Large amplitude free vibration of size-dependent circular microplates based on the modified couple stress theory

2013 ◽  
Vol 71 ◽  
pp. 51-57 ◽  
Author(s):  
Yong-Gang Wang ◽  
Wen-Hui Lin ◽  
Ning Liu
Keyword(s):  
Free Vibration ◽  
Large Amplitude ◽  
Couple Stress ◽  
Couple Stress Theory ◽  
Modified Couple Stress Theory ◽  
Stress Theory ◽  
Size Dependent ◽  
Modified Couple Stress

Large Amplitude Free Vibration Analysis of Nanobeams Based on Modified Couple Stress Theory

2021 ◽  
pp. 2150129
Author(s):  
Ehsan Raeisi Estabragh ◽  
Gholam Hossein Baradaran
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Large Amplitude ◽  
Vibration Analysis ◽  
Couple Stress ◽  
Couple Stress Theory ◽  
Free Vibration Analysis ◽  
Modified Couple Stress Theory ◽  
Stress Theory ◽  
Modified Couple Stress

In this study, the large amplitude free vibration of nanobeams based on the modified couple stress theory was developed by using Total Lagrangian finite element formulation. In this study, Timoshenko beam theory has been used in free vibration analysis of nanobeams. Minimal kinematic assumptions have been used to model nanobeams. With this model, free vibration of nanobeams with small to large amplitude and with arbitrary boundary conditions can be analyzed. The numerical results obtained for free vibration based on the modified couple stress theory with small amplitude and the results obtained for free vibration with large amplitude without considering the modified couple stress theory are in good agreement with the similar results reported in previous research. Effects of the dimensionless length scale parameter, slenderness ratio, vibration amplitude and different boundary conditions on the nonlinear frequency ratio of nanobeams have been investigated. The results show the importance of considering nonlinear and size effects in the free vibration analysis of nanobeams with large amplitude.

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