Improved Duhamel integral algorithm for Legendre series solutions to time-varying dynamic system

被引：0

作者：

Jin, Pengfei ^{[1
]}

Shi, Zhiyu ^{[1
]}

Peng, Xujun ^{[1
]}

机构：

[1] State Key Lab of Mechanies and Control for Aerospace Structures, Nanjing University of Aeronautics and Astronautics, Nanjing

来源：

Zhendong yu Chongji/Journal of Vibration and Shock | 2024年 / 43卷 / 17期

关键词：

Legendre polynomial approximation; linear superposition; time domain response; time-varying system;

D O I：

10.13465/j.cnki.jvs.2024.17.029

中图分类号：

学科分类号：

摘要：

The calculation theory of forced vibration response in time-varying systems is still incomplete, and numerical solutions can't correctly reflect analytical nature of vibration response. Legendre polynomial approximation method (LPAM) can be used to obtain continuous approximate function solutions to time-varying system responses, but its computational efficiency is relatively low. Here, the time-domain response solving theory of time-invariant systems was transplanted to time-varying systems. On the basis of the superposition principle of linear systems, improved Legendre series algorithm based on Duhamel integration was proposed. Legendre polynomial approximation of Dirac function and Duhamel integration were used to solve response of time-varying system. The effectiveness of the improved algorithm was demonstrated through a set of first-order non-homogeneous variable coefficient ordinary differential equations. Simulation examples of a single-DOF system with both stiffness and damping linear changes and nonlinear changes were designed, and the system's displacement responses under transient excitation and simple harmonic excitation obtained with this method were compared to the calculation results of the system responses with the 4th order Runge-Kutta numerical integration method to show convergence and divergence problems of the improved algorithm and improvement of calculation speed. © 2024 Chinese Vibration Engineering Society. All rights reserved.

引用

页码：260 / 268

页数：8

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