Segmented B-spline wavelet periodic response calculation method of collision vibration system

Abstract

The invention discloses a piecewise B-spline wavelet periodic response calculation method for a collision vibration system, which comprises the following steps: (1) establishing a dynamic equation for wavelet discretization, discretizing a dynamic control equation of a collision-vibration system by using a 4-order B-spline wavelet basis function, and establishing a nonlinear algebraic equation set about a wavelet coefficient; (2) carrying out segmented iterative solution on the time domain, dividing the whole time domain into a plurality of sub-time periods which are connected in sequence, and carrying out iterative solution on the nonlinear algebraic equation set in each sub-time period to obtain a global wavelet coefficient; and (3) establishing periodic response reconstruction and analysis, reconstructing displacement, speed and acceleration response of the system based on the wavelet coefficient, and judging periodic response characteristics through judgment conditions. The invention aims to provide a method for calculating the periodic response of a collision-vibration system directly, accurately and efficiently based on a segmented 4-order B-spline wavelet technology.

Description

Technical Field

[0001] This invention relates to the field of computational mechanics and nonlinear dynamics numerical analysis technology, and in particular to a method for calculating the periodic response of a piecewise B-spline wavelet system in a collision vibration system. It is especially suitable for calculating and analyzing the periodic response of an oscillator system containing discontinuous characteristics such as gaps and collisions. Background Technology

[0002] In engineering practice, clearance constraints are unavoidable due to manufacturing errors, assembly requirements, and wear during operation. For example, they are commonly found in mechanical transmission systems (gear meshing clearance), robot manipulators during contact and disengagement from their environment, bearing fault diagnosis, spacecraft extension and docking systems (where joint clearances cause transmission errors and induce internal collisions), aero-engine rotor-stator collision analysis, and oil and gas exploration impact drilling. Collision-vibration phenomena caused by clearances and constraints are prevalent in these fields. Collision vibration systems with clearances are generally multi-parameter, high-dimensional systems. These systems exhibit strong nonlinearity and discontinuity, which poses significant challenges to traditional structural vibration analysis and the practical application of its conclusions.

[0003] Currently, methods for analyzing the periodic response of collision-oscillator systems mainly rely on numerical integration techniques, such as the Runge-Kutta method and the target-shooting method. These methods have the following inherent limitations:

[0004] (1) Poor convergence: For strongly nonlinear systems, traditional numerical methods often fail to converge to an accurate periodic solution.

[0005] (2) Low computational efficiency: It requires a long transient simulation to obtain a steady-state periodic response, which consumes a lot of computational resources.

[0006] (3) Limited accuracy: Numerical errors accumulate and affect the accuracy of periodic response calculation.

[0007] (4) Difficulty in obtaining analytical results: Due to the complexity of dynamics, previous studies on multi-degree-of-freedom collision systems have mainly focused on qualitative or numerical aspects, making it difficult to obtain quantitative analytical results.

[0008] Therefore, there is an urgent need for a method based on piecewise 4th-order B-spline wavelet technology that can directly, accurately, and efficiently calculate the periodic response of collision-vibration systems. Summary of the Invention

[0009] The purpose of this invention is to overcome the shortcomings of the prior art and to provide a method for calculating the periodic response of a collision-vibration system directly, accurately, and efficiently based on piecewise 4th-order B-spline wavelet technology.

[0010] To achieve the above objectives, the present invention is implemented through the following technical solution:

[0011] A method for calculating the periodic response of a piecewise B-spline wavelet system in a collision vibration system, characterized by the following steps:

[0012] (1) Establish wavelet discretization of dynamic equations. Use the fourth-order B-spline wavelet basis function to discretize the dynamic control equations of the collision-oscillator system and establish a set of nonlinear algebraic equations about the wavelet coefficients.

[0013] (2) Solve the time domain piecewise iteratively, dividing the entire time domain into multiple sequentially connected sub-time periods, and iteratively solving the nonlinear algebraic equation system in each sub-time period to obtain the global wavelet coefficients;

[0014] (3) Establish periodic response reconstruction and analysis. Based on the wavelet coefficients, reconstruct the displacement, velocity and acceleration response of the system, and determine the periodic response characteristics through the judgment conditions.

[0015] Furthermore, in step (1), the velocity and acceleration terms of the system are expressed as a linear combination of fourth-order B-spline wavelet basis functions, and the expressions for displacement and velocity are obtained through a first integration. Finally, the differential equation is transformed into a system of nonlinear algebraic equations G with respect to the wavelet coefficients. n (a,b)=0, where the state-space form of the dynamic control equations of the collision-oscillator system is:

[0016] (1)

[0017] Where u(t) represents displacement and v(t) represents velocity. (t) represents the derivative of displacement with respect to time. , (t) represents the derivative of velocity with respect to time. F represents the acceleration term expression of the collision-vibration system. A 4th-order B-spline wavelet scaling function is used. With wavelet function Zhang Cheng approximates the solution in space, and the system's velocity term and acceleration term Represented as a linear combination of fourth-order B-spline wavelet basis functions:

[0018] (2)

[0019] in, and Let be the wavelet coefficient vector to be determined, W(t) be the wavelet basis function vector, and J be the maximum decomposition scale. The displacement is obtained by integrating the wavelet basis functions once. and speed The expression:

[0020] (3)

[0021] Where P(t) is the first-order integral vector of W(t), and u0 and v0 are the initial displacement and initial velocity of the system, respectively. Substituting the expression into formula (1) and forcing the equation to be satisfied on a pre-selected collocation set, the ordinary differential equation is transformed into a system of partial linear algebraic equations concerning wavelet techniques a and b:

[0022] (4)

[0023] Where G is the residual equation of the wavelet coefficients.

[0024] Furthermore, in step (2), the Newton-Raphson method is used to solve the nonlinear equations related to the wavelet coefficients in each sub-time period, and the iterative format is as follows: It sets convergence criteria including residual tolerance and maximum number of iterations. The time domain is divided into N sequentially connected sub-time periods, assuming the time domain is [0 T]. , n=1,2,...,N, where t (1) =0,t (N+1) =T, the length of the nth segment is given by d n express In each time period, a local time coordinate is introduced. Introduce local time in the nth time period:

[0025] (5)

[0026] Under the local time coordinate, the derivative relationship in formula (1) becomes:

[0027] (6)

[0028] Within each sub-time period, repeat the discretization process of step (1) to establish the wavelet coefficients a within that time period. n b n The nonlinear algebraic equation system G n (a n ,b n The initial condition of this system of equations is provided by the final value of the previous time interval, i.e., ) = 0. The Newton-Raphson iterative method is used to solve the nonlinear equations for each sub-time period, and the following iterative scheme is established:

[0029] (7)

[0030] Where k is the iteration step, and the Jacobian matrix of the wavelet coefficient governing equation in the nth time domain is: The iterative convergence condition includes the residual norm. or number of iterations At the same time, set global calculation time determination conditions. .

[0031] Furthermore, in step (3), the displacement of the system over the entire time domain is reconstructed. ,speed and acceleration for:

[0032] (8)

[0033] (9)

[0034] (10)

[0035] Where P(t) is the first integral vector of the wavelet basis function vector W(t), and u0 and v0 are the initial displacement and initial velocity of the system, respectively. Construct a displacement-velocity phase plane diagram. Furthermore, a Poincaré section is introduced for quantitative analysis. Considering the characteristics of this system being subjected to periodic excitation (ω), the Poincaré section is defined using sampling at equal time intervals:

[0036] (11)

[0037] Where Σ represents the Poincaré section, defined as the state point of the system on the phase plane (u(t)). n ), v(t n The set of state points, which belong to the two-dimensional real space R², i.e., the phase plane spanned by displacement and velocity, and are spaced at fixed time intervals t. n = t0 + nT is used for sampling, where t0 is the initial sampling phase, T is the external excitation period, and n is the sampling sequence number (n = 0, 1, 2, …). By analyzing the distribution pattern of the point set on this cross section, the periodic motion characteristics of the system can be effectively determined.

[0038] It also includes a time-frequency feature extraction system for a collision vibration system, and a method for calculating the periodic response of a collision vibration system based on a piecewise B-spline wavelet, comprising a discretization module, a solution module, and an analytical module. The discretization module is used to perform the wavelet discretization step of the dynamic equation, the solution module is used to perform the piecewise iterative solution step in the time domain, and the analytical module is used to perform the time-frequency feature analysis step.

[0039] It also includes a computer device comprising a memory, a processor, and a computer program stored in the memory and running on the processor, wherein when the processor executes the computer program, it performs a calculation of the periodic response of the collision oscillator system based on a segmented B-spline wavelet periodic response calculation method for the collision vibration system.

[0040] It also includes a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, performs a calculation of the periodic response of a collision oscillator system based on a segmented B-spline wavelet periodic response calculation method for a collision vibration system.

[0041] Compared with the prior art, the present invention has the following beneficial effects:

[0042] This invention directly solves for the periodic response of a system using wavelet collocation technology, avoiding the lengthy transient process simulations of traditional methods. Based on the excellent approximation properties of wavelet basis functions, it can accurately capture the nonlinear characteristics of the collision system and obtain high-precision periodic solutions. For example, it can clearly capture the dynamic characteristics of the colliding oscillator system: the acceleration response exhibits instantaneous abrupt changes. It also avoids lengthy numerical integration processes, significantly improving the computational efficiency of the periodic response. Attached Figure Description

[0043] Figure 1 This is a flowchart of a method according to an embodiment of the present invention;

[0044] Figure 2 This is a schematic diagram of the single-sided elastic constraint collision-oscillator system used in the embodiment;

[0045] Figure 3 The result of the system periodic response calculation in Example 1;

[0046] Figure 4 This is a reconstruction diagram of the system's time-domain response when the initial value is [0,1] in Example 2;

[0047] Figure 5 This is a reconstruction diagram of the system's time-domain response when the initial value is [-2, 1] in Example 2;

[0048] Figure 6 for Figure 4 The calculation results and response characteristics analysis diagram;

[0049] Figure 7 for Figure 5 The calculation results and response characteristics analysis diagram. Detailed Implementation

[0050] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0051] Example 1

[0052] like Figure 1 and Figure 2 As shown, the method for calculating the piecewise B-spline wavelet periodic response of a collision vibration system includes the following steps:

[0053] (1) Establish wavelet discretization of dynamic equations. Use the fourth-order B-spline wavelet basis function to discretize the dynamic control equations of the collision-oscillator system and establish a set of nonlinear algebraic equations about the wavelet coefficients.

[0054] (2) Solve the time domain piecewise iteratively, dividing the entire time domain into multiple sequentially connected sub-time periods, and iteratively solving the nonlinear algebraic equation system in each sub-time period to obtain the global wavelet coefficients;

[0055] (3) Establish periodic response reconstruction and analysis. Based on the wavelet coefficients, reconstruct the displacement, velocity and acceleration response of the system, and determine the periodic response characteristics through the judgment conditions.

[0056] The specific steps of the calculation method in this embodiment are as follows:

[0057] (1) Figure 2 Consider a collision-oscillator system with a unilateral elastic constraint. The oscillator has mass m and is connected to the foundation via a linear spring with stiffness coefficient k1 and a damper with damping coefficient c. It is subjected to a simple harmonic excitation with amplitude A and frequency Ω. When the displacement X reaches the gap E, the oscillator comes into contact with a linear spring with stiffness k2. Assume there is no energy loss during the collision process.

[0058] The velocity and acceleration terms of the system are expressed as a linear combination of fourth-order B-spline wavelet basis functions. Expressions for displacement and velocity are obtained through a first integration, ultimately transforming the differential equations into a system of nonlinear algebraic equations G concerning the wavelet coefficients. n (a,b)=0.

[0059] Typically, the dynamic governing equations of a collision-oscillator system have the following form:

[0060] (1)

[0061] Specifically, the dynamic control equations of the collision-oscillator system in this embodiment are:

[0062] (1-1)

[0063] Where u represents dimensionless displacement and v represents dimensionless velocity. This represents the derivative of displacement with respect to time. Let ξ represent the derivative of velocity with respect to time, β = k2 / k1 be the damping ratio, f be the dimensionless excitation amplitude, and ξ be the damping ratio. For frequency ratio, The system's inherent frequency is used in this embodiment. Let e ​​be the Heaviside step function, where e is a dimensionless parameter.

[0064] Using a 4th-order B-spline wavelet scaling function With wavelet function Zhang Cheng approximates the solution in space, and the system's velocity term and acceleration term Represented as a linear combination of fourth-order B-spline wavelet basis functions:

[0065] (2)

[0066] in, and Let be the wavelet coefficient vector to be determined, W(t) be the wavelet basis function vector, and J be the maximum decomposition scale.

[0067] The scaling basis function is:

[0068] (2-1)

[0069] The specific expression for the scaling basis function is:

[0070] Handling non-uniform boundary data: ,

[0071] Handling non-uniform boundary data: ,

[0072] Boundary scale function:

[0073] Internal scaling function: ,

[0074] .

[0075] The wavelet basis functions are:

[0076] (2-2)

[0077] in, .

[0078] The specific expression for the wavelet basis function is:

[0079] Internal wavelet basis functions:

[0080] (2-3)

[0081] Boundary wavelet basis functions:

[0082] Left boundary wavelet basis function: ,

[0083] Right boundary wavelet basis functions: ,

[0084] in, .

[0085] The wavelet coefficients will be determined by satisfying the interpolation conditions for collocation points, that is, the approximate expression represented by formula (2-1) satisfies the requirements at the collocation points. W is the wavelet basis function. Formulas (2-2) and (2-4) form a collocation point matrix at the collocation points. The expression for the collocation points is:

[0086] (2-4)

[0087] Where L is the wavelet computation interval, and the number of collocation points is... The number of collocation points is equal to the sum of the number of scale basis functions (2-1) and wavelet basis functions (2-2).

[0088] The displacement is obtained by integrating the velocity and acceleration expressions represented by formula (2). and speed The expression for the displacement is obtained by performing an integral over the wavelet basis function vector, since the wavelet coefficients are constant. and speed The expression:

[0089] (3)

[0090] Where P(t) is the first-order integral vector of W(t), and u0 and v0 are the initial displacement and initial velocity of the system, respectively.

[0091] The calculation of P(t) is quite complicated. This embodiment only shows the integration process of some basis functions:

[0092] Scaling basis function integral:

[0093]

[0094] First integral of wavelet basis function:

[0095]

[0096] in,

[0097]

[0098] The above Substituting the expression into formula (1) and forcing the equation to be satisfied on a pre-selected collocation set, the ordinary differential equation is transformed into a system of partial linear algebraic equations concerning wavelet techniques a and b:

[0099] (4)

[0100] Here, G is the residual equation of the wavelet coefficients, and the dynamic equation of the collision-oscillator system has now been discretized by wavelet.

[0101] (2) The Newton-Raphson method is used to solve the nonlinear equations related to the wavelet coefficients in each sub-time period. The iterative format is as follows: The algorithm includes residual tolerance and maximum iteration count convergence criteria. To handle collision-induced response abrupt changes and improve the numerical stability of long-term computations, a time-domain segmentation strategy is introduced. The time-domain segmentation method assumes a time domain of [0T] and divides it into N sequentially connected sub-time periods. , n=1,2,...,N, where t (1) =0,t (N+1) =T, the length of the nth segment is given by d n express .

[0102] Introduce local time coordinates within each time period. Introduce local time in the nth time period:

[0103] (5)

[0104] Under the local time coordinate, the derivative relationship in formula (1) becomes:

[0105] (6)

[0106] Within each sub-time period, repeat the discretization process of step (1) to establish the wavelet coefficients a within that time period. n b n The nonlinear algebraic equation system G n (a n ,b n The initial condition of this system of equations is provided by the final value of the previous time interval, i.e., ) = 0. .

[0107] The Newton-Raphson iterative method is used to solve the nonlinear equations for each sub-time period, and the following iterative scheme is established:

[0108] (7)

[0109] Where k is the iteration step, and the Jacobian matrix of the wavelet coefficient governing equation in the nth time domain is: The convergence condition for the iteration is that within a given number of iterations... Under the condition, residual norm At the same time, set global calculation time determination conditions. .

[0110] (3) After solving all N sub-time periods in sequence, the global wavelet coefficient sequence is obtained. Based on this sequence, the system's displacement over the entire time domain is reconstructed. ,speed and acceleration for:

[0111] (8)

[0112] (9)

[0113] (10)

[0114] Where P(t) is the first integral vector of the wavelet basis function vector W(t), and u0 and v0 are the initial displacement and initial velocity of the system, respectively. Construct a displacement-velocity phase plane diagram. Furthermore, a Poincaré section is introduced for quantitative analysis. Considering the characteristics of this system being subjected to periodic excitation (ω), the Poincaré section is defined using sampling at equal time intervals:

[0115] (11)

[0116] Where Σ represents the Poincaré section, defined as the state point of the system on the phase plane (u(t)). n ), v(t n The set of state points, which belong to the two-dimensional real space R², i.e., the phase plane spanned by displacement and velocity, and are spaced at fixed time intervals t. n = t0 + nT is used for sampling, where t0 is the initial sampling phase, T is the external excitation period, and n is the sampling sequence number (n = 0, 1, 2, …). By analyzing the distribution pattern of the point set on this cross section, the periodic motion characteristics of the system can be effectively determined.

[0117] The periodicity of the system is determined by the distribution of the point set on the Poincaré section. By analyzing the distribution and convergence of the Poincaré point set {Pn}, the periodic motion state and stability of the system can be accurately identified, thereby completing the quantitative calculation and characteristic extraction of the periodic response.

[0118] The parameter inputs for this embodiment are shown in Table 1.

[0119]

[0120] Using the parameters shown in Table 1, such as Figure 3 The displacement, velocity, and acceleration responses reconstructed using the method of this invention are shown. The results demonstrate that this method can clearly capture the dynamic characteristics of the colliding oscillator system: the acceleration response exhibits instantaneous abrupt changes, while the velocity displays a typical step phenomenon. The calculation results of this invention are compared with analytical solutions. Figure 3 As can be seen from the enlarged view of the displacement, velocity, and acceleration on the right, the calculated results and the analytical solution show a high degree of consistency in both overall trend and local details, which fully verifies that the method of the present invention has high accuracy and reliability in calculating the response of the collision oscillator system.

[0121] Example 2

[0122] The parameter inputs for this embodiment are shown in Table 2.

[0123] Table 2 Summary of parameters for the second set of embodiments

[0124]

[0125] Using the parameters shown in Table 2, such as Figure 4 and Figure 5 The displacement, velocity, and acceleration responses reconstructed using the method of this invention are shown in the figure, compared with those of the present invention. Figure 6 and Figure 7 The results show that, firstly, the two sets of solutions converge to different trajectories only when the initial values ​​are different. Secondly, this method can clearly capture the dynamic characteristics of the colliding oscillator system: the acceleration response exhibits instantaneous abrupt changes, while the velocity shows a typical step phenomenon. Thirdly, comparing the calculation results of the method of this invention with the analytical solution, through... Figures 4 to 7 As can be seen from the enlarged view on the right, the calculated results and the analytical solution exhibit a high degree of consistency in both overall trend and local details, fully verifying that the method of this invention has high accuracy and reliability in calculating the response of a colliding oscillator system. Figure 4 and Figure 5 The system response shown was subjected to Poincaré section analysis, and the results are as follows: Figure 6 and Figure 7 As shown, the cross-sectional points cluster into clear discrete points, a morphology that clearly indicates the system is in a periodic motion state. Furthermore, the results obtained by the method of this invention are in high agreement with the analytical solution on the cross-section, which not only verifies the high computational accuracy and reliability of this method but also further confirms the correctness of the conclusions drawn from the analysis of the system's periodic characteristics.

Claims

1. A method for calculating the periodic response of a piecewise B-spline wavelet of a vibro-impact system, characterized in that: Comprising the following steps: (1) wavelet discretization of dynamic equation, using 4-order B-spline wavelet basis function to discretize the dynamic control equation of the impact-vibrator system, and establishing a nonlinear algebraic equation group about the wavelet coefficients; (2) time domain segmentation iterative solving, dividing the whole time domain into multiple sequentially connected sub-periods, and iteratively solving the nonlinear algebraic equation group in each sub-period to obtain global wavelet coefficients; (3) periodic response reconstruction and analysis, reconstructing the displacement, velocity and acceleration responses of the system based on the wavelet coefficients, and determining the periodic response characteristics through a determination condition.

2. The method of claim 1, wherein: In step (1), the velocity and acceleration terms of the system are expressed as linear combinations of 4th order B-spline wavelet basis functions, and the expressions of displacement and velocity are obtained by one integration. Finally, the differential equation is transformed into a nonlinear algebraic equation group G n where the state space form of the dynamics control equation of the collision-oscillator system is （1） where u(t) represents displacement, v(t) represents velocity, (t) represents the derivative of displacement with respect to time , (t) represents the derivative of velocity with respect to time , F represents the expression of the acceleration term of the impact- vibration system. The 4th order B-spline wavelet scaling function and the wavelet function spanned space are used to approximate the solution, and the velocity term and the acceleration term of the system are expressed as the linear combination of the 4th order B-spline wavelet basis function: （2） where, and is the wavelet coefficient vector to be solved, W(t) is the wavelet basis function vector, and J is the maximum decomposition scale. By integrating the wavelet basis function once, the expressions for displacement and velocity are obtained. （3） where P(t) is the first integral vector of W(t), u0and v0are the initial displacement and initial velocity of the system, respectively. Substituting the above expression of W(t) into equation (1) and enforcing the equation on a pre-selected set of collocation points, the ordinary differential equation is converted into a set of linear algebraic equations with respect to the wavelet coefficients a, b: where P(t) is the first integral vector of W(t), u0and v0are the initial displacement and initial velocity of the system, respectively. Substituting the above expression of W(t) into equation (1) and enforcing the equation on a pre-selected set of collocation points, the ordinary differential equation is converted into a set of linear algebraic equations with respect to the wavelet coefficients a, b: （4） Wherein, G is the residual equation of the wavelet coefficients.

3. The method of claim 1, wherein: The Newton-Raphson method is used to solve the nonlinear equations related to the wavelet coefficients in each sub-period in step (2), and the iteration format is , and the convergence judgment condition of residual tolerance and maximum iteration number is set, wherein the time domain division mode is that the time domain is assumed as [0 T], and is divided into N sequentially connected sub-periods , n = 1, 2,..., N, wherein t (1) = 0, t (N+1) = T, the length of the nth period is represented as d n In each period, the local time coordinate is introduced, and the local time in the nth period is introduced.​ （5） In the local time coordinate, the derivative relationship in formula (1) becomes: （6） In each sub-interval, the discretization procedure of step (1) is repeated to establish the nonlinear algebraic system of equations G n (a n ,b n )=0 for the wavelet coefficients a n ,b n in this interval, the initial conditions of which are provided by the end values of the previous interval, i.e. The nonlinear system of equations for each sub-interval is solved using the Newton-Raphson iterative method, establishing the following iterative scheme: （7） Wherein, k is the iteration step number, the wavelet coefficient control equation Jacobian matrix of the nth time domain is The iteration convergence condition includes the residual norm Or the iteration step number At the same time, the global calculation duration determination condition is set .

4. The method of claim 1, wherein: The displacement of the reconstructed system in the whole time domain in step (3) is: velocity and acceleration : （8） （9） （10） Where P(t) is the first integral vector of the wavelet base function vector W(t), u0 and v0 are the initial displacement and initial velocity of the system, respectively, the displacement-velocity phase plane diagram is constructed ), and the Poincare section is introduced for quantitative analysis. According to the characteristics of the system subjected to periodic excitation (ω), the Poincare section is defined by equal time interval sampling: （11） where Σ denotes the Poincare section, defined as the set of state points (u(t n ), v(t n )) of the system on the phase plane, which belongs to the two-dimensional real number space R², i.e. the phase plane spanned by displacement and velocity, and is sampled at fixed time intervals t n = t0 + nT, t0 being the initial sampling phase, T the period of external excitation, and n the sampling number (n = 0, 1, 2,…). By analyzing the distribution pattern of the point set on the section, the periodic motion characteristics of the system can be effectively identified.

5. A time-frequency feature extraction system for a collision vibration system, characterized by: The segmented B-spline wavelet periodic response calculation method of the impact-vibration system according to any one of claims 1-4 comprises a discretization module, a solving module and an analysis module, the discretization module is used to execute the wavelet discretization of dynamic equation step, the solving module is used to execute the time domain segmentation iterative solving step, and the analysis module is used to execute the time-frequency characteristic analysis step.

6. A computer device comprising a memory, a processor, and a computer program stored on the memory and running on the processor, wherein when the processor executes the computer program, it is characterized by: The segmented B-spline wavelet periodic response calculation method of the impact-vibration system according to any one of claims 1-4 is used to complete the calculation of the periodic response of the impact-vibrator system.

7. A computer readable storage medium having stored thereon a computer program, wherein the computer program, when executed by a processor, causes the processor to perform: The segmented B-spline wavelet periodic response calculation method of the impact-vibration system according to any one of claims 1-4 is used to complete the calculation of the periodic response of the impact-vibrator system.

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