中心典型形状开口的矩形薄板自由振动特性分析

摘要

[目的]工程中存在着大量的开口结构,对开口板的振动特性进行研究具有重要意义.[方法]通过引入改进的傅里叶级数模拟开口矩形板的位移容许函数,并采用位移弹簧和转角弹簧模拟任意边界条件.在求解整体能量泛函时,将开口部分的动能与应变能减去,基于Rayleigh-Ritz法构造结构的拉格朗日能量泛函,并对傅里叶级数中的未知系数进行变分求极值,将原先的振动问题转化成求解特征值方程的问题.最后,研究不同开口形状及开口大小对矩形板自由振动的影响.[结果]经与有限元软件ANSYS的计算结果的对比,表明采用的方法准确可靠,[结论]所做研究可为实际工程提供参考.%[Objectives]A large number of structures with openings are used in engineering projects, which is of great significance for studying the vibration characteristics of plates with openings.[Methods] By introducing an improved Fourier series,the permissible displacement function of rectangular plates with openings is simulated. By using displacement springs and angle springs,arbitrary boundary conditions are simulated. While obtaining the overall energy functional,the kinetic energy and strain energy of the opening part are subtracted. Based on the Rayleigh-Ritz method,the Lagrange energy functional of the structure is constructed and the variational extremum of unknown coefficients in the Fourier series obtained,transforming the original vibration problem into a problem of eigenvalue equations.The paper studies the influence on the free vibration of rectangular plates with different shaped and sized openings.[Results]A comparison with the results of finite element software ANSYS shows that the current method is accurate and reliable,[Conclusions]providing a reference for practical engineering.