双频激励下微弯液压管道的非线性振动研究

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振动与冲击 ›› 2023, Vol. 42 ›› Issue (20) : 181-187.

论文

双频激励下微弯液压管道的非线性振动研究

范鑫1,2，舒送1，张俊宁3，肖璐3，毛晓晔3，丁虎3

作者信息 +

A study on nonlinear vibration of slightly curved hydraulic pipes under dual frequency excitation

FAN Xin1,2,SHU Song1,ZHANG Junning3,XIAO Lu3,MAO Xiaoye3,DING Hu3

Author information +

文章历史 +

摘要

首次研究了双频激励下两端固支微弯液压管道的非线性振动，分析了拍振现象发生时管路非线性受迫振动特性。利用广义哈密顿原理建立微曲管道控制方程，使用Galerkin法将非线性偏微分积分方程离散为非线性耦合常微分方程组，采用龙格库塔法数值求解，并用微分求积单元法(Differential Quadrature Element Method, DQEM)进行数值验证，得到了微曲管道受迫振动响应。在此基础上，讨论了两个激励频率差值对管道中点受迫振动响应的影响，并分析了系统横向振动在一阶固有频率附近的分岔现象，考察了液压管道的混沌特性。分析结果表明，两个激励频率相差较小时会出现混沌现象，随着频率差值的减小，管道的混沌区域先增大后减小。这些结论为多频激励下液压管道系统复杂振动的研究提供了理论依据和研究方法。

Abstract

The nonlinear combined vibration of a slightly curved hydraulic pipe with two fixed supports under dual frequency excitation is studied. The nonlinear forced vibration characteristics are analyzed when the beat vibration phenomenon occurs. Generalized Hamiltonian principle is used to establish the governing equation of the slightly curved pipe. The nonlinear partial differential integral equation is discretized into a set of nonlinearly coupled ordinary differential equations (ODEs) via Galerkin method (GM). The numerical solutions of the forced vibration are obtained by the Runge Kutta method based on the discrete ordinary differential equations. The differential quadrature element method (DQEM) verifies the accuracy of it. On this basis, the influence of the frequency gap between two excitations on the forced vibration of the pipe’s midpoint is discussed. The bifurcation and chaos of the transverse vibration near the first order natural frequency is analyzed. The analysis results show that when the frequency gap is small, chaos will appear. With the decrease of frequency gap, the chaotic frequency band increases and then decreases. These conclusions provide theoretical basis and research methods for the study of complex vibration of hydraulic pipe systems under multi-frequency excitation.

导出引用

范鑫1,2，舒送1，张俊宁3，肖璐3，毛晓晔3，丁虎3. 双频激励下微弯液压管道的非线性振动研究[J]. 振动与冲击, 2023, 42(20): 181-187

FAN Xin1,2,SHU Song1,ZHANG Junning3,XIAO Lu3,MAO Xiaoye3,DING Hu3. A study on nonlinear vibration of slightly curved hydraulic pipes under dual frequency excitation[J]. Journal of Vibration and Shock, 2023, 42(20): 181-187

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