中国舰船研究2017，Vol.12Issue(4)：102-109,8.DOI:10.3969/j.issn.1673-3185.2017.04.016
基于傅里叶级数法的开孔板振动固有特性分析
Free vibration characteristics analysis of rectangular plate with rectangular opening based on Fourier series method
摘要
Abstract
Plate structures with openings are common in many engineering structures. The study of the vibration characteristics of such structures is directly related to the vibration reduction, noise reduction and stability analysis of an overall structure. This paper conducts research into the free vibration characteristics of a thin elastic plate with a rectangular opening parallel to the plate in an arbitrary position. We use the improved Fourier series to represent the displacement tolerance function of the rectangular plate with an opening. We can divide the plate into an eight zone plate to simplify the calculation. We then use linear springs, which are uniformly distributed along the boundary, to simulate the classical boundary conditions and the boundary conditions of the boundaries between the regions. According to the energy functional and variational method, we can obtain the overall energy functional. We can also obtain the generalized eigenvalue matrix equation by studying the extremum of the unknown improved Fourier series expansion coefficients. We can then obtain the natural frequencies and corresponding vibration modes of the rectangular plate with an opening by solving the equation. We then compare the calculated results with the finite element method to verify the accuracy and effectiveness of the method proposed in this paper. Finally, we research the influence of the boundary condition, opening size and opening position on the vibration characteristics of a plate with an opening. This provides a theoretical reference for practical engineering application.关键词
任意开口位置/开口矩形板/改进傅立叶级数/能量法Key words
arbitrary opening position/rectangular plate with an opening/improved Fourier series method/energy variational method分类
交通工程引用本文复制引用
王旻昊,李凯,邱永康,李天匀,朱翔..基于傅里叶级数法的开孔板振动固有特性分析[J].中国舰船研究,2017,12(4):102-109,8.基金项目
国家自然科学基金资助项目(51379083,51579109) （51379083,51579109）
