Solving and stability analysis of periodic response of nonlinear system based on time finite element method

ZHENG Yongjin, WANG Li, LIU Zuoqiu

Journal of Vibration and Shock ›› 2024, Vol. 43 ›› Issue (1) : 276-282.

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PDF(1611 KB)
Journal of Vibration and Shock ›› 2024, Vol. 43 ›› Issue (1) : 276-282.

Solving and stability analysis of periodic response of nonlinear system based on time finite element method

  • ZHENG Yongjin, WANG Li, LIU Zuoqiu
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Abstract

Nonlinear phenomena widely exist in structural analysis. Obtaining the periodic response of nonlinear systems is crucial to analyzing the frequency response characteristics, bifurcation and stability characteristics of structures. Therefore, a method for solving the periodic response of nonlinear systems based on time finite element method is proposed. On the basis of Galerkin time finite element method, in this method, periodic boundary conditions are introduced and combined with Newton iterative method to solve problem. The advantages of this method are: (a) it can simply deal with nonsmooth periodic loads (such as step or impact periodic loads), and (b) it can directly calculate the transfer matrix and Floquet multiplier according to the system matrix of the time finite element, and then determine the stability of the periodic solution. Finally, the correctness, convergence and accuracy of the proposed time finite element method in the periodic response solution and stability analysis of nonlinear systems are verified by numerical examples.

Key words

nonlinear systems / time finite method / Non-smooth periodic loads / analysis of stability / Steady-state response.

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ZHENG Yongjin, WANG Li, LIU Zuoqiu. Solving and stability analysis of periodic response of nonlinear system based on time finite element method[J]. Journal of Vibration and Shock, 2024, 43(1): 276-282

References

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