CN109635500B - Aviation pipeline three-dimensional fluid-solid coupling parameter resonance response characteristic prediction method and device - Google Patents
Aviation pipeline three-dimensional fluid-solid coupling parameter resonance response characteristic prediction method and device Download PDFInfo
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Abstract
The utility model relates to the technical field of dynamic design of aviation flow transmission pipelines, and provides a method and a device for predicting resonance response characteristics of three-dimensional fluid-solid coupling parameters of aviation pipelines. The method for predicting the resonance response characteristics of the three-dimensional fluid-solid coupling parameters of the aviation pipeline establishes a three-dimensional fluid-solid coupling dynamics model of the aviation flow transmission pipeline according to related parameters; establishing a three-dimensional fluid-solid coupling dynamic motion equation of the aviation flow transmission pipeline according to the dynamic model; obtaining a finite-dimension matrix equation according to the dynamic motion equation; and obtaining the parameter resonance response characteristic of the aviation flow transmission pipeline in a preset pulsation frequency range according to the finite-dimension matrix equation. The parameter resonance response characteristic is obtained, the resonance interval can be effectively avoided, the occurrence of parameter resonance is prevented, and the service life and the safety of the aviation flow transmission pipeline are improved.
Description
Technical Field
The utility model relates to the technical field of dynamic design of aviation flow transmission pipelines, in particular to a method and a device for predicting resonance response characteristics of three-dimensional fluid-solid coupling parameters of aviation pipelines.
Background
Aviation hydraulic and fuel pipeline systems have important roles in medium transmission and energy transfer. The load environment is special compared with the traditional industrial flow transmission pipeline. Is under the combined action of complex internal pressure pulsation and external structural vibration excitation. The change of the fluid movement state in the pipe can interact with the pipe wall structure, and can generate fluid-solid coupling phenomenon to induce the vibration of the pipe structure. In particular, when the pump source is used for pumping fluid, the flow rate of the pipeline is not ideal and stable, and the aviation pipeline is subjected to alternating oil sucking and discharging actions of the pump, and the flow rate of the fluid in the pipeline is in a pulsating form in most cases. When the flow rate, the pulsation frequency and the pulsation amplitude meet certain conditions, parameter resonance occurs in the flow transmission pipeline. The negative stiffness term of the system is time-varying and has a resonance phenomenon that occurs at twice the natural frequency of the system or at the sum of some two orders of natural frequencies.
Such parameter resonances can cause noise diffusion within the pipe, reduced pipe life and damage to the pipe joint, which can seriously impact the safety of the aviation flow pipeline system.
Therefore, it is necessary to provide a new method and device for predicting the resonance response characteristics of three-dimensional fluid-solid coupling parameters of an aviation pipeline.
The above information disclosed in the background section is only for enhancement of understanding of the background of the utility model and therefore it may contain information that does not form the prior art that is already known to a person of ordinary skill in the art.
Disclosure of Invention
The utility model aims to overcome the defect of low safety of an aviation pipeline system caused by the fact that the parameter resonance response characteristic cannot be predicted by the aviation pipeline in the prior art, and provides a prediction method and a prediction device for the three-dimensional fluid-solid coupling parameter resonance response characteristic of the aviation pipeline, which can predict the parameter resonance response characteristic of the aviation pipeline so as to improve the safety of the aviation pipeline.
Additional aspects and advantages of the utility model will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the utility model.
According to one aspect of the utility model, a method for predicting resonance response characteristics of three-dimensional fluid-solid coupling parameters of an aviation pipeline comprises the following steps:
establishing a three-dimensional fluid-solid coupling dynamics model of the aviation flow transmission pipeline according to the related parameters;
establishing a three-dimensional fluid-solid coupling dynamic motion equation of the aviation flow transmission pipeline according to the dynamic model;
obtaining a finite-dimension matrix equation according to the dynamic motion equation;
and obtaining the parameter resonance response characteristic of the aviation flow transmission pipeline in a preset pulsation frequency range according to the finite-dimension matrix equation.
In an exemplary embodiment of the present disclosure, the related parameters include:
geometric parameters including an inner diameter, an outer diameter, and an overall length of the flow conduit;
physical parameters including modulus of elasticity and density of the flow conduit;
the working condition parameters comprise the average flow velocity, the pulsation amplitude and the pulsation frequency of the fluid in the fluid delivery pipeline.
In one exemplary embodiment of the present disclosure, deriving a finite-dimensional matrix equation from the kinetic motion equation includes:
and obtaining the finite-dimension matrix equation by adopting a Galerkin method according to the dynamic motion equation.
In one exemplary embodiment of the present disclosure, deriving the parametric resonance response characteristic of the aviation flow conduit from the finite-dimensional matrix equation includes:
and calculating the parameter resonance response characteristic of the flow transmission pipeline by adopting a Dragon-Gregory tower method according to the finite-dimension matrix equation.
In one exemplary embodiment of the present disclosure, the parametric resonance response characteristic includes:
the three-dimensional fluid-solid coupling parameter resonance response characteristic of the aviation flow transmission pipeline when the fluid speed in the aviation flow transmission pipeline is lower than the critical flow rate and the three-dimensional fluid-solid coupling parameter resonance response characteristic of the aviation flow transmission pipeline when the fluid speed in the aviation flow transmission pipeline exceeds the critical flow rate.
In an exemplary embodiment of the disclosure, the parameter resonance response characteristic is a vibration amplitude of an aviation flow pipeline corresponding to different pulsation frequencies in a preset pulsation frequency range.
In an exemplary embodiment of the present disclosure, the method for predicting the resonance response characteristic of the three-dimensional fluid-solid coupling parameter of the aviation pipeline further includes:
and carrying out eigenvalue analysis on the dynamic matrix equation to obtain natural frequency.
In an exemplary embodiment of the present disclosure, the natural frequency includes:
the fluid velocity in the aviation flow conduit is below the critical flow rate and the natural frequency of the aviation flow conduit is above the critical flow rate.
In one exemplary embodiment of the present disclosure, the accuracy of the parametric resonance response characteristic is detected from the natural frequency.
According to one aspect of the present disclosure, there is provided a prediction apparatus for resonance response characteristics of three-dimensional fluid-solid coupling parameters of an aviation pipeline, including:
the model building module is used for building a three-dimensional fluid-solid coupling dynamics model of the aviation flow transmission pipeline;
the equation building module is used for building a three-dimensional fluid-solid coupling dynamic matrix equation of the aviation pipeline according to the dynamic model;
the equation conversion module is used for obtaining a finite-dimension matrix equation according to the dynamic matrix equation;
and the calculation module is used for obtaining the parameter resonance response characteristic of the aviation flow transmission pipeline according to the finite-dimensional matrix equation.
According to the technical scheme, the utility model has at least one of the following advantages and positive effects:
the utility model relates to a method for predicting resonance response characteristics of three-dimensional fluid-solid coupling parameters of an aviation pipeline, which comprises the steps of establishing a three-dimensional fluid-solid coupling dynamics model of the aviation flow transmission pipeline according to related parameters; establishing a three-dimensional fluid-solid coupling dynamic motion equation according to the dynamic model, further obtaining a finite-dimensional matrix equation, and obtaining the parameter resonance response characteristic of the aviation flow transmission pipeline in a preset pulsation frequency range through the finite-dimensional matrix equation; the parameter resonance response characteristic is obtained, the resonance interval can be effectively avoided, the occurrence of parameter resonance is prevented, and the service life and the safety of the aviation flow transmission pipeline are improved.
Drawings
The above and other features and advantages of the present utility model will become more apparent by describing in detail exemplary embodiments thereof with reference to the attached drawings.
FIG. 1 is a flow chart of a method for predicting the resonance response characteristics of three-dimensional fluid-solid coupling parameters of an aviation pipeline;
FIG. 2 is a schematic diagram of the relevant parameters;
FIG. 3 is a schematic diagram of a solution process for natural frequencies;
FIG. 4 is a classification chart of the parametric resonance response characteristics;
FIG. 5 is a schematic representation of a three-dimensional fluid-solid coupling dynamics model of an aviation flow conduit;
FIG. 6 is a schematic illustration of natural frequencies before and after buckling in an aircraft flow duct plane;
FIG. 7 is a schematic illustration of natural frequencies before and after out-of-plane buckling of an air flow pipeline;
FIG. 8 is a graph of the amplitude versus frequency response before buckling;
FIGS. 9-19 are cloud diagrams of time-space responses;
fig. 20 to 28 show the pulsation frequency ω p Response plot of =15;
fig. 29 to 36 show the pulsation frequency ω p Response plot of =45;
fig. 37 to 41 show the pulsation frequency ω p Motion trace plot=45;
fig. 42 to 46 show the pulsation frequency ω p Motion trace plot=400;
FIG. 47 is a graph of amplitude versus frequency response after buckling;
fig. 48 to 56 show the pulsation frequency ω p Response plot of=14;
fig. 57 to 65 show the pulsation frequency ω p Response of =395.
Detailed Description
Example embodiments will now be described more fully with reference to the accompanying drawings. However, the exemplary embodiments can be embodied in many forms and should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the concept of the example embodiments to those skilled in the art. The same reference numerals in the drawings denote the same or similar structures, and thus detailed descriptions thereof will be omitted.
The utility model firstly provides a method for predicting resonance response characteristics of three-dimensional fluid-solid coupling parameters of an aviation pipeline. Referring to fig. 1, the method for predicting the resonance response characteristics of the three-dimensional fluid-solid coupling parameters of the aviation pipeline may include the following steps:
step S110, a three-dimensional fluid-solid coupling dynamics model of the aviation flow transmission pipeline is established according to relevant parameters;
step S120, a three-dimensional fluid-solid coupling dynamic motion equation of the aviation fluid transmission pipeline is established according to the dynamic model;
step S130, obtaining a finite-dimension matrix equation according to the dynamic motion equation;
and step S140, obtaining the parameter resonance response characteristic of the aviation flow transmission pipeline in a preset pulsation frequency range according to the finite-dimension matrix equation.
The above steps are described in detail below.
In step S110, a three-dimensional fluid-solid coupling dynamics model of the aviation flow pipeline is established according to the relevant parameters.
In step S120, a three-dimensional fluid-solid coupling kinetic motion equation of the aviation fluid transport pipeline is established according to the kinetic model.
Referring to FIG. 2, the relevant parameters may include geometric parameters, physical parameters, and operating condition parameters the geometric parameters may include an inner diameter, an outer diameter, and an overall length of the flow conduit; physical parameters may include modulus of elasticity and density of the flow conduit; the operating parameters may include average flow rate, pulsation amplitude and pulsation frequency of the fluid in the fluid delivery line.
The length of the pipeline is L, and the mass per unit length is m p Young's modulus E, section moment of inertia I, and pipe cross-sectional area A p The mass per unit length of the fluid is m f The fluid velocity is U. The equilibrium state of the pipeline is along the x-axis, and the pipeline is assumed to be an Euler beam model, and two mutually perpendicular displacements of the y-o-z plane are respectively W (x, t) and V (x, t).
In the present example embodiment, the following assumptions are followed: the diameter of the pipeline is very small relative to the length of the pipeline, the application condition of the Euler beam model is met, and the shearing deformation and the moment of inertia of the pipeline are ignored; the fluid is non-stick and incompressible; gravity effects are ignored; irrespective of the external axial forces of the pipe and the fluid pressure.
The conduit is considered for its viscoelastic damping effect, and the viscoelastic damping coefficient of the conduit is E. The axial force in the pipe is
Where epsilon is the axial strain of the pipe,is the first derivative of axial strain with respect to time. Considering the effect of geometrical nonlinearity, the axial strain of the pipe can be expressed as
Substituting the expression (2) into the expression (1) to obtain the axial force is expressed as
And (3) carrying the motion equation (3) into a classical motion equation of the flow transmission pipeline to obtain a nonlinear three-dimensional motion equation of the flow transmission pipeline:
the fluid flow rate in the system is a pulsating flow rate
U＝U 0 (1+μcos(Ω p t)) (6)
Referring to fig. 3, the following dimensionless parameters are introduced for convenience:
ζ represents a space coordinate, w and v represent non-dimensionality positions, τ represents non-dimensionality time, u represents a non-dimensionality flow rate, β represents a mass ratio, ω represents a non-dimensionality frequency, α represents a non-dimensionality damping coefficient, and S represents a quantification of a pipeline length and a group system, and the non-dimensionality parameters are constant values at a certain time of the pipeline.
Substituting the dimensionless parameters into formulas (16) and (17) to obtain a dimensionless motion equation:
the boundary conditions of the two ends of the simple support are
Where η may comprise w and v as displacement parameters.
In step S130, a finite-dimensional matrix equation is obtained from the kinetic motion equation.
In step S140, the parameter resonance response characteristic of the aviation flow transmission pipeline in the preset pulsation frequency range is obtained according to the finite-dimension matrix equation.
Referring to fig. 3, the method for predicting the resonance response characteristics of the three-dimensional fluid-solid coupling parameters of the aviation pipeline according to the present utility model may further include performing eigenvalue analysis on the dynamic matrix equation to obtain a natural frequency of the aviation pipeline when the fluid velocity in the aviation pipeline is lower than the critical flow velocity and a natural frequency of the aviation pipeline when the fluid velocity in the aviation pipeline exceeds the critical flow velocity.
Referring to fig. 4, obtaining the parameter resonance response characteristic of the aviation flow transmission pipeline in the preset pulsation frequency range according to the finite-dimensional matrix equation may include obtaining a three-dimensional fluid-solid coupling parameter resonance response characteristic of the aviation flow transmission pipeline when the fluid velocity in the aviation flow transmission pipeline is lower than the critical flow velocity and obtaining a three-dimensional fluid-solid coupling parameter resonance response characteristic of the aviation flow transmission pipeline when the fluid velocity in the aviation flow transmission pipeline exceeds the critical flow velocity.
According to the dynamic matrix equation, a Galerkin method is adopted to obtain a finite-dimension matrix equation, equations (16) and (17) describe a three-dimensional motion model of a flow transmission pipeline system, the Garerkin method is used for discretizing the model, and two transverse displacements of a pipeline can be set as solutions
Wherein w is r (τ) and v r (τ) is the generalized coordinates of the discrete system, N is the Garierkn cutoff number, φ r (ζ) is a mode function of bending vibration of the simply supported beam model at two ends
Substituting (19), (20) and (21) into (16), (17), and obtaining a second-order nonlinear simplified model by using a Garierkn method
Wherein the method comprises the steps of
Second derivative of generalized coordinates to dimensionless time coordinates, +.>First derivative of generalized coordinates to dimensionless time coordinates, w j (τ)、v j (τ) is the generalized coordinates.
In the present exemplary embodiment, the Garlerkin truncation number takes 6, and the generalized coordinates may be set in the form of the following vectors
w＝[w 1 w 2 w 3 w 4 w 5 w 6 ] T (28)
v＝[v 1 v 2 v 3 v 4 v 5 v 6 ] T (29)
Equations (22), (23) can be written as matrix equations
The equation is finished to obtain
Introducing a state variable u 1 ，u 2 ，u 3 ，u 4 ，
Substituting (34) into (32), (33)
Fourth order Long Geku tower iterative format:
h is the iteration step length, T 0 Is the starting point of iteration and therefore has
t 1 First derivative of state variable at time
t 2 State variable of time of day
t 2 First derivative of state variable at time
t 3 State variable of time of day
t 3 First derivative of state variable at time
t 4 State variable of time of day
State variable after one iteration
Performing one million iterative operations to obtain stable u 2 、u 4 Thereby obtaining stable vibration amplitude of the aviation flow transmission pipeline, namely u 2 、u 4 Vector sum values.
The utility model is illustrated by a specific embodiment below:
in the present exemplary embodiment, the iteration step=0.0005 is taken, and the total number of iterations is 1000000.
In numerical calculation, a steel pipe is selected as an object, the Young modulus of the pipeline is E=210 GPa, and the density of the pipeline is ρ p ＝7850kg/m 3 The outer diameter of the pipeline is D o =12 mm, inner diameter D i Tube length l=1m =10mm, fluid density ρ f ＝870kg/m 3 。
To solve for the natural frequency of the pre-buckling (fluid flow rate less than critical flow rate) flow conduit, equations (16) and (17) can be simplified to
Referring to fig. 3, the method for predicting the resonance response characteristics of the three-dimensional fluid-solid coupling parameters of the aviation pipeline according to the present utility model may further include performing eigenvalue analysis on the dynamic matrix equation to obtain a natural frequency of the aviation pipeline when the fluid velocity in the aviation pipeline is lower than the critical flow velocity and a natural frequency of the aviation pipeline when the fluid velocity in the aviation pipeline exceeds the critical flow velocity. Equations (44) and (45) are processed according to the Galerkin method, and then eigenvalue analysis is performed to obtain a system where iteration step h=0.0005 is taken, and the total number of iterations is 1000000.
In numerical calculation, a steel pipe is selected as an object, the Young modulus of the pipeline is E=210 GPa, and the density of the pipeline is ρ p ＝7850kg/m 3 The outer diameter of the pipeline is D o =12 mm, inner diameter D i Tube length l=1m =10mm, fluid density ρ P ＝870kg/m 3 。
In order to solve the natural frequency of the fluid delivery pipeline before buckling, the geometric nonlinear term and the viscoelastic damping term are ignored, equations (44) and (45) are processed according to the Galerkin method, and then the natural frequency of the system is obtained through eigenvalue analysis.
When the fluid flow rate exceeds the critical flow rate (the first-order natural frequency is equal to zero), the flow transmission pipeline can generate buckling deformation, the system is not subjected to instability and damage due to the existence of geometric nonlinearity, but is balanced in a curved configuration state, only the first-order buckling is discussed, and the buckling displacement can be set as
Wherein the displacement amplitude in the y and z directions is a 1 、a 2 The displacement distribution function is a first order modal function
To solve for the buckling configuration of the post buckling (fluid flow rate less than the critical flow rate) flow conduit, the time-dependent terms in equations (16) and (17) are omitted to obtain the following equation:
substituting (46) and (47) into (48) and (49) to obtain
To solve for the natural frequency of the post-buckling flow conduit, the displacement of the flow conduit may be assumed to include a static portion and a dynamic portion
Wherein w is 0 (ξ)、v 0 (xi) represents the static part of the device,and->Representing the dynamic part.
Substituting equation (51) into equations (16) and (17) to obtain the linear vibration equation of the post-buckling flow conduit
The garlicin method discretizes equations (52) and (53), and then performs eigenvalue analysis to obtain the natural frequency of the buckled flow pipeline.
Referring to fig. 6 and 7, when the pipe is deformed by buckling, vibration of the pipe is in-plane and out-of-plane, and when the dimensionless flow velocity is zero, the natural frequency of the first third order dimensionless is omega n1 ＝9.87、ω n2 =39.48 and ω n3 =88.83. Table 1 gives the first 6 th order dimensionless for the case of dimensionless flow rates of u=2 and u=3.5Natural frequency.
Table 1: dimensionless natural frequency of fluid velocity u=2 and u=3.5
The fluid velocity being the pulsating velocity
u＝u 0 (1+μcos(ω p τ)) (54)
Wherein u is 0 Is the average flow rate, μ is the pulsation amplitude, ω p Is the pulsing frequency. The Dragon-Greek tower method solves the response of the flow transmission pipeline, and the initial condition is thatv(1)＝[0,-0.0001,0,0,0,0]' the damping coefficient is alpha 1 =0.0001, dimensionless fluid velocity u 0 Pulse amplitude is μ=0.2, =2.
Referring to FIG. 8, the pulsation frequency is 13<ω p <17(r 1-1 )，43<ω p <47(r 1-2 )，71<ω p <79(r 2-2 )，121<ω p <128(r 2-3 )，166<ω p <182(r 3-3 )，237<ω p <248(r 3-4 )，298<ω p <327(r 4-4 )，393<ω p <408(r 4-5 )，469<ω p <512(r 5-5 )，591<ω p <607(r 5-6 )，681<ω p <740(r 6-6 ) Parameter resonance occurs in the fluid delivery pipeline, and subharmonic resonance and combined resonance alternately occur as the pulsation frequency is continuously increased.
Referring to fig. 9 to 19, r 1-1 ，r 2-2 ，r 3-3 ，r 4-4 ，r 5-5 ，r 6-6 ，r 1-2 ，r 2-3 ，r 3-4 ，r 4-5 ，r 5-6 The subharmonic resonance and the combined resonance alternate, and it can be seen that the subharmonic resonance is only a single mode vibration, while the combined resonance is a superposition of successive two-order modes.
Response curve at amplitude-frequencySelecting frequency point omega on line p =15, the response at a total distance of 3/10 from the end was recorded.
Reference pulse frequency omega p Response of =15: fig. 20 and 21 are steady state responses, fig. 22 and 23 are fourier transforms of the responses, fig. 24 and 25 are phase diagrams and poincare cross sections, fig. 26 is a motion trajectory, and fig. 27 and 28 are two lateral snap maps.
Referring to fig. 20 to 28, the pulsation frequency is ω p At=15, the first-order modal periodic vibration of the system is excited, and the motion trajectory is on a plane, and the inclination angle of the plane is related to the initial condition.
The above snapshot of the lateral motion of harmonic resonance shows that there is a phase difference in the response of the flow conduit at each point in the axial direction, i.e. the vibration of the conduit is not a standard standing wave vibration, where the vibration also includes a small amount of traveling wave components.
Referring to fig. 29 to 41, a frequency point ω is selected on the amplitude-frequency response curve p =45 and ω p =400, the response at a total distance of 3/10 from the end was recorded.
The pulsation frequency is omega p Response of=45: fig. 29 and 30 are steady state responses, fig. 31 and 32 are fourier transforms of the responses, fig. 33 and 34 are phase diagrams and poincare cross sections, and fig. 35 and 36 are two transverse direction snap maps.
The pulsation frequency is omega p Motion trace plot=45: in fig. 37, ζ=1/10, in fig. 38, ζ=3/10, in fig. 9, ζ=5/10, in fig. 40, ζ=7/10, in fig. 41, ζ=9/10.
The pulsation frequency is omega p When=45, the first-order and second-order modal vibrations of the system are excited, and the pulsation frequency is approximately equal to the sum ω of the response frequencies p ≈ω 1 +ω 2 Approximately equal to 8.795+36.44, the response frequency is approximately equal to the first and second order natural frequencies ω n1 =7.55 and ω n) = 37.51. The two lateral direction motion snapshots show that the pipe motion is interconverted between a first order mode shape and a second order mode shape.
The motion trail is in a space shape, the motion trail at each position is provided with 5 sharp points,this is related to the response frequency, the ratio of which is ω 1 /ω ) =0.241, approximately equal to 1/4, the number of points being equal to the sum of the numerator and denominator of the ratio.
Referring to fig. 42 to 46, the pulsation frequency is ω p Motion trace plot of=400: in fig. 42, ζ=1/10, in fig. 43, ζ=3/10, in fig. 44, ζ=5/10, in fig. 45, ζ=7/10, in fig. 46, ζ=9/10.
The pulsation frequency is omega p When=400, fourth-order and fifth-order modal vibrations of the system are excited, and the pulsation frequency is approximately equal to the sum ω of the response frequencies p ≈ω 4 +ω 5 Approximately 158.3+242.5, the response frequency is approximately equal to the fourth and fifth natural frequencies ω n4 = 156.06 and ω n5 ＝244.91。
The motion trail is of a space shape, the motion trail at each position is provided with 5 sharp points, the motion trail is related to the response frequency, and the ratio of the response frequency is omega 4 /ω 5 =0.653, approximately equal to 2/3, the number of points being equal to the sum of the numerator and denominator of the ratio.
The parameter resonance response characteristics of the fluid delivery pipeline after buckling are studied, and the dimensionless fluid speed is u 0 Pulse amplitude μ=0.2, =3.5.
Referring to FIG. 47, the fluid flow rate is u 0 =3.5 exceeding critical flow rate m, theoretical first-order buckling amplitude isThe magnitude of the numerically solved buckling was 0.004, both very close.
The phenomenon of self-locking of the response of the flow transmission pipeline after buckling can be observed, and subharmonic resonance or combined resonance of the flow transmission pipeline can occur in a specific frequency range. There is a similar "quenching" phenomenon in the parametric resonance frequency region above the critical flow rate, i.e., the jump parameter resonance response, which responds at the boundary of resonance and non-resonance, suddenly drops below the buckling amplitude.
The pulsation frequency is omega p Response of=14: FIGS. 48 and 49 steady state responses, FIGS. 50 and 51 are Fourier transforms of the responses, FIGS. 52 and 49Fig. 53 is a phase diagram and poincare section, fig. 54 is a motion trajectory, and fig. 55 and 56 are two lateral direction snap views.
Referring to fig. 48 to 56, the pulsation frequency is ω p At=14, the first-order modal periodic vibration of the system is excited, and the motion trajectory is in one plane, and the inclination angle of the motion plane is related to the initial condition.
The pulsation frequency is omega p Response of =395: fig. 57 and 58 are steady state responses, fig. 59 and 60 are fourier transforms of the responses, fig. 61 and 62 are phase diagrams and poincare cross sections, fig. 63 is a motion trajectory, and fig. 64 and 65 are two lateral direction snap maps.
Referring to fig. 57 to 65, the pulsation frequency is ω p When =395, the fourth and fifth order modal vibrations of the system are excited, the pulsation frequency is approximately equal to the sum ω of the response frequencies p ≈ω 4 +ω 5 Approximately 158.3+236.2, the response frequency is approximately equal to the fourth and fifth natural frequencies ω n4 =153 and ω n5 =242. The two lateral direction motion snapshots show that the pipe motion is interconverted between the fourth order mode and the fifth order mode. The motion trail is a spatial configuration, the motion trail at each position is provided with 5 sharp points, the motion trail is related to the response frequency, and the ratio of the response frequency is omega 4 /ω 5 =0.67, approximately equal to 2/3, and the number of points is equal to the sum of the numerator and denominator of the ratio.
The utility model further provides a device for predicting the resonance response characteristics of the three-dimensional fluid-solid coupling parameters of the aviation pipeline, which can comprise a following module
The model building module is used for building a three-dimensional fluid-solid coupling dynamics model of the aviation flow transmission pipeline;
the equation building module is used for building a three-dimensional fluid-solid coupling dynamic matrix equation of the aviation pipeline according to the dynamic model;
the equation conversion module is used for obtaining a finite-dimension matrix equation according to the dynamic matrix equation;
the calculation module is used for obtaining the parameter resonance response characteristic of the aviation flow transmission pipeline according to the finite-dimensional matrix equation
The above described features, structures or characteristics may be combined in any suitable manner in one or more embodiments, such as the possible, interchangeable features as discussed in connection with the various embodiments. In the above description, numerous specific details are provided to give a thorough understanding of embodiments of the utility model. One skilled in the relevant art will recognize, however, that the inventive aspects may be practiced without one or more of the specific details, or with other methods, components, materials, and so forth. In other instances, well-known structures, materials, or operations are not shown or described in detail to avoid obscuring aspects of the utility model.
The terms "about" and "approximately" are used in this specification to generally mean within 20%, preferably within 10%, and more preferably within 5% of a given value or range. The numbers given herein are about numbers, meaning that the meaning of "about," "approximately" may still be implied without specific recitation.
Although relative terms such as "upper" and "lower" are used in this specification to describe the relative relationship of one component of an icon to another component, these terms are used in this specification for convenience only, such as in terms of the orientation of the examples described in the figures. It will be appreciated that if the device of the icon is flipped upside down, the recited "up" component will become the "down" component. Other relative terms such as "high," "low," "top," "bottom," "front," "back," "left," "right," etc. are also intended to have similar meanings. When a structure is "on" another structure, it may mean that the structure is integrally formed with the other structure, or that the structure is "directly" disposed on the other structure, or that the structure is "indirectly" disposed on the other structure through another structure.
In the present specification, the terms "a," "an," "the," "said" and "at least one" are used to indicate the presence of one or more elements/components/etc.; the terms "comprising," "including," and "having" are intended to be inclusive and mean that there may be additional elements/components/etc., in addition to the listed elements/components/etc.; the terms "first," "second," and "third," etc. are used merely as labels, and do not limit the number of their objects.
It should be understood that the utility model is not limited in its application to the details of construction and the arrangement of components set forth in the specification. The utility model is capable of other embodiments and of being practiced and carried out in various ways. The foregoing variations and modifications are intended to fall within the scope of the present utility model. It should be understood that the utility model disclosed and defined in this specification extends to all alternative combinations of two or more of the individual features mentioned or evident from the text and/or drawings. All of these different combinations constitute various alternative aspects of the present utility model. The embodiments described in this specification illustrate the best mode known for carrying out the utility model and will enable those skilled in the art to make and use the utility model.
Claims (5)
1. The method for predicting the resonance response characteristics of the three-dimensional fluid-solid coupling parameters of the aviation pipeline is characterized by comprising the following steps of:
establishing a three-dimensional fluid-solid coupling dynamics model of the aviation flow transmission pipeline according to the related parameters; wherein the relevant parameters include: geometric parameters including an inner diameter, an outer diameter, and an overall length of the flow conduit; physical parameters including modulus of elasticity and density of the flow conduit; the working condition parameters comprise the average flow velocity, the pulsation amplitude and the pulsation frequency of the fluid in the fluid conveying pipeline;
establishing a three-dimensional fluid-solid coupling dynamic motion equation of the aviation flow transmission pipeline according to the dynamic model; wherein, the three-dimensional fluid-solid coupling dynamic motion equation is:
wherein, xi is a space coordinate, w and v are non-dimensionalized positions, tau is non-dimensionalized time, u is non-dimensionalized flow velocity, beta is mass ratio, alpha is non-dimensionalized damping coefficient, S is a quantification of pipeline length and a group system;
obtaining a finite-dimension matrix equation by adopting a Galerkin method according to the dynamic motion equation;
calculating the parameter resonance response characteristic of the aviation flow transmission pipeline in a preset pulsation frequency range by adopting a Dragon library tower method according to the finite-dimension matrix equation; the parametric resonance response characteristics include: the three-dimensional fluid-solid coupling parameter resonance response characteristic of the aviation flow transmission pipeline when the fluid speed in the aviation flow transmission pipeline is lower than the critical flow speed and the three-dimensional fluid-solid coupling parameter resonance response characteristic of the aviation flow transmission pipeline when the fluid speed in the aviation flow transmission pipeline exceeds the critical flow speed; and the parameter resonance response characteristic is the vibration amplitude of the aviation flow transmission pipeline corresponding to different pulsation frequencies in a preset pulsation frequency range.
2. The method for predicting the resonance response characteristics of three-dimensional fluid-solid coupling parameters of an aviation pipeline according to claim 1, wherein the method for predicting the resonance response characteristics of three-dimensional fluid-solid coupling parameters of an aviation pipeline further comprises:
and carrying out eigenvalue analysis on the dynamic motion equation to obtain the natural frequency.
3. The method for predicting the resonance response characteristics of three-dimensional fluid-solid coupling parameters of an aviation pipeline according to claim 2, wherein the natural frequencies comprise:
the fluid velocity in the aviation flow conduit is below the critical flow rate and the natural frequency of the aviation flow conduit is above the critical flow rate.
4. The method for predicting the resonance response characteristics of three-dimensional fluid-solid coupling parameters of an aviation pipeline according to claim 3, wherein the accuracy of the resonance response characteristics of the parameters is detected according to the natural frequency.
5. The device for predicting the resonance response characteristics of the three-dimensional fluid-solid coupling parameters of the aviation pipeline is characterized by comprising the following components:
the model building module is used for building a three-dimensional fluid-solid coupling dynamics model of the aviation flow transmission pipeline according to the related parameters; wherein the relevant parameters include: geometric parameters including an inner diameter, an outer diameter, and an overall length of the flow conduit; physical parameters including modulus of elasticity and density of the flow conduit; the working condition parameters comprise the average flow velocity, the pulsation amplitude and the pulsation frequency of the fluid in the fluid conveying pipeline;
the equation building module is used for building a three-dimensional fluid-solid coupling dynamic motion equation of the aviation fluid transmission pipeline according to the dynamic model; wherein, the three-dimensional fluid-solid coupling dynamic motion equation is:
wherein, xi is a space coordinate, w and v are non-dimensionalized positions, tau is non-dimensionalized time, u is non-dimensionalized flow velocity, beta is mass ratio, alpha is non-dimensionalized damping coefficient, S is a quantification of pipeline length and a group system;
the equation conversion module is used for obtaining a finite-dimension matrix equation by adopting a Galerkin method according to the dynamic motion equation;
the calculation module is used for calculating the parameter resonance response characteristic of the aviation flow transmission pipeline in a preset pulsation frequency range by adopting a Dragon library tower method according to the finite-dimension matrix equation; the parametric resonance response characteristics include: the three-dimensional fluid-solid coupling parameter resonance response characteristic of the aviation flow transmission pipeline when the fluid speed in the aviation flow transmission pipeline is lower than the critical flow speed and the three-dimensional fluid-solid coupling parameter resonance response characteristic of the aviation flow transmission pipeline when the fluid speed in the aviation flow transmission pipeline exceeds the critical flow speed; and the parameter resonance response characteristic is the vibration amplitude of the aviation flow transmission pipeline corresponding to different pulsation frequencies in a preset pulsation frequency range.
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| CN111967204B (en) * | 2020-08-12 | 2022-07-15 | 西北工业大学 | Anti-resonance reliability and sensitivity analysis method for flow transmission pipeline |
| CN112100892B (en) * | 2020-09-18 | 2023-08-18 | 哈尔滨工业大学（威海） | Method for predicting natural frequency of in-band flow flexible pipeline under different boundary conditions |
| CN114459714A (en) * | 2022-02-17 | 2022-05-10 | 中国核电工程有限公司 | Method capable of reducing pipeline flow-induced vibration, pipeline and verification device |
| 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 |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105205258A (en) * | 2015-09-22 | 2015-12-30 | 中国核动力研究设计院 | Method for analyzing vortex shedding induced vibration of heat exchanger heat transfer pipe |
| CN107063295A (en) * | 2016-10-26 | 2017-08-18 | 中国矿业大学(北京) | A kind of method for analyzing stability of resonant mode gyro |
| CN107688703A (en) * | 2017-08-25 | 2018-02-13 | 西北工业大学 | The length ratio design method of the soft or hard pipeline that connects |
| CN108763628A (en) * | 2018-04-13 | 2018-11-06 | 西北工业大学 | The design method and device of multispan functionally gradient fluid conveying pipe |
| CN109063305A (en) * | 2018-07-25 | 2018-12-21 | 中南大学 | Defeated stream straight pipeline Vibration Absorption Designing method under random vibration environment |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| DE102008059920B4 (en) * | 2008-12-02 | 2016-07-14 | Krohne Meßtechnik GmbH & Co KG | Method for operating a resonance measuring system and related resonance measuring system |
-
2019
- 2019-01-02 CN CN201910001794.6A patent/CN109635500B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105205258A (en) * | 2015-09-22 | 2015-12-30 | 中国核动力研究设计院 | Method for analyzing vortex shedding induced vibration of heat exchanger heat transfer pipe |
| CN107063295A (en) * | 2016-10-26 | 2017-08-18 | 中国矿业大学(北京) | A kind of method for analyzing stability of resonant mode gyro |
| CN107688703A (en) * | 2017-08-25 | 2018-02-13 | 西北工业大学 | The length ratio design method of the soft or hard pipeline that connects |
| CN108763628A (en) * | 2018-04-13 | 2018-11-06 | 西北工业大学 | The design method and device of multispan functionally gradient fluid conveying pipe |
| CN109063305A (en) * | 2018-07-25 | 2018-12-21 | 中南大学 | Defeated stream straight pipeline Vibration Absorption Designing method under random vibration environment |
Non-Patent Citations (3)
| Title |
|---|
| Nonlinear vibration of slightly curved pipe with conveying pulsating fluid;Yun-dong Li 等;《Nonlinear Dynamics》;20170223;第88卷;第2513-2529页 * |
| Three-dimensional dynamics of supported pipes conveying fluid;L. Wang 等;《Acta Mechanica Sinica》;20171019;第33卷(第6期);第1065-1074页 * |
| 分布式运动约束下悬臂输液管的参数共振研究;王乙坤 等;《http://kns.cnki.net/kcms/detail/11.2062.O3.20181128.1639.004.html》;20181128;第1-12页 * |
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