噪声与振动控制

噪声与振动控制 ›› 2018, Vol. 38 ›› Issue (5): 21-26.DOI: 10.3969/j.issn.1006-1355.2018.05.004

• 振动理论与数值解法 • 上一篇    下一篇

基于改进傅里叶级数的矩形板薄板振动特性分析

陈林 1，肖伟 2，刘见华 1，杜圆 3   

  1. （ 1. 中国船舶及海洋工程设计研究院，上海200011； 2. 中国舰船研究设计中心，武汉430064；
    3. 哈尔滨工程大学船舶工程学院，哈尔滨150001 ）
  • 收稿日期:2018-01-08 修回日期:2018-03-07 出版日期:2018-10-18 发布日期:2018-10-18
  • 通讯作者: 杜圆

Vibration Characteristic Analysis of Rectangular Thin Plates based on Improved Fourier Series Method

  • Received:2018-01-08 Revised:2018-03-07 Online:2018-10-18 Published:2018-10-18

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摘要：

基于改进傅里叶级数对任意边界条件下的矩形薄板振动特性进行分析，通过傅立叶正弦级数的引入，修正了边界条件上的不连续性；此外，通过改变横向位移约束弹簧刚度值k和旋转约束弹簧刚度值K来模拟任意边界下矩形薄板的振动情形，克服了以往只能求解某些特定简化边界条件下振动问题的缺陷。通过与文献及有限元软件计算结果的对比，验证了此方法的有效性；研究表明，矩形薄板不同边界条件下固有频率值差异较大，但均随长宽比增大而减小。

关键词: 振动与波, 改进傅里叶级数, 矩形薄板, 振动特性, 任意边界条件

Abstract:

Abstract: Based on the theory of Improved Fourier Series Method (IFSM), the vibration characteristic of rectangular thin plate with arbitrary boundary condition is studied. Besides, sine function term is introduced to modify the discontinuity of boundary condition. What’s more, through changing the values of the restraint stiffness k and the rotational restraint stiffness K, arbitrary boundary conditions can be simulated. Therefore, defects of the ordinary method dealing with structure vibration that could only be solved under some simplified boundary conditions have been overcome. The effectiveness of this method has been verified by comparing with the results of Literature and FEM software. Based on large amount of calculation, we found natural frequency differs greatly in varied boundary conditions. Besides, natural frequency of rectangular thin plate decreases with the growth of aspect ratio.