CN-121981018-A - Stability parameter prediction method for multi-suspension-span elastic support flow conveying pipe

CN121981018ACN 121981018 ACN121981018 ACN 121981018ACN-121981018-A

Abstract

The invention discloses a stability parameter prediction method for a multi-span elastic support flow transmission pipe, and relates to the technical field of flow transmission pipe vibration characteristic analysis. The multi-span pipeline is split into a plurality of sections of independent pipe sections at the supporting position, a vibration control equation describing each span pipeline is respectively established, and the vibration control equation only considers the coupling action of bending force, centrifugal force, gravity, coriolis force and inertia force of the pipeline and does not contain any intermediate supporting constraint item, so that the intermediate supporting constraint is completely written into the span-to-span coupling boundary condition, and the traditional Dirac is avoided The method comprises the steps of obtaining a characteristic equation, a characteristic function and a characteristic value under the complex boundary condition by means of deduction through the combination of the end elastic boundary and inter-span coupling constraint by introducing dimensionless parameters to a vibration differential equation, converting a partial differential equation into a normal differential equation set, and then matrixing and solving to finally obtain an accurate predicted value of natural frequency.

Inventors

FU GUANGMING
WANG YAJING
LI WENZHEN
GUO MENGCHEN
WANG BOYING
SU JIAN
WANG ZHIYUAN
SUN BAOJIANG

Assignees

中国石油大学(华东)

Dates

Publication Date: 20260505
Application Date: 20260403

Claims (3)

1. A method for predicting stability parameters of a multi-span elastically supported flowtube, comprising: s1, establishing a vibration differential equation of a multi-span flow transmission pipe with N-1 spring supports in the middle and with wire springs and torsion spring constraints at two ends, wherein the vibration differential equation of an nth pipe section of the multi-span flow transmission pipe with N-1 spring supports in the middle and with wire springs and torsion spring constraints at two ends is as follows: (1); Wherein, the For the bending stiffness of the flow tube, Is the first The lateral displacement of the segment of tubing, For the coordinates along the length of the flow tube, Is the first The position coordinates of the end point of the section suspension span flow conveying pipe, Is the mass of liquid per unit length of the liquid, Is the mass of the pipeline in unit length, For the fluid velocity in the flow tube, In order to be able to take time, For the total number of spans of the flow transmission pipe, Numbering the axial segments of the flow transmission pipe; S2, introducing dimensionless parameters, dimensionless to a vibration differential equation, and establishing a coupling boundary condition between an end elastic boundary and a span; The following dimensionless parameters were introduced: (2); Substituting formula (2) into formula (1) to obtain a dimensionless form of the vibration differential equation: (3); Wherein, the Is the position of each point of the dimensionless pipeline, Is the first The dimensionless lateral displacement of the segment pipe, In order to be a dimensionless time, the method comprises the steps of, In the form of a dimensionless flow rate, Is the ratio of the dimensionless liquid to the total mass of the pipeline, Is the first The non-dimensional position of the end point of the section suspension span flow conveying pipe, For the length of the pipe to be the same, 、 The elastic coefficients of the torsion springs at the left end and the right end are respectively, 、 The elastic coefficients of the left end wire spring and the right end wire spring are respectively, Is the first The elastic coefficient of the middle wire spring, 、 Is in a dimensionless form of the rigidity of the torsion springs at the left end and the right end respectively, 、 Is in a dimensionless form of the spring stiffness of the left end line and the right end line respectively, Is the first A dimensionless version of the individual mid-line spring rates; The end elastic boundary conditions and the inter-span coupling boundary conditions in a dimensionless form are shown as corresponding continuous conditions of formulas (4) - (11): at both ends of the pipeline, the elastic supporting constraint of the combination of the linear spring and the torsion spring is satisfied: (4); (5); (6); (7); at each span supporting position, the conditions of continuous displacement, continuous rotation angle, continuous bending moment and shear balance are satisfied: , (8); , (9); , (10); , (11); S3, deducing a characteristic equation, a characteristic value and a characteristic function, and defining an integral transformation pair; S4, converting the partial differential equation into a normal differential equation, and then matrixing to solve the natural frequency.
2. The method of predicting stability parameters of a multi-span flexible support flowtube of claim 1, wherein in S3, the eigen equation, eigen value and eigen function are derived based on two-terminal flexible support and multi-span coupling constraints, and an integral transformation pair is defined, comprising the steps of: based on a basic transformation form of generalized integral transformation, an Euler-Bernoulli beam vibration equation is selected as an approximate form of a formula (3), and the steps of deducing a corresponding characteristic equation, a characteristic value and a characteristic function are as follows: (12); Wherein, the Is the mass per unit length of the beam; The following dimensionless parameters were introduced: (13); Wherein, the A dimensionless time of formula (12); The beam vibration equation is in dimensionless form: (14); Definition solution The separation variable form of (a) is: (15); substituting formula (15) into formula (14): (16); Order the The characteristic equation of formula (3) is written as: (17); the general solution form of the characteristic equation is: (18); is an integral constant, determined by boundary conditions; The end elastic boundary conditions and inter-span coupling boundary conditions are as follows: (19); (20); (21); (22); , (23); , (24); , (25); , (26); substituting equations (19) - (26) into equation (18) yields the following matrix equation: (27); Wherein the method comprises the steps of Is related to the characteristic value The order matrix is used to determine the order matrix, Concerning integral constant Rank vectors; The equation satisfied by the eigenvalue is further solved by equation (27): (28); obtaining an integration constant by the formulas (27) and (28); substituting the integral constant into the formula (18) to obtain a characteristic function of the multi-span elastic supporting condition; Normalizing the characteristic function: (29); obtaining normalized characteristic functions from normalization conditions: (30); After normalization processing, the orthogonal normalization conditions of the characteristic function are as follows: (31); The integral transform pair is defined for equation (3) as follows: (32); (33)。
3. the method for predicting stability parameters of a multi-span flexible support flow tube as claimed in claim 1, wherein in S4, the partial differential equation is converted into a normal differential equation set by integral transformation and solved in a matrix manner, comprising the steps of: Multiplying each item of (3) by the characteristic function after orthonormalized And at The medium integration, the following normal differential transformation forms are obtained: (34); (35); (36); (37); the normal differential transformation equation set obtained by adding the formulas (34) to (37) is as follows: (38); The coefficients of the ordinary differential equation set are as follows: (39); (40); Equation (38) is the final form after conversion of the vibration differential equation; Truncating equation (38) to a finite truncate number And rewrites it into a matrix form: (41); In the matrix The elements being represented respectively , The representation is composed of A diagonal matrix is formed and is arranged, Equal to 1 to the truncated number; The standard form of formula (38) is as follows: (42); (43); In the formula, , In the form of a quality matrix, In order to provide a damping matrix, Is a rigidity matrix; The solution to equation (42) is written as follows: (44); In the formula, Is a vector of a constant magnitude and is used for the vector, Is angular frequency; substituting formula (44) into formula (42): (45); If equation (45) has a non-zero solution, then: (46); the matrix in brackets is subjected to determinant and the natural frequency of the flow transmission pipe is obtained by solving the formula (46).

Description

Stability parameter prediction method for multi-suspension-span elastic support flow conveying pipe Technical Field The invention relates to the technical field of vibration characteristic analysis of a flow transmission pipeline, in particular to a stability parameter prediction method of a multi-span elastic support flow transmission pipeline. Background The flow transmission pipeline is widely applied to the engineering fields of aerospace, petrochemical industry, hydraulic transmission and the like, and is a core component of a fluid conveying system. When the flow velocity of the fluid in the pipe exceeds a critical value, the pipeline is easy to generate fluid-solid coupling vibration instability, and the buckling deformation and resonance are shown, so that the safety of the system and the service life of the structure are seriously threatened. In order to restrain vibration and improve stability, an intermediate support is often adopted in engineering to locally restrain a pipeline, and meanwhile, the end part adopts an elastic support boundary of a linear spring-torsion spring combination to simulate actual installation working conditions. As shown in FIG. 1, the existing flow pipeline vibration modeling mostly adopts an integral pipe model, and the intermediate support is constrained by DiracThe function is directly embedded into the vibration control equation, and the method has the advantages that the derivation is simple and convenient, but the problems that the physical meaning is fuzzy due to the deep coupling of the constraint term and the main path, the influence of the support on the sectional mechanical behavior of the pipeline is difficult to intuitively embody, the calculation error is easy to introduce when the numerical value is discrete due to the introduction of the singular function into the main path, the 'mechanical behavior of the pipeline' cannot be clearly distinguished from the 'supporting constraint effect', the numerical value calculation is difficult to converge and the like exist. Research shows that the parameter combination of the middle support and the end elastic constraint can significantly influence the critical flow rate and vibration characteristics of the pipeline, and the traditional integral pipe model has limitation in describing the multi-constraint effect. Therefore, a multi-span modeling method is needed, wherein support constraints are written into boundary conditions to realize stability parameter prediction of the flow transmission pipeline with middle support and end elastic constraint, and reliable basis is provided for engineering vibration reduction design. Disclosure of Invention The invention aims at overcoming the defects and provides a stability parameter prediction method of a multi-span elastic support flow transmission pipe, which avoids Dirac in a traditional integral pipe model by splitting a pipeline into a plurality of sections of independent structures at a supporting position, completely writing intermediate supporting constraint into inter-span coupling boundary conditionsAnd the functions are embedded into the main equation to cause the defects of fuzzy physical meaning, difficult convergence of numerical calculation and the like. The invention adopts the following technical scheme: a method for predicting stability parameters of a multi-span elastically supported flow tube, comprising: s1, establishing a vibration differential equation of a multi-span flow transmission pipe with N-1 spring supports in the middle and with wire springs and torsion spring constraints at two ends, wherein the vibration differential equation of an nth pipe section of the multi-span flow transmission pipe with N-1 spring supports in the middle and with wire springs and torsion spring constraints at two ends is as follows: (1); Wherein, the For the bending stiffness of the flow tube,For the lateral displacement of the pipe,For the coordinates along the length of the flow tube,Is the mass of liquid per unit length of the liquid,Is the mass of the pipeline in unit length,For the fluid velocity in the flow tube,In order to be able to take time,For the total number of spans of the flow transmission pipe,Numbering the axial segments of the flow transmission pipe; S2, introducing dimensionless parameters, dimensionless to a vibration differential equation, and establishing a coupling boundary condition between an end elastic boundary and a span; The following dimensionless parameters were introduced: (2); Substituting formula (2) into formula (1) to obtain a dimensionless form of the vibration differential equation: (3); Wherein, the Is the position of each point of the dimensionless pipeline,For the transverse displacement of the dimensionless pipeline,In order to be a dimensionless time, the method comprises the steps of,In the form of a dimensionless flow rate,Is the ratio of the dimensionless liquid to the total mass of the pipeline,Is the firstThe non-dimen