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Indexed by:期刊论文

Date of Publication:2017-10-01

Journal:JOURNAL OF VIBRATION ENGINEERING & TECHNOLOGIES

Included Journals:SCIE、Scopus

Volume:5

Issue:5

Page Number:441-450

ISSN No.:2321-3558

Key Words:Symplectic method; Nanobeam; Eringen's nonlocal elasticity; Free vibration; Analytical solution

Abstract:An analytical symplectic approach is introduced to the free vibration of nanobeams based on the Euler-Bernoulli beam theory and Eringen's nonlocal theory. In symplectic space, the governing equations or Hamiltonian equations are formed by a total unknown vector consisting of the transverse displacement, rotate of angle, bending moment and shear force. The method of separation of variables is employed to solve the Hamiltonian equations of eigenvalue problem. Analytical frequency equations for various boundary conditions are obtained without any trial functions. Natural frequency has the good agreement with existing results. A parametric study is preformed also.