Analytical study on post-buckling and nonlinear free vibration analysis of FG beams resting on nonlinear elastic foundation under thermo-mechanical loadings using VIM

2014 ◽  
Vol 17 (5) ◽  
pp. 753-776 ◽  
Author(s):  
Hessameddin Yaghoobi ◽  
Mohammad Sadegh Valipour ◽  
Abdolhossein Fereidoon ◽  
Pooria Khoshnevisrad
Keyword(s):  
Free Vibration ◽  
Elastic Foundation ◽  
Vibration Analysis ◽  
Analytical Study ◽  
Free Vibration Analysis ◽  
Nonlinear Free Vibration ◽  
Nonlinear Elastic Foundation ◽  
Post Buckling ◽  
Nonlinear Elastic

Free Vibration Analysis for Disconnected Thin Rectangular Plate with Four Free Edges on Nonlinear Elastic Foundation

2011 ◽  
Vol 52-54 ◽  
pp. 1309-1314 ◽  
Author(s):  
Yong Gang Xiao ◽  
Cui Ping Yang
Keyword(s):  
Free Vibration ◽  
Rectangular Plate ◽  
Elastic Foundation ◽  
Vibration Analysis ◽  
Harmonic Balance Method ◽  
Free Vibration Analysis ◽  
Variation Principle ◽  
Thin Rectangular Plate ◽  
Nonlinear Elastic Foundation ◽  
Nonlinear Elastic

In this paper, the free vibration analysis of thin rectangular plate with dowels on nonlinear elastic foundation is investigated. The load transfer on dowels is modeled as vertical springs, whose stiffness depends on the dowel properties and the dowel-plate interaction. Based on Hamilton variation principle, the nonlinear governing equations of thin rectangular plate with discontinuities on nonlinear elastic foundation are established, and the suitable expressions of trial functions satisfying all boundary conditions are proposed. Then, the equations are solved by using Galerkin method and harmonic balance method. The numerical simulation reveals the effects of the dowel parameters and the other ones of the system on free vibration behaves of the disconnected thin rectangular plate.

A new mixed method for nonlinear fuzzy free vibration analysis of nanobeams on nonlinear elastic foundation

2016 ◽  
Vol 24 (24) ◽  
pp. 5765-5773
Author(s):  
AR Vosoughi ◽  
MR Nikoo
Keyword(s):  
Free Vibration ◽  
Elastic Foundation ◽  
Mixed Method ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Small Scale ◽  
Governing Equations ◽  
Nonlinear Elastic Foundation ◽  
Fuzzy Transformation ◽  
Nonlinear Elastic

A new mixed method for nonlinear fuzzy free vibration analysis of nanobeams on nonlinear elastic foundation is introduced. The governing equations are derived based on the first-order shear deformation theory (FSDT) in conjunction with the von-Kármán’s assumptions and the Eringen’s nonlocal elasticity theory. The differential quadrature method (DQM) is employed to discretize the governing equations and the related boundary conditions. The direct displacement control iterative method is used to solve the discretized system of equations. The fuzzy transformation method (FTM) is coupled with the solution to incorporate effects of different uncertainties such as the small scale effect parameter, nonlinear elastic foundation parameters and vibration amplitude of the nanobeam. Applicability, rapid rate of convergence and high accuracy of the presented method are shown and significant effects of the nonlinearity on the response of nanobeams are investigated via solving some examples.

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