above analysis, piping unit shape function is only related to x, and each shape function substitution formula (13) can be obtained To piping unit mass matrix:
[Mp]e=[Mt]e+[Ma]e+[Mr]e (14)
Wherein, [Mt]eIndicate transverse inertia domino effect mass matrix:
[Ma]eIndicate axial inertia effect mass matrix:
[Mr]eIndicate rotator inertia effect quality matrix:
Pipeline mechanism damping is considered as very little, therefore is ignored.Influence of the tube fluid to pipeline can be considered as External force of the fluid matasomatism on tube wall, these power depend on the node variable of pipe-line system, including pipeline centrifugal force, Coriolis Power and translation inertia force.Fluid flows through pipeline with constant speed, and thinks that fluid is the compressible steady motion of a fluid, fluid structurecoupling unit matter Moment matrix, fluid structurecoupling damping matrix and fluid structurecoupling stiffness matrix may be expressed as:
Wherein, [Mf]eFor solid-liquid coupling element mass matrix, [Cf]eFor solid-liquid coupling unit damping matrix, [Kf]eIt is solid Liquid coupling unit stiffness matrix, P indicate tube fluid pressure, and v indicates fluid flow rate, mfIndicate fluid units linear mass, ρfTable Show fluid density,Indicate fluid cross-section the moment of inertia, other letter meanings and front analysis are identical.
It is damped due to having ignored pipeline configuration, then the unit damping matrix of entire pipe-line system are as follows:
[C]e=[Cf]e (21)
The element mass matrix of entire pipe-line system is the sum of piping unit mass matrix and solid-liquid coupling mass matrix:
[M]e=[Mp]e+[Mf]e (22)
The element stiffness matrix of entire pipe-line system is the sum of piping unit stiffness matrix and solid-liquid coupling stiffness matrix:
[K]e=[Kp]e+[Kf]e (23)
On the basis of above-mentioned analysis, the overall quality matrix of entire defeated stream straight pipeline can be obtained by unit assembling [M], damping matrix [C], stiffness matrix [K].
Step 2: defeated stream straight pipeline vibration maths model solves
Model is solved using DISCRETE ANALYSIS METHOD OF RANDOM VIBRATION:
Write formula (1) as state equation form:
Wherein:
{ S ' (t) } indicates to carry out first derivation to { S (t) }.
It is theoretical according to random vibration discrete analysis, formula (24) are substituted into the system state equation and change of (n-1+ β) time Δt Letter obtains the relational expression between { S (n) } and { S (n-1) } are as follows:
Known to analysis as β=0.5, the recurrence method of random vibration discrete analysis theory is unconditional stability.To formula (25) both sides take mathematic expectaion that can obtain hydraulic straight pipeline mean value response formula:
To formula (25), the right side multiplies respective transposition and takes mathematic expectaion respectively again, while considering that white-noise excitation and response are mutual It is incoherent.Hydraulic straight pipeline can be obtained and just respond expression formula are as follows:
Wherein,For the mean-square value of actuation duration function.
By two above formula it is found that all referring in calculating process to matrixThe problem of inverting, this A matrix is the asymmetric high level matrix in broadband, and direct finding the inverse matrix needs considerable calculating memory and time, but also It will affect the accuracy and applicability of calculating.Therefore it needs to carry out transformation appropriate to two above calculation formula.Formula (26) Both sides while premultiplicationObtain equation block form:
Wherein:
For moment n Δ t, b1(n-1) and b2(n-1) formula (28) can be solved and can be obtained as known terms:
Wherein:
Use matrixPremultiplication formula (27), while with its transposed matrixRight multiplier (27) both sides obtain piecemeal equation:
Wherein, [Ryy] indicate that piping displacement responds autocorrelation matrix,Indicate pipeline speed responsive autocorrelation matrix,Indicate the cross-correlation matrix of piping displacement response and speed responsive.R for moment n Δ t, in above formula1(n-1), r2(n- And r 1)3(n-1) it is known terms, is respectively as follows:
Simultaneous (2-84), (2-85), (2-86) and formula (2-83) can obtain:
It, can be in the hope of pipeline configuration stress response covariance matrix according to the relationship of element stress and displacement are as follows:
Wherein, [Rσ(n)] stress response covariance matrix, [K] are indicatedeFor pipeline overall cell stiffness matrix；[Ryy(n)] For dynamic respond covariance matrix；For speed responsive covariance matrix.
Diagonal entry is respectively hydraulic direct piping displacement response mean-square value, speed responsive in formula (38), (39) and (40) Mean-square value and stress response mean-square value.
First primarily determine pipeline configuration parameter, setting pipeline material attribute and intraluminal fluid pressure oil parameter.Pass through site inspection Pipeline work condition, determines the flow velocity and pressure of fluids within pipes, determines duct thickness, internal diameter and length by national standard, Determine variable bound collection.
1 pipeline analysis major parameter of table
Pipeline position is set up according to formula (38), (39) and (40) in conjunction with intraluminal fluid pressure oil parameter according to pipeline material attribute It moves response covariance and stress response mean-square value solves equation.The form of probability of random vibration is mostly normal state point in engineering Cloth, therefore in order to reduce the complexity of modeling and theory analysis, the random vibration source for acting on hydraulic straight pipeline is set as high This white noise.
Step 2: determining the design variable of optimization, establish constraint condition, be then based on required piping displacement response association side Difference and stress response mean-square value solve formula and set up objective function.
By the design conditions of theory analysis and engineering hydraulic straight pipeline in practice, it is determined that three parameters are design variable, It is respectively: δ-pipeline wall thickness, d- internal diameter of the pipeline, L- duct length.That is:
Z=[z1,z2,z3]=[δ, d, L] (42)
The main target of vibration damping is the stress response and dynamic respond for reducing pipeline, and the speed responsive mean-square value of pipeline It is identical therefore square with the maximum displacement mean-square value and maximum stress of pipeline with the changing rule and displacement mean-square value of pipe parameter Value is designed as objective function.Obtained dynamic respond covariance matrix and stress response mean-square value square are solved by aforementioned The available design object function of battle array is as follows:
By site inspection pipeline work condition, the flow velocity and pressure of fluids within pipes are determined, determined by existing standard Duct thickness, internal diameter and length determine variable bound collection are as follows:
Step 3: utilizing genetic algorithm, the objective function of foundation is solved, obtain globally optimal solution, that is, solve and send as an envoy to Piping displacement responds mean-square value and the smallest pipeline configuration parameter of stress response mean-square value.
The primary operating parameter of genetic algorithm has: string length l, the number of individuals n in initial population, crossover probability Pc, Mutation probability PmDeng.String length is the length of chromosome, depends primarily on the precision of Solve problems needs.Population Size Also known as population size, its value is related to the nonlinear degree of problem, is usually taken to be 20-200, if problem is non-linear Degree is more serious, then the scale of group should obtain greatly.Intersect in calculating process and mutation operator play an important role, Crossover operator can make the well part in population between each individual obtain reconfiguring to generate more excellent filial generation, favorably In improving search speed in Evolution of Population, and mutation operator is conducive to maintain the diversity of genes of individuals in population.Intersect general The rate value the big more is conducive in population individual combination and intersects, but simultaneously also easier loss excellent genes mode and cause to search Suo Buzai is carried out towards optimal direction, and small crossover probability is conducive to the search of globally optimal solution, but will lead to speed of service mistake Slowly the stagnation of search is resulted even in, crossover probability is usually taken to be 0.4~0.99.Mutation operation, which can supplement in crossing operation, to be lost The gene of mistake avoids the local optimum of algorithm from restraining.The diversity of group is related to mutation probability, and mutation probability crosses conference reduction The performance of algorithm leads to the loss of excellent genes in population, and mutation probability value is too small, then can not inhibit precocious phenomenon, and variation is general Rate is usually taken to be 0.0001~0.1.Based on the analysis results with the practical significance of problem, determine that operating parameter value is as shown in table 2.
2 genetic algorithm operating parameter of table
According to the operating parameter of upper fixed problem constraint set and genetic algorithm, it is with random vibration acceleration variance 1000m2/s4, mean value 0, fluid flow rate 5m/s, Fluid pressure is 2 × 107When Pa for two fixed ends pipeline, write suitable For the multi-objective genetic algorithm program of hydraulic direct pipe parameter design, stopping criterion for iteration is set as 50 generations.Figure 5-8 is most It is excellent solution and population objective function mean value with the number of iterations situation of change.Wherein, Fig. 5 and Fig. 7 contains the solution of objective function Change with the number of iterations, for the variation for representing objective function solution being more clear, individually indicates target with Fig. 6 and Fig. 8 The variation of Function Solution.As seen from the figure, as the increase target function value of the number of iterations is gradually reduced, problem is become closer to most Excellent solution, first object function have obtained the optimal solution of problem when the number of iterations was about 35 generation, and the second objective function is in iteration The optimal solution of problem has been obtained when number was about 20 generation.
In order to which comparative analysis designs front and rear pipes dynamic respond mean-square value of pipeline, stress response under random vibration effect Mean-square value and speed responsive mean-square value are analyzed using the most commonly used two fixed ends pipeline as research object, as a result as schemed Shown in 9- Figure 11.
By analysis it is found that the pipeline maximum displacement mean-square value after design decreases before compared to design, managed after design Road maximum displacement mean-square value reduces about 16.21%, while maximum stress mean-square value reduces 21.04%, due to structural parameters It is consistent to the affecting laws of dynamic respond to the affecting laws and its of pipeline speed responsive, therefore pipeline maximum speed is equal after design Side's value also reduces 17.61%.It follows that vibration of the pipeline under random vibration effect after design has obtained effectively subtracting It is small, be conducive to the resistance to shock for improving pipeline.The design method is effective and feasible.Parametric results after design are as shown in table 3.
3 genetic algorithm optimization result of table
Compared to the method for solving of other multi-objective genetic algorithms, paratactic selection method is that sub-group distributes specific item scalar functions, Each specific item scalar functions carry out independent selection in group, and the new sub-group of each group is finally merged into a complete novel species Group, is conducive to avoid the occurrence of locally optimal solution in this way, has good of overall importance.
Within the scope of design variable, it is desirable that piping displacement, stress response value are the smaller the better, therefore target value is smaller, pipeline Vibration characteristics it is better, parameter value at this time is the parameter after designing.
It is described that defeated stream straight pipeline structure is designed, it is that pipeline configuration parameter is determined by multi-objective genetic algorithm. According to the practical significance of Such analysis result and problem, genetic algorithm operating parameter value is determined.According to design variable, target letter Several and algorithm operating parameter, writes program using GAs Toolbox and is resolved, and objective function optimal solution restrains then algorithm Effectively.
The design method is suitable for multiple target multiple constraint problem, is not easy to sink into local extremum, can obtain globally optimal solution. It is all the same to represent meaning unless make specifically defined outer for the definition of each character involved in each formula in the present embodiment.
Above-described embodiment is only to clearly demonstrate examples made by the present invention, rather than the restriction to embodiment.For For those of ordinary skill in the art, other various forms of variations or change can also be made on the basis of the above description It is dynamic.Here without can not be also exhaustive to all embodiments.And the obvious variation or change thus amplified out It is dynamic to be still in the protection scope of this invention.

Claims (10)

1. a kind of defeated stream straight pipeline Vibration Absorption Designing method under random vibration environment, which comprises the steps of:
S1: defeated stream straight pipeline vibration maths model under random vibration environment is established；
S2: solving pipe vibration mathematical model using DISCRETE ANALYSIS METHOD OF RANDOM VIBRATION, obtains piping displacement response association The solution formula of variance and stress response covariance；
S3: determining the design variable of optimization, establish constraint condition, is then based on piping displacement response association side required in S2 step Difference and stress response covariance solve formula and set up objective function；
S4: utilizing genetic algorithm, and the objective function established to S3 step solves, and obtains globally optimal solution, that is, solves and send as an envoy to Piping displacement responds mean-square value and the smallest pipeline configuration parameter of stress response mean-square value.
2. defeated stream straight pipeline Vibration Absorption Designing method under random vibration environment according to claim 1, it is characterised in that: described Vibration maths model are as follows:
Wherein: [M] is straight pipeline mass matrix, and [K] is straight pipeline stiffness matrix, and [C] is straight pipeline damping matrix, and { y } is pipe Road dynamic respond vector, { p } are density of load vector, indicate load active position and intensity,For transverse acceleration white noise Sound；AndPipeline acceleration and speed responsive vector are respectively indicated, that is, is respectively the second order and first derivative of displacement.
3. defeated stream straight pipeline Vibration Absorption Designing method under random vibration environment according to claim 2, which is characterized in that described In vibration maths model straight pipeline mass matrix [M], stiffness matrix [C] and damping matrix [K] by corresponding element mass matrix, Element stiffness matrix and unit damping matrix assemble, in which:
The unit damping matrix [C] of entire pipe-line systemeAre as follows:
[C]e=[Cf]e
The element mass matrix [M] of entire pipe-line systemeAre as follows:
[M]e=[Mp]e+[Mf]e
The element stiffness matrix [K] of entire pipe-line systemeAre as follows:
[K]e=[Kp]e+[Kf]e
In above-mentioned formula:
Wherein, [Mf]eFor solid-liquid coupling element mass matrix, [Cf]eFor solid-liquid coupling unit damping matrix, [Kf]eFor solid-liquid coupling Element stiffness matrix is closed, A indicates piping unit cross-sectional area；P indicates tube fluid pressure, and v indicates fluid flow rate, mfIt indicates Fluid units linear mass, ρfIndicate fluid density, IfIndicating fluid cross-section the moment of inertia, x indicates piping unit longitudinal coordinate, under X expression is marked to the partial derivative of corresponding Matrix Calculating x, a indicates piping unit length, and [N] indicates lateral displacement shape function matrix,Indicate that section rotated shape Jacobian matrix, [U] indicate length travel shape function matrix.
4. defeated stream straight pipeline Vibration Absorption Designing method under random vibration environment according to claim 2 or 3, it is characterised in that: The solution formula of piping displacement response covariance are as follows:
Wherein,[M] is straight pipeline mass matrix, and [C] is stiffness matrix, and [K] is Damping matrix；R for moment n Δ t, in above formula1(n-1), r2(n-1) and r3It (n-1) is known terms；
The solution formula of pipe stress response covariance are as follows:
Wherein, [Rσ(n)] stress response covariance matrix, [K] are indicatedeFor pipeline overall cell stiffness matrix；[RyyIt (n)] is position Move response covariance matrix.
5. defeated stream straight pipeline Vibration Absorption Designing method under random vibration environment according to claim 4, it is characterised in that: each shape Element in shape Jacobian matrix is as follows:
Wherein, a indicates piping unit length, and E is pipeline elasticity modulus, and I is pipeline section the moment of inertia, and κ indicates shearing factor, G Indicate modulus of shearing, A indicates that piping unit cross-sectional area, x indicate piping unit longitudinal coordinate.
6. defeated stream straight pipeline Vibration Absorption Designing method under random vibration environment according to claim 4, it is characterised in that: S3 step Suddenly the objective function established are as follows:
7. defeated stream straight pipeline Vibration Absorption Designing method under random vibration environment according to claim 4, it is characterised in that: S2 step The detailed process that pipe vibration mathematical model is solved using DISCRETE ANALYSIS METHOD OF RANDOM VIBRATION in rapid are as follows:
S21: vibration maths model is converted into state equation form:
Wherein:
S22: it is theoretical according to random vibration discrete analysis, obtain the relational expression between { S (n) } and { S (n-1) } are as follows:
S23: taking β=0.5, and the recurrence method of the theory of random vibration discrete analysis at this time is unconditional stability, to above-mentioned formula Both sides take mathematic expectaion to obtain hydraulic straight pipeline mean value response formula:
S24: to the formula in S22 step, the right side multiplies respective transposition and takes mathematic expectaion respectively again, while considering white-noise excitation With response be it is irrelevant, obtain hydraulic straight pipeline and just respond expression formula are as follows:
Wherein,For the mean-square value of actuation duration function；
S25: transformation solution is carried out to above formula and obtains dynamic respond covariance matrix [Ryy(n)] solution formula:
According to the relationship of element stress and displacement, pipeline configuration stress response covariance matrix is acquired are as follows:
Wherein, [Rσ(n)] stress response covariance matrix, [K] are indicatedeFor pipeline overall cell stiffness matrix.
8. defeated stream straight pipeline Vibration Absorption Designing method under random vibration environment according to claim 7, which is characterized in that S3 step In rapid, design variable are as follows: pipeline wall thickness, internal diameter of the pipeline and duct length, constraint condition are as follows:
Wherein: z1For pipeline wall thickness；z2For internal diameter of the pipeline；z3For duct length.
9. defeated stream straight pipeline Vibration Absorption Designing method under random vibration environment according to claim 8, it is characterised in that: heredity The operating parameter of algorithm is provided that
The length of chromosome is 20；
Initial scale is 100；
Crossover probability is 0.7；
Mutation probability is 0.01.
10. according to right want 1 described in defeated stream straight pipeline Vibration Absorption Designing method under random vibration environment, it is characterised in that: it is described Genetic algorithm uses parallelism selection genetic algorithm.
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Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109635500A (en) * 2019-01-02 2019-04-16 西北工业大学 Aviation pipeline three-dimensional flow consolidates coupling parameter resonance response characteristic prediction method and device
CN112100932A (en) * 2020-08-13 2020-12-18 中冶南方都市环保工程技术股份有限公司 Numerical simulation method and system for vibration and blockage problems of industrial pipeline
CN113217484A (en) * 2021-05-21 2021-08-06 福州大学 Hydraulic soft switching transformer for realizing pressure lifting and working method thereof
CN114818292A (en) * 2022-04-15 2022-07-29 中国核动力研究设计院 Energy band structure analysis method for phononic crystal current-carrying pipeline

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
GB2131517A (en) * 1982-12-04 1984-06-20 Festo Maschf Stoll G Adjustable bellows-type shock absorber
CN1867919A (en) * 2003-10-15 2006-11-22 里特技术股份公司 Method for determining optimal damping treatments layouts and panel shape layouts
CN104504226A (en) * 2015-01-25 2015-04-08 中南大学 Fluid conveying pipeline vibration resisting support under strong vibration environment and design method thereof

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
GB2131517A (en) * 1982-12-04 1984-06-20 Festo Maschf Stoll G Adjustable bellows-type shock absorber
CN1867919A (en) * 2003-10-15 2006-11-22 里特技术股份公司 Method for determining optimal damping treatments layouts and panel shape layouts
CN104504226A (en) * 2015-01-25 2015-04-08 中南大学 Fluid conveying pipeline vibration resisting support under strong vibration environment and design method thereof

Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109635500A (en) * 2019-01-02 2019-04-16 西北工业大学 Aviation pipeline three-dimensional flow consolidates coupling parameter resonance response characteristic prediction method and device
CN109635500B (en) * 2019-01-02 2024-02-02 西北工业大学 Aviation pipeline three-dimensional fluid-solid coupling parameter resonance response characteristic prediction method and device
CN112100932A (en) * 2020-08-13 2020-12-18 中冶南方都市环保工程技术股份有限公司 Numerical simulation method and system for vibration and blockage problems of industrial pipeline
CN113217484A (en) * 2021-05-21 2021-08-06 福州大学 Hydraulic soft switching transformer for realizing pressure lifting and working method thereof
CN114818292A (en) * 2022-04-15 2022-07-29 中国核动力研究设计院 Energy band structure analysis method for phononic crystal current-carrying pipeline
CN114818292B (en) * 2022-04-15 2023-08-25 中国核动力研究设计院 Phonon crystal current carrying pipeline energy band structure analysis method

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