CN115600342B - Damper system model construction method, damper system solving method and device - Google Patents
Damper system model construction method, damper system solving method and device Download PDFInfo
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Abstract
The application provides a damper system model construction method, a damper system solving method and a damper system solving device, wherein a transfer function of a target damper system is firstly obtained; then, a dynamic equation of the transfer function is established by utilizing the transfer function of the target damper system; then determining the spring coefficient of the spring in the dynamic equation as a state variable, and constructing a state equation according to the state variable; then constructing a linear time-invariant model of the target system according to the state equation; setting the coefficient value of the state variable as the coefficient value which changes along with the input of external force; and finally, converting the linear time-invariant model into a damper system model by utilizing the variable state variable coefficient value. According to the method, the damper system model is built by using the transfer function, and the coefficient value of the variable state variable is set, so that the linear time-invariant system model is converted into the damper system model by using the transfer function, and the building difficulty of the damper system model is effectively reduced.
Description
Technical Field
The present disclosure relates to the field of model construction technologies, and in particular, to a method for constructing a damper system model, a method and an apparatus for solving a damper system.
Background
A mass-spring-damper system is a relatively common mechanical vibration system, and the mass-spring-damper system can be regarded as a damper system with an input of a changing external force and an output of an object displacement corresponding to the external force, and research on the system is of great significance to our life and technology. For example, an automobile buffer is a device capable of consuming movement energy, and is a necessary device for ensuring driving safety of a driver. A damper system is introduced in the building earthquake-resistant reinforcement measures, so that the self-vibration characteristics of the structure are changed, the damping of the structure is increased, the earthquake energy is absorbed, and the influence of the earthquake effect on the building is reduced.
Generally, the transfer function can only be used for modeling a linear time-invariant system, so for modeling and solving a damper system, in the prior art, a high-order Chang Weifen equation is usually established by selecting a proper state variable, a Gao Jiechang differential equation is utilized for establishing a damper system model and solving the damper system, but the process for establishing the high-order Chang Weifen equation is complicated, and the calculation amount of the solving process of the high-order Chang Weifen equation is large, so that the solving efficiency of the damper system is low.
Disclosure of Invention
Based on the method, the method and the device for constructing the damper system and solving the damper system are provided, and the difficulty of modeling the damper system is reduced.
In a first aspect, an embodiment of the present application provides a method for constructing a damper system model, where the method includes:
acquiring a transfer function of a target damper system, wherein the target damper system comprises a spring, a mass block and a damping block;
establishing a dynamic equation of the transfer function by utilizing the transfer function of the target damper system;
determining the displacement of the mass block in the dynamic equation as a state variable, and constructing a first state equation according to the state variable;
constructing a linear time-invariant model of the target damper system according to the first state equation, wherein the linear time-invariant model refers to a model with a state variable coefficient value of a fixed value in the first state equation;
replacing the fixed coefficient value of the state variable of the first state equation with the coefficient value of the elastic coefficient of the spring, which changes along with time, to obtain a second state equation;
and converting the linear time-invariant model into a damper system model by taking the second state equation as a constraint condition.
Optionally, using a transfer function of the target damper system, establishing a dynamic equation of the transfer function includes:
converting a transfer function of the target damper system into a form of a sum of a constant and a true partial formula, wherein the true partial formula refers to a partial formula with a denominator order greater than a molecular order;
decomposing the true partial formula and introducing an intermediate variable, and converting the transfer function into a differential equation set form, wherein the intermediate variable is the ratio of an external force input expression to a characteristic polynomial of the target damper system;
a dynamic equation of the transfer function is constructed by setting at least one variable in the differential equation set as a state variable.
Optionally, using the second state equation as a constraint condition, converting the linear time-invariant model into the damper system model includes:
filling coefficient values of the spring force coefficients of the springs in the second state equation, which change along with time, into a coefficient matrix;
constructing a third state equation by using the product of the coefficient matrix and the variable;
and converting the linear time-invariant model into a damper system model by using the third state equation as a constraint condition.
In a second aspect, embodiments of the present application provide a method for solving a damper system, the method including:
obtaining a damper system model, wherein the damper system model is constructed by the method of any one of the preceding first aspects;
acquiring a second state equation contained in the damper system model;
acquiring an initial value of a spring force coefficient in the second state equation and a coefficient value of the spring force coefficient changing along with time;
and solving the second state equation to obtain a displacement curve of the mass block which changes along with time.
Optionally, solving the second state equation to obtain a displacement curve of the mass block that changes with time includes:
and solving the second state equation by using a fourth-order Dragon-Gregory tower method to obtain a displacement curve of the mass block which changes along with time.
In a third aspect, an embodiment of the present application provides a damper system model construction apparatus, including:
the transfer function acquisition module is used for acquiring a transfer function of a target damper system, wherein the target damper system comprises a spring, a mass block and a damping block;
a first construction module for establishing a dynamic equation of a transfer function of the target damper system using the transfer function;
the second construction module is used for determining the displacement of the mass block in the dynamic equation as a state variable and constructing a first state equation according to the state variable;
the first model construction module is used for constructing a linear time-invariant model of the target damper system according to the first state equation, wherein the linear time-invariant model refers to a model with a state variable coefficient value of a fixed value in the first state equation;
the third construction module is used for replacing the fixed coefficient value of the state variable of the first state equation with the coefficient value of the spring coefficient changing along with time to obtain a second state equation;
and the second model construction module is used for converting the linear time-invariant model into a damper system model by taking the second state equation as a constraint condition.
In a fourth aspect, embodiments of the present application provide a damper system solver, the device comprising:
the model acquisition module is used for acquiring a damper system model;
the state equation acquisition module is used for acquiring a second state equation contained in the damper system model;
the numerical value acquisition module is used for acquiring an initial value of the spring elastic coefficient in the second state equation and a coefficient value of the spring elastic coefficient changing along with time;
and the equation solving module is used for solving the second state equation to obtain a displacement curve of the mass block, which changes along with time.
In a fifth aspect, embodiments of the present application provide an apparatus, where the apparatus includes a memory and a processor, where the memory is configured to store instructions or codes, and the processor is configured to execute the instructions or codes, so that the apparatus performs the damper system model construction method or the damper system solving method according to any one of the foregoing first aspect and the second aspect.
In a sixth aspect, embodiments of the present application provide a computer storage medium having code stored therein, where when the code is executed, an apparatus that executes the code implements the damper system model construction method or the damper system solving method of any one of the foregoing first and second aspects.
Compared with the prior art, the method provided by the application has the following beneficial effects:
firstly, acquiring a transfer function of a target damper system, wherein the target damper system comprises a spring, a mass block and a damping block; then, a dynamic equation of the transfer function is established by utilizing the transfer function of the target damper system; then determining the spring coefficient of the spring in the dynamic equation as a state variable, and constructing a state equation according to the state variable; then constructing a linear time-invariant model of the target system according to the state equation; setting the coefficient value of the state variable as the coefficient value which changes along with the input of external force; and finally, converting the linear time-invariant model into a damper system model by utilizing the variable state variable coefficient value.
According to the method, the damper system model is built by using the transfer function, and the coefficient value of the variable state variable is set, so that the linear time-invariant system model is converted into the damper system model by using the transfer function, and the building difficulty of the damper system model is effectively reduced.
Drawings
In order to more clearly illustrate the present embodiments or the technical solutions in the prior art, the drawings that are required for the embodiments or the description of the prior art will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present application, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a method flow chart of a method for constructing a damper system model according to an embodiment of the present disclosure;
FIG. 2 is a schematic diagram of a damper system according to an embodiment of the present disclosure;
FIG. 3 is a schematic diagram of a model of a damper system constructed using a transfer function method according to an embodiment of the present application;
FIG. 4 is a schematic diagram of a damper system model constructed using the higher order differential equation method provided by embodiments of the present application;
FIG. 5 is a method flow chart of a method for solving a damper system according to an embodiment of the present disclosure;
FIG. 6 is a graph of mass displacement obtained by solving a damper system model constructed using a transfer function method according to an embodiment of the present application;
FIG. 7 is a graph of mass displacement obtained by solving a damper system model constructed using a higher order differential equation method according to an embodiment of the present application;
FIG. 8 is a schematic structural diagram of a device for constructing a damper system model according to an embodiment of the present disclosure;
fig. 9 is a schematic structural diagram of a solution device for a damper system according to an embodiment of the present application.
Detailed Description
Generally, transfer functions can only be used for modeling of linear time-invariant systems, so for modeling and solving of damper systems, the prior art generally builds a higher-order Chang Weifen equation by selecting appropriate state variables, constrains the damper system model with Gao Jiechang differential equations, and describes the damper system operation by solving the higher-order differential equations.
However, the process of establishing the high-order Chang Weifen equation is complicated, and when the multi-differential process in the high-order differential equation is difficult to establish and the number of variables is large, the calculation amount of the Gao Jiechang differential equation solving process is large, so that the solving efficiency of the damper system is low.
Based on this, the embodiment of the present application first obtains a transfer function of a target damper system, where the target damper system includes a spring, a mass, and a damping mass; then, a dynamic equation of the transfer function is established by utilizing the transfer function of the target damper system; then, the spring coefficient of the spring in the dynamic equation is determined as a state variable, and the state equation is constructed according to the state variable; then constructing a linear time-invariant model of the target system according to the state equation; setting the coefficient value of the state variable as the coefficient value which changes along with the input of external force; and finally, converting the linear time-invariant model into a damper system model through the set variable state variable coefficient value.
According to the method, the damper system model is built by using the transfer function, and the coefficient value of the variable state variable is set, so that the linear time-invariant system model is converted into the damper system model by using the transfer function, and the building difficulty of the damper system model is effectively reduced.
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present application, but not all embodiments. All other embodiments, which can be made by one of ordinary skill in the art without undue burden from the present disclosure, are within the scope of the present disclosure.
Referring to fig. 1, fig. 1 is a flowchart of a method for constructing a damper system model according to an embodiment of the present application, including:
s101: a transfer function of the target damper system is obtained.
Referring now to FIG. 2, FIG. 2 is a schematic illustration of a target damper system including springs, masses, and damping masses.
Transfer function refers to the ratio of the laplace transform (or z-transform) of the response (i.e., output) quantity to the laplace transform of the excitation (i.e., input) quantity of the linear system at zero initial conditions. Let G(s) =y (s)/U(s), where Y(s), U(s) are laplace transforms of the output and input quantities, respectively.
The Laplace transform refers to a method for converting a time domain equation into a frequency domain equation, and the variable value is converted from a real number to a complex number for calculation, so that the time domain problem solving can be simplified, and the specific method is as follows:
let the real function f (t), if:
when t < 0, f (t) =0;
when t is greater than or equal to 0, the integral of the real function f (t)
Converging within a certain domain of s.
The laplace transform defining f (t) is then
And is denoted as F(s) =l [ F (t)]Where s is a complex number, the above formula realizes the conversion from the time domain variable t to the frequency domain complex variable s, and thus converts the time domain problem into the frequency domain problem.
For ease of understanding, specific processes will be described in the remainder of the specification.
S102: and establishing a dynamic equation of the transfer function by utilizing the transfer function of the target damper system.
Wherein the dynamic equation is an equation describing the dynamic change process of the system output according to the external stimulus (input) change.
In one possible implementation, using the transfer function of the target damper system, establishing a dynamic equation for the transfer function includes:
converting the transfer function of the target damper system into a form of a sum of a constant and a true partial formula;
decomposing true components and introducing intermediate variables, and converting a transfer function into a differential equation set;
the dynamic equation of the transfer function is obtained by setting at least one variable in the differential equation set as a state variable.
Wherein, the true partial formula refers to a partial formula with the denominator order being larger than the molecular order; the intermediate variable is the ratio of the external force input expression to the characteristic polynomial of the target damper system.
Since the order of the denominator in the transfer function must be greater than or equal to the order of the numerator, in order to establish a dynamic equation for the transfer function, it is necessary to take the transfer function as the sum of a constant and a true equation, assuming that the resulting system transfer function is as shown in equation (1):
where y(s) is the Laplace transform of the system output, where b 0 ，b 1 …b m-1 ，b m Is a polynomial coefficient, is a fixed constant, u(s) is the Laplacian transform of the system input, a 0 ，a 1 …a m-1 ，a m Is a polynomial coefficient, also a fixed constant, s is a variable.
Converting equation (1) into the sum of a constant and a true equation, such as equation (2):
wherein b 0 ，b 1 …b n-1 ，b n The coefficients of the polynomials are fixed constants, and the true partial formula is finally obtained and shown as a formula (3):
decomposing the true partial formula G(s) and introducing an intermediate variable Z(s), and converting the formula (3) into a form of a differential equation set, as shown in the formula (4):
in the equation, z and y are variables, a 0 ,a 1 ,.....,a n-1 、β 0 ,β 1 ,.....,β n-1 Is a coefficient of a variable in an equation, the value of which is a fixed constant. n is the order of the differential equation set,
representing the first derivative of z, z (n) Representing the nth derivative of z.
The relationship between the intermediate variable z(s) and the variable y(s) and other polynomials is shown in formula (5):
y(s)＝z(s)*N(s) (5)
s103: and determining the displacement of the mass block in the dynamic equation as a state variable, and constructing a first state equation according to the state variable.
The specific steps are expressed as follows:
selecting mass displacement as a state variable according to equation (5)
Finally, a first state equation shown in a formula (6) is obtained:
...
y＝β 0 x 1 +β 1 x 2 +...+β n-1 x n (6)
wherein,,
respectively x 1 ,x 2 ....x n Is a first derivative of (a). X is x 1 ,x 2 ....x n A is a state variable 0 ,a 1 ,.....,a n-1 、β 0 ,β 1 ,.....,β n-1 The coefficient of the variable in the equation has a fixed constant, u is the external input, and y is the output of the displacement of the mass.
S104: and constructing a linear time-invariant model of the target damper system according to the first state equation.
The linear time-invariant model refers to a model with a state variable coefficient value of a fixed value in the first state equation.
The construction of the linear time-invariant model of the target damper system from the first state equation essentially takes the first state equation as a model constraint from which the linear time-invariant model is constructed.
S105: and replacing the fixed coefficient value of the state variable of the first state equation with the coefficient value of the elastic coefficient of the spring changing along with time to obtain a second state equation.
In the above formula (6), each coefficient of variation is a fixed coefficient, and the function of this step is to change the fixed coefficient value into a variable and input it in the form of external input, thereby realizing a time-varying system.
S106: and converting the linear time-invariant model into a damper system model by taking the second state equation as a constraint condition.
The function of this step is to use the second state equation as a model constraint that is used to transform the linear time-invariant model into a damper system model.
In one possible implementation, converting the linear time-invariant model to the damper system model using the second state equation as a constraint includes:
filling coefficient values of the spring force coefficients of the springs in the second state equation, which change with time, into a coefficient matrix;
constructing a third state equation by using the product of the coefficient matrix and the state variable;
and converting the linear time-invariant model into a damper system model by using the third state equation as a constraint condition.
The formula of the specific implementation steps of the implementation mode is as follows:
filling coefficient values of the spring force coefficient of the spring in the second state equation, which change with time, into a coefficient matrix as shown in formula (7):
wherein a is 0 ,a 1 ,...a n-1 I.e. the coefficient value of the spring coefficient of the spring which varies with time.
A third state equation is constructed using the product of the coefficient matrix (7) and the state variable X, which is formed as equation (8):
where u refers to external force input, X refers to a column vector matrix composed of state variables, B refers to an enhancement coefficient column matrix composed of enhancement coefficients of external force input, and specific values are generally preset as needed.
The column vector matrix composed of state variables is shown in equation (9):
by using the third state equation shown in the formula (8) as a constraint condition, the linear time-invariant model can be converted into a damper system model, and the damper system model finally obtained by conversion is shown in fig. 3.
In order to compare with the existing method for constructing the damper system model by using the high-order differential equation method, the embodiment of the application also utilizes the high-order differential equation method to construct the damper system model shown in fig. 4, and the comparison of the model structures of fig. 3 and fig. 4 can show that the method for constructing the damper system model provided by the embodiment of the application uses fewer modules compared with the prior art, so that the modeling process is more concise and efficient; according to the embodiment of the application, the damper system model is built by using the transfer function, and the coefficient value of the variable state variable is set, so that the linear time-invariant system model is converted into the damper system model by using the transfer function, and the building difficulty of the damper system model is effectively reduced.
In the embodiment of the application, a solution method for a damper system is also provided, and is described below. It should be noted that the implementations presented in the following description are only exemplary and not representative of all implementations of the embodiments of the present application.
Referring to fig. 5, the method is a flow chart of a method for solving a damper system model, and specifically includes:
s501: a damper system model is obtained.
The damper system model is built through the method for building the damper system model.
S502: a second state equation contained in the damper system model is obtained.
The step is to acquire constraint equations in the model and lay a foundation for solving the subsequent state equations.
S503: and acquiring an initial value of the spring force coefficient in the state equation and a coefficient value of the spring force coefficient changing along with time.
In the damper system as shown in fig. 2, the transfer function is established as:
where s is the frequency domain state quantity characterizing the displacement of the mass.
Then its state equation can be established as:
wherein x is 1 For mass displacement, x 2 For the speed of the mass of the object,
is the derivative of the displacement of the mass, i.e. mass speed,/->
And y is the output of the displacement of the object block, which is the derivative of the speed of the object block, i.e. the acceleration of the object block.
For the damper system shown in FIG. 2, let its state variable initial value be x 1 ＝0.1；x 2 =0.2, the spring rate varies with time as:
k 2 ＝0.995k 1 (12)
wherein k is 1 Is the spring force coefficient, k of the spring at the first moment 2 Refers to the spring rate at a second instant, the first instant being continuous with the second instant.
S504: and solving the second state equation to obtain a displacement curve of the mass block which changes along with time.
This step is the solution to the second state equation, and the resulting displacement curve of the mass is time-dependent, i.e. the above-mentioned y-dependent change.
In one possible implementation, solving the second state equation to obtain a time-varying displacement curve of the mass includes:
and solving a second state equation by using a fourth-order Dragon-Gregory tower method to obtain a displacement curve of the mass block which changes with time.
The fourth-order Dragon-Gregory tower method is a differential equation solving method taking calculation time interval as consideration, is more common in the current differential equation solving process, is not repeated herein, and finally obtains a mass displacement curve as shown in fig. 6.
In order to compare with the existing method for constructing the damper system model by the higher-order differential equation method, the embodiment of the application further solves the damper system model constructed by the higher-order differential equation method as shown in fig. 4, the obtained object block displacement curve is shown in fig. 7, and as can be seen by comparing fig. 6 with fig. 7, the object block displacement curve finally output by the damper system model constructed by the embodiment of the application is consistent with the object block displacement curve finally output by the damper system model constructed by the existing higher-order differential equation method, which illustrates that the solving method provided by the embodiment of the application is consistent with the prior art in result, but the calculating method is simpler and more convenient.
The above is some specific implementation manners of the damper system model construction method and the damper system solving method provided in the embodiments of the present application, and based on this, the present application further provides a corresponding device. The apparatus provided in the embodiments of the present application will be described from the viewpoint of functional modularization.
Referring to a schematic structural view of a damper system model construction apparatus shown in fig. 8, the apparatus includes:
a transfer function obtaining module 801, configured to obtain a transfer function of a target damper system, where the target damper system includes a spring, a mass, and a damping block;
a first construction module 802 for establishing a dynamic equation of a transfer function of the target damper system using the transfer function;
a second construction module 803, configured to determine a displacement of the mass in the dynamic equation as a state variable, and construct a first state equation according to the state variable;
a first model building module 804, configured to build a linear time-invariant model of the target damper system according to the first state equation, where the linear time-invariant model refers to a model in which a state variable coefficient value in the first state equation is a constant value;
a third construction module 805, configured to replace a fixed coefficient value of a state variable of the first state equation with a coefficient value of a spring coefficient that changes with time, so as to obtain a second state equation;
a second model building module 806, configured to convert the linear time-invariant model into a damper system model using the second state equation as a constraint.
In one possible implementation, the first building block 802 includes:
a first conversion unit for converting a transfer function of the target damper system into a form of a sum of a constant and a true partial formula, wherein the true partial formula refers to a partial formula in which a denominator order is greater than a numerator order;
a second transformation unit for decomposing the true partial expression and introducing an intermediate variable, which is a ratio of an external force input expression to a characteristic polynomial of the target damper system, to transform the transfer function into a form of a differential equation set;
and the dynamic equation construction unit is used for setting at least one variable in the differential equation set as a state variable and constructing a dynamic equation of the transfer function.
In one possible implementation, the second model building module 806 includes:
a coefficient value filling unit for filling coefficient values of the spring force coefficients of the springs in the second state equation, which change with time, into a coefficient matrix;
the state equation construction unit is used for constructing a third state equation by using the product of the coefficient matrix and the variable;
and the model conversion unit is used for converting the linear time-invariant model into a damper system model by using the third state equation as a constraint condition.
According to the embodiment of the application, the damper system model is built by using the transfer function, and the coefficient value of the variable state variable is set, so that the linear time-invariant system model is converted into the damper system model by using the transfer function, and the building difficulty of the damper system model is effectively reduced.
Correspondingly, the embodiment of the application also provides a device for solving a damper system, referring to fig. 9, fig. 9 is a schematic structural diagram of the device for solving a damper system provided in the embodiment of the application, and the device specifically includes:
the model acquisition module 901 is used for acquiring a damper system model;
a state equation obtaining module 902, configured to obtain a second state equation included in the damper system model;
a value obtaining module 903, configured to obtain an initial value of the spring force coefficient in the second state equation and a coefficient value of the spring force coefficient that changes with time;
and an equation solving module 904, configured to solve the second state equation, so as to obtain a displacement curve of the mass block that changes with time.
In one possible implementation, the equation solving module 904 is specifically configured to:
and solving the second state equation by using a fourth-order Dragon-Gregory tower method to obtain a displacement curve of the mass block which changes along with time.
The embodiment of the application comprises the steps of firstly obtaining a damper system model; acquiring a second state equation contained in the damper system model; then, acquiring an initial value of the spring force coefficient and a coefficient value of the spring force coefficient changing along with time in a second state equation; finally, the second state equation is solved, the displacement curve of the mass block which changes along with time is obtained, the calculation process is simple and convenient, and the fourth-order Dragon-Grating-tower method is used for solving the second state equation, so that the calculation result is more accurate due to the consideration of the time interval of two times of calculation.
The embodiment of the application also provides corresponding equipment and a computer storage medium, which are used for realizing the scheme provided by the embodiment of the application.
The device comprises a memory and a processor, wherein the memory is used for storing instructions or codes, and the processor is used for executing the instructions or codes to enable the device to execute the damper system model building method or the damper system solving method according to any embodiment of the application.
The computer storage medium stores codes, and when the codes are executed, equipment for executing the codes realizes the damper system model construction method or the damper system solving method according to any embodiment of the application.
The "first" and "second" in the names of "first", "second" (where present) and the like in the embodiments of the present application are used for name identification only, and do not represent the first and second in sequence.
From the above description of embodiments, it will be apparent to those skilled in the art that all or part of the steps of the above described example methods may be implemented in software plus general hardware platforms. Based on such understanding, the technical solutions of the present application may be embodied in the form of a software product, which may be stored in a storage medium, such as a read-only memory (ROM)/RAM, a magnetic disk, an optical disk, or the like, including several instructions for causing a computer device (which may be a personal computer, a server, or a network communication device such as a router) to perform the methods described in the embodiments or some parts of the embodiments of the present application.
In this specification, each embodiment is described in a progressive manner, and identical and similar parts of each embodiment are all referred to each other, and each embodiment mainly describes differences from other embodiments. In particular, for the device embodiments, since they are substantially similar to the method embodiments, the description is relatively simple, and reference is made to the description of the method embodiments for relevant points. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of this embodiment. Those of ordinary skill in the art will understand and implement the present invention without undue burden.
The foregoing is merely exemplary embodiments of the present application and is not intended to limit the scope of the present application.
Claims (10)
1. A method of constructing a damper system model, the method comprising:
acquiring a transfer function of a target damper system, wherein the target damper system comprises a spring, a mass block and a damping block;
establishing a dynamic equation of the transfer function by utilizing the transfer function of the target damper system;
determining the displacement of the mass block in the dynamic equation as a state variable, and constructing a first state equation according to the state variable;
constructing a linear time-invariant model of the target damper system according to the first state equation, wherein the linear time-invariant model refers to a model with a state variable coefficient value of a fixed value in the first state equation;
replacing the fixed coefficient value of the state variable of the first state equation with the coefficient value of the elastic coefficient of the spring, which changes along with time, to obtain a second state equation;
and converting the linear time-invariant model into a damper system model by taking the second state equation as a constraint condition.
2. The method of claim 1, wherein the establishing a dynamic equation of the transfer function using the transfer function of the target damper system comprises:
converting a transfer function of the target damper system into a form of a sum of a constant and a true partial formula, wherein the true partial formula refers to a partial formula with a denominator order greater than a molecular order;
decomposing the true partial formula and introducing an intermediate variable, and converting the transfer function into a differential equation set form, wherein the intermediate variable is the ratio of an external force input expression to a characteristic polynomial of the target damper system;
a dynamic equation of the transfer function is constructed by setting at least one variable in the differential equation set as a state variable.
3. The method of claim 1, wherein said converting the linear time-invariant model into a damper system model using the second state equation as a constraint condition comprises:
filling coefficient values of the spring force coefficients of the springs in the second state equation, which change along with time, into a coefficient matrix;
constructing a third state equation by using the product of the coefficient matrix and the state variable;
and converting the linear time-invariant model into a damper system model by using the third state equation as a constraint condition.
4. A method of solving a damper system, the method comprising:
obtaining a damper system model, wherein the damper system model is constructed by the method of any one of claims 1-3;
acquiring a second state equation contained in the damper system model;
acquiring an initial value of a spring force coefficient in the second state equation and a coefficient value of the spring force coefficient changing along with time;
and solving the second state equation to obtain a displacement curve of the mass block which changes along with time.
5. The method of claim 4, wherein solving the second state equation to obtain a time-dependent displacement curve of the mass comprises:
and solving the second state equation by using a fourth-order Dragon-Gregory tower method to obtain a displacement curve of the mass block which changes along with time.
6. A damper system model construction apparatus, characterized by comprising:
the transfer function acquisition module is used for acquiring a transfer function of a target damper system, wherein the target damper system comprises a spring, a mass block and a damping block;
a first construction module for establishing a dynamic equation of a transfer function of the target damper system using the transfer function;
the second construction module is used for determining the displacement of the mass block in the dynamic equation as a state variable and constructing a first state equation according to the state variable;
the first model construction module is used for constructing a linear time-invariant model of the target damper system according to the first state equation, wherein the linear time-invariant model refers to a model with a state variable coefficient value of a fixed value in the first state equation;
the third construction module is used for replacing the fixed coefficient value of the state variable of the first state equation with the coefficient value of the spring coefficient changing along with time to obtain a second state equation;
and the second model construction module is used for converting the linear time-invariant model into a damper system model by taking the second state equation as a constraint condition.
7. A damper system solving apparatus, said apparatus comprising:
the model acquisition module is used for acquiring a damper system model; wherein the damper system model is constructed by the method of any one of claims 1-3;
the state equation acquisition module is used for acquiring a second state equation contained in the damper system model;
the numerical value acquisition module is used for acquiring an initial value of the spring elastic coefficient in the second state equation and a coefficient value of the spring elastic coefficient changing along with time;
and the equation solving module is used for solving the second state equation to obtain a displacement curve of the mass block, which changes along with time.
8. A damper system model building apparatus, characterized by comprising:
a memory for storing instructions or code for constructing a damper system model;
a processor for executing the instructions or code for constructing a damper system model to implement the method for constructing a damper system model of any one of claims 1-3.
9. A damper system solving apparatus, said apparatus comprising:
a memory for storing instructions or code for solving the damper system;
a processor for executing instructions or code for solving a damper system to implement a method for solving a damper system as claimed in any one of claims 4-5.
10. A computer storage medium, wherein code is stored in the computer storage medium, and when the code is executed, a device executing the code implements the method of constructing a model of a damper system according to any one of claims 1 to 3 or the method of solving a damper system according to any one of claims 4 to 5.
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