用无网格法分析带压电层的裂纹板的振动特性

王 砚;王忠民

振动与冲击 ›› 2010, Vol. 29 ›› Issue (9) : 167-169,.

PDF(1050 KB)
PDF(1050 KB)
振动与冲击 ›› 2010, Vol. 29 ›› Issue (9) : 167-169,.
论文

用无网格法分析带压电层的裂纹板的振动特性

  • 王 砚;王忠民
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The Element Free Method for Vibration Characteristics of a Cracked Plate with Piezoelectric layers

  • WANG Yan;WANG Zhongmin
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摘要

将无网格伽辽金法(EFGM)应用于求解含压电层裂纹板的横向自由振动问题。建立了系统的能量泛函,根据弹性动力学推广的Hamilton原理和引入无量纲量,推导了含压电层的裂纹矩形薄板的变分式;建立了无网格伽辽金法离散的控制方程。通过数值计算,得出了薄板的无量纲固有频率随裂纹和压电片几何参数的变化曲线,分析了裂纹的参数和数量对矩形薄板的横向振动特性的影响。

Abstract

The element free Galerkin method (EFGM) is proposed to solve the transverse free vibration of the cracked plate with piezoelectric layers. The energy function of the system is established, based on the extended Hamilton’s principle for the elastic dynamics system and introduced the dimensionless variables and parameters, the variational expression of the cracked plate with piezoelectric layers is deduced. The governing equations for EFGM are obtained. By numerical calculation the curves of the dimensionless natural frequency of thin plate versus the geometry parameters of cracks and piezoelectric layers are plotted. The effects of the factors for the crack parameters and number on the transverse vibration characteristics of the thin plate are analyzed.

关键词

无网格法 / 推广的Hamilton原理 / 压电层 / 裂纹 / 横向振动

Key words

Element free method / Extended Hamilton’s principle / Piezoelectric layer / Cracks / Transverse vibration

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导出引用
王 砚;王忠民. 用无网格法分析带压电层的裂纹板的振动特性[J]. 振动与冲击, 2010, 29(9): 167-169,
WANG Yan;WANG Zhongmin. The Element Free Method for Vibration Characteristics of a Cracked Plate with Piezoelectric layers[J]. Journal of Vibration and Shock, 2010, 29(9): 167-169,

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