An Analytical Symplectic Approach for Vibration Analysis of Orthotropic Graphene Sheets 
作者Xinsheng Xu; Dalun Rong; C.W. Lim; Changyu Yang; Zhenhuan Zhou
期刊名称Acta Mechanica Sinica
摘要A nonlocal continuum orthotropic plate model is proposed to study the vibration behavior of single layered graphene sheets (SLGSs) by using an analytical symplectic approach. A Hamiltonian system is established by introducing a total unknown vector consisting of the displacement amplitude, rotation angle, shear force and bending moment. The high-order governing differential equation of the vibration of SLGSs is transformed into a set of ordinary differential equations in symplectic space. Exact solutions for free vibration are obtianed by the method of separation of variables without any trial shape functions and can be expanded in series of symplectic eigenfunctions. Analytical frequency equations are derived for all six possible boundary conditions. Vibration modes are expressed in terms of the symplectic eigenfunctions. In the numerical examples, comparison is presented to verify the accuracy of the proposed method. Comprehensive numerical examples for graphene sheets with Levy-type boundary conditions are given. A parametric study of the natural frequency is also included.
关键词Hamiltonian system; analytical method; nonlocal elasticity theory; orthotropic graphene sheet; natural frequency

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