Release Time:2020-10-08  Hits:

Indexed by: Journal Article

Date of Publication: 2019-01-01

Journal: EUROPEAN JOURNAL OF MECHANICS A-SOLIDS

Included Journals: Scopus、EI、SCIE

Volume: 73

Page Number: 22-33

ISSN: 0997-7538

Key Words: Symplectic method; Forced vibration; Completely free nanoplate; Nonlocal elasticity theory; Viscoelastic foundation

Abstract: Exact solutions for forced vibration of completely free orthotropic rectangular nanoplates resting on viscoelastic foundations are obtained by an analytical Hamiltonian-based method. Eringen's nonlocal theory is employed to take into account the small size effect. In the present method, a Hamiltonian system for the vibration of the orthotropic rectangular nanoplate is established by introducing a new total unknown vector. The vibration analysis is reduced to an eigenproblem in the symplectic space. Closed-form solutions of the completely free nanoplate are derived by using the solution of a guided supported nanoplate and a superposition of boundaries. Numerical examples including comparison studies are presented to illustrate the efficiency and accuracy of the proposed method. A detailed parametric study and some new results are provided also.