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 ...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.展开更多
This paper presents a new method for solving the vibration of arbitrarily shaped membranes with ela.stical supports at points. The reaction forces of elastical supports at points are regarded as unknown external force...This paper presents a new method for solving the vibration of arbitrarily shaped membranes with ela.stical supports at points. The reaction forces of elastical supports at points are regarded as unknown external forces acting on the membranes. The exact solution of the equation of motion is given which includes terms representing the unknown reaction forces. The frequency equation is derived by the use of the linear relationship of the displacements with the reaction forces of elastical supports at points. Finally the calculating formulae of the frequency equation of circular membranes are analytically performed as examples and the inherent frequencies of circular membranes with symmetric elastical supports at two points are numerically calculated.展开更多
基金supported by the National Natural Science Foundation of China(Nos.52005256,12072154)the Natural Science Foundation of Jiangsu Province(No.BK20190394)+1 种基金the Jiangsu Post-Doctoral Research Funding Program(No.2020Z437)the Priority Academic Program Development of Jiangsu Higher Education Institutions.
文摘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.
文摘This paper presents a new method for solving the vibration of arbitrarily shaped membranes with ela.stical supports at points. The reaction forces of elastical supports at points are regarded as unknown external forces acting on the membranes. The exact solution of the equation of motion is given which includes terms representing the unknown reaction forces. The frequency equation is derived by the use of the linear relationship of the displacements with the reaction forces of elastical supports at points. Finally the calculating formulae of the frequency equation of circular membranes are analytically performed as examples and the inherent frequencies of circular membranes with symmetric elastical supports at two points are numerically calculated.
