Duffing振子激励下平板声振特性研究

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振动与冲击 ›› 2015, Vol. 34 ›› Issue (6) : 122-126.

论文

针对非线性振动激励下结构声辐射问题，由变分原理导出Duffing振子激励下平板声振耦合动力学方程，由模态展开法及增量谐波平衡法导出轻流体中耦合动力学方程的近似解析解，给出多频激励下平板表面平均振速及辐射声功率表达式，研究激励力频率、非线性项对系统振动及声辐射特性影响。结果表明，Duffing振子激励下平板的声振耦合问题为含离散与连续系统的复杂动力学问题；耦合运动下Duffing振子出现二次跳跃现象与新的共振特性；平板声振特性主要由三次谐波决定。研究结果可为隔振结构的声振设计提供理论依据。

作者信息 +

Vibro-acoustic characteristics of plate under Duffing oscillator’s excitation

For the acoustic radiation problem of structure under nonlinear vibration excitations, the vibro-acoustic coupling dynamic equations of plate under Duffing oscillator’s excitation were derived based on variational principle. The approximately analytical solution of coupled equations in light liquid was given by modal expansion and incremental harmonic balance method. The expressions of quadratic velocity and acoustic radiation power under multi-frequency also were given. Then the influences of excitation frequency and nonlinear stiffness to the nonlinear vibration and acoustic radiation were investigated. The results show that the vibro-acoustic coupling problem of plate under Duffing oscillator’s excitation is a complex dynamic problem containing discrete and continuous system. There are second jump phenomena and new resonant characters in Duffing oscillator’s motion. The vibro-acoustic characteristics of plate are determined by third harmonic component. The results are significant for the vibro-acoustic designing of vibration isolation.

Author information +

文章历史 +

摘要

针对非线性振动激励下结构声辐射问题，由变分原理导出Duffing振子激励下平板声振耦合动力学方程，由模态展开法及增量谐波平衡法导出轻流体中耦合动力学方程的近似解析解，给出多频激励下平板表面平均振速及辐射声功率表达式，研究激励力频率、非线性项对系统振动及声辐射特性影响。结果表明，Duffing振子激励下平板的声振耦合问题为含离散与连续系统的复杂动力学问题；耦合运动下Duffing振子出现二次跳跃现象与新的共振特性；平板声振特性主要由三次谐波决定。研究结果可为隔振结构的声振设计提供理论依据。

Abstract

For the acoustic radiation problem of structure under nonlinear vibration excitations, the vibro-acoustic coupling dynamic equations of plate under Duffing oscillator’s excitation were derived based on variational principle. The approximately analytical solution of coupled equations in light liquid was given by modal expansion and incremental harmonic balance method. The expressions of quadratic velocity and acoustic radiation power under multi-frequency also were given. Then the influences of excitation frequency and nonlinear stiffness to the nonlinear vibration and acoustic radiation were investigated. The results show that the vibro-acoustic coupling problem of plate under Duffing oscillator’s excitation is a complex dynamic problem containing discrete and continuous system. There are second jump phenomena and new resonant characters in Duffing oscillator’s motion. The vibro-acoustic characteristics of plate are determined by third harmonic component. The results are significant for the vibro-acoustic designing of vibration isolation.

导出引用

周奇郑，王德石. Duffing振子激励下平板声振特性研究[J]. 振动与冲击, 2015, 34(6): 122-126

ZHOU Qi-zheng，WANG De-shi. Vibro-acoustic characteristics of plate under Duffing oscillator’s excitation[J]. Journal of Vibration and Shock, 2015, 34(6): 122-126

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