Nonlinear vibration of laminated plates on a nonlinear elastic foundation

2005 ◽  
Vol 70 (1) ◽  
pp. 90-99 ◽  
Author(s):  
Rean-Der Chien ◽  
Chun-Sheng Chen
Keyword(s):  
Nonlinear Vibration ◽  
Elastic Foundation ◽  
Laminated Plates ◽  
Nonlinear Elastic Foundation ◽  
Nonlinear Elastic

scholarly journals Postbuckling and Free Nonlinear Vibration of Microbeams Based on Nonlinear Elastic Foundation

2018 ◽  
Vol 2018 ◽  
pp. 1-17 ◽  
Author(s):  
Dang Van Hieu
Keyword(s):  
Nonlinear Vibration ◽  
Elastic Foundation ◽  
Scale Parameter ◽  
Length Scale Parameter ◽  
Length Scale ◽  
Nonlinear Elastic Foundation ◽  
Material Length Scale Parameter ◽  
Material Length Scale ◽  
Nonlinear Elastic ◽  
Material Length

In this paper, post-buckling and free nonlinear vibration of microbeams resting on nonlinear elastic foundation subjected to axial force are investigated. The equations of motion of microbeams are derived by using the modified couple stress theory. Using Galerkin’s method, the equation of motion of microbeams is reduced to the nonlinear ordinary differential equation. By using the equivalent linearization in which the averaging value is calculated in a new way called the weighted averaging value, approximate analytical expressions for the nonlinear frequency of microbeams with pinned–pinned and clamped–clamped end conditions are obtained in closed-forms. Comparisons with previous solutions are showed accuracy of the present solutions. Effects of the material length scale parameter and the axial compressive force on the frequency ratios of microbeams; and effect of the material length scale parameter on the buckling load ratios of microbeams are investigated in this paper.

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