任意边界条件下变厚度中厚矩形板的静动态特性分析

Static and dynamic characteristics analysis of moderately thick rectangular plates with arbitrary boundary supports

文章基于改进傅立叶级数方法,在Mindlin一阶剪切变形板理论的基础上,对任意边界条件下变厚度中厚板矩形板的静动态特性进行了研究。矩形板的横向位移函数与旋转位移函数被表示为包含正弦三角级数的改进傅立叶级数,正弦三角级数的引入,能够有效地解决在边界处存在的不连续或者跳跃现象。在此基础上,将位移容许函数的未知傅立叶展开系数看作广义变量,采用能量原理建立结构的能量泛函,结合Rayleigh-Ritz法对未知傅立叶展开系数求极值,将结构的静动态特性问题转换为一个求解标准特征值问题。通过大量的数值算例,并与现有文献解及有限元方法计算结果进行对比,验证了文中方法的合理性,并且具有良好的收敛速度与计算精度。

Based on Mindlin first order shear deformation plate theory,the static and dynamic characteristic of moderately thick rectangular plates with variable thickness and arbitrary boundary conditions along each edge was presented by employing improved Fourier Series Method(IFSM).Arbitrary boundary supports can be physically realized by setting three type springs along each edge in the current method.Regardless of boundary conditions,the plate admissible functions were invariantly sought as an improved Fourier cosine series,and a sine series was introduced to overcome all the relevant discontinuities or jumps of elastic boundary conditions.The expansion coefficients were considered as the generalized coordinates,and determined by using the Rayleigh-Ritz technique.A standard eigenvalue problem concerning the unknown displacement expansion coefficient was derived from which the static and dynamic characteristic can be solved readily.The results of moderately thick rectangular plates with various boundary conditions and variable thickness were presented and compared with the results published in literatures and finite element method results to demonstrate the effectiveness and reliability of the current method.