A Novel Approximate Analytical Method for Nonlinear Vibration Analysis of Euler–Bernoulli and Rayleigh Beams on the Nonlinear Elastic Foundation

2014 ◽  
Vol 39 (4) ◽  
pp. 3279-3287 ◽  
Author(s):  
Hossein Rafieipour ◽  
S. Mehrdad Tabatabaei ◽  
Mohammad Abbaspour
Keyword(s):  
Nonlinear Vibration ◽  
Elastic Foundation ◽  
Analytical Method ◽  
Vibration Analysis ◽  
Approximate Analytical Method ◽  
Nonlinear Elastic Foundation ◽  
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.

Nonlinear Forced Vibration Analysis for Thin Rectangular Plate on Nonlinear Elastic Foundation

2012 ◽  
Vol 204-208 ◽  
pp. 4716-4721 ◽  
Author(s):  
Yong Gang Xiao ◽  
Cui Ping Yang ◽  
Hui Hu
Keyword(s):  
Rectangular Plate ◽  
Elastic Foundation ◽  
Forced Vibration ◽  
Vibration Analysis ◽  
Thin Rectangular Plate ◽  
Nonlinear Elastic Foundation ◽  
Nonlinear Forced Vibration ◽  
Forced Vibration Analysis ◽  
Nonlinear Elastic ◽  
Free Edges

In this paper, nonlinear forced vibration analysis for thin rectangular plate with four free edges on nonlinear elastic foundation is researched. Based on Hamilton variation principle, the equations of nonlinear vibration motion for the thin rectangular plate under period loads on nonlinear elastic foundation are established. In the case of four free edges, the suitable expressions of trial functions satisfied all boundary conditions for the problem are proposed. Then, we convert the equations to a system of nonlinear algebraic equations by using Galerkin method and they are solved by using harmonic balance method. In the analysis of numerical computations, the effect to the amplitude-frequency characteristic curve which due to change of the structural parameters of plate、the parameters of foundation and the parameters of excitation force are discussed.

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