任意边界条件下正交各向异性薄板自由振动特性分析

上海交通大学学报（自然版） ›› 2014, Vol. 48 ›› Issue (03): 434-438.

任意边界条件下正交各向异性薄板自由振动特性分析

史冬岩，王青山，石先杰，庄重

(哈尔滨工程大学机电工程大学，哈尔滨 150001)

收稿日期:2013-08-26
基金资助:
国家安全重大基础研究项目（613157），国家自然科学基金重点项目（50939002）

Free Vibration Analysis of Orthotropic Thin Plates in General Boundary Conditions

SHI Dongyan,WANG Qingshan,SHI Xianjie,ZHUANG Zhong

(College of Mechanical and Electrical Engineering, Harbin Engineering University, Harbin 150001, China)

Received:2013-08-26

摘要/Abstract

摘要：

以典型的正交各向异性薄板结构为研究对象，采用改进傅里叶级数方法（IFSM）对其自由振动特性进行计算分析.将正交各向异性薄板结构的弯曲位移函数表示为一种改进傅里叶级数形式，并引入4项单正弦傅里叶级数来解决边界不连续或跳跃现象.将位移函数的傅里叶展开系数看作广义坐标，采用RayleighRitz方法对其进行求解.通过对不同边界条件下的正交各向异性薄板自由振动特性进行计算，并与有限元法结果相比较，验证了文中方法的正确性和有效性.

关键词: 正交各向异性, 改进傅里叶级数, 任意边界条件, 能量法, 薄板

Abstract:

In this paper, the free vibration characteristics of orthotropic thin plates were investigated using improved Fourier series method (IFSM). The displacement functions of flexural vibration were expressed as an improved form of Fourier series, and the sine Fourier series was introduced to eliminate all the boundary discontinuities or jumps. The expansion coefficients of the displacement function were treated as the generalized coordinates, and determined using the RayleighRitz method. The results of orthotropic thin plates in different boundary conditions were presented and checked against the results published in the literature to demonstrate the efficiency and accuracy of the present method.

Key words: orthotropic, improved Fourier series method, general boundary condition, energy method, thin plates

中图分类号:

O 326

史冬岩，王青山，石先杰，庄重. 任意边界条件下正交各向异性薄板自由振动特性分析[J]. 上海交通大学学报（自然版）, 2014, 48(03): 434-438.

SHI Dongyan,WANG Qingshan,SHI Xianjie,ZHUANG Zhong. Free Vibration Analysis of Orthotropic Thin Plates in General Boundary Conditions[J]. Journal of Shanghai Jiaotong University, 2014, 48(03): 434-438.

参考文献

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