Free vibration of plates with stepped variations in thickness on non-homogeneous elastic foundations
Free vibration of plates with stepped variations in thickness on non-homogeneous elastic foundations
复制标题
非均匀弹性地基上厚度阶梯变化板的自由振动
DOI：
10.1006/jsvi.1995.0269
复制
发表时间：
1995
影响因子：
4.7
通讯作者：
K. H. Lee
中科院分区：
文献类型：
--
作者：
F. Ju;H. Lee;K. H. Lee
建立了非均匀弹性地基上多阶梯变厚度板自由振动的有限元模型。该模型基于Mindlin板理论，在阶梯截面相对于中面偏心的情况下，考虑了横向剪切变形和弯拉耦合。将板单元下方的弹性基础截面作为单独的基础单元处理。使这些基础单元的横向变形与被支承的板单元的挠度一致，从而使弹性基础的刚度矩阵保持一致。数值计算结果与已有报道的结果吻合较好。阶梯段位置偏心对固有频率的影响是不可忽略的。发现弹性基础对均匀板和阶梯板的基本固有频率都有显著的影响。给出了非均匀弹性地基上多个偏心阶梯截面的矩形板和圆板的固有频率和振型。
A finite element model is presented for the analysis of the free vibration of plates with multiple stepped variations in thickness resting on non-homogeneous elastic foundations. Based on Mindlin plate theory, the model includes transverse shear deformation as well as bending-extension coupling in cases of plates with stepped sections eccentrically located with respect to the mid-planes. The section of elastic foundation under a plate element is treated as a separate foundation element. The transverse deformation of these foundation elements is made to be consistent with the deflection of plate elements being supported, resulting in a consistent stiffness matrix for the elastic foundation. Numerical results are in good agreement with the available reported results. The effect of eccentricity of the locations of stepped sections on the natural frequencies is found to be not negligible. The elastic foundations are found to have a significant effect on the fundamental natural frequencies of both uniform and stepped plates. Natural frequencies and mode shapes of rectangular plates and circular plates with multiple eccentrically stepped sections resting on non-homogeneous elastic foundations are presented.