摘要
The aim of the present study is to develop an efficient weak form quadrature element for free vibration analysis of arbitrarily shaped membranes.The arbitrarily shaped membrane is firstly mapped into a regular domain using blending functions,and the displacement in the element is assumed as the trigonometric functions.Explicit formulations are worked out for nodes of any type and a varying number of nodes.For verifications,results are compared with exact solutions and data obtained by other numerical methods.It is demonstrated that highly accurate frequencies can be obtained with a small number of nodes by present method.
本文目的是建立一种能够高效分析任意形状膜的自由振动的弱式求积单元。先采用融合函数将任意形状变换成规则的区域,然后将单元内的位移场假设为三角函数,最终导出了节点数目可变和节点类型任意的单元的显式表达式。为了验证本文方法的有效性,将得到的结果与精确解和采用其他数值方法的结果进行了对比。研究表明:本文方法可以用很少的节点数目给出高精度自由振动频率。
基金
supported by the National Natural Science Foundation of China(Nos.52005256,12072154)
the Natural Science Foundation of Jiangsu Province(No.BK20190394)
the Jiangsu Post-Doctoral Research Funding Program(No.2020Z437)
the Priority Academic Program Development of Jiangsu Higher Education Institutions.
