Nonlinear free vibration analysis of generic coupled induced strain actuated piezo-laminated beams

2008 ◽  
Vol 72 (3) ◽  
pp. 153-162 ◽  
Author(s):  
K. Jayakumar ◽  
D. Yadav ◽  
B. Nageswara Rao
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Laminated Beams ◽  
Nonlinear Free Vibration

scholarly journals Nonlinear Free Vibration Analysis of Axisymmetric Polar Orthotropic Circular Membranes under the Fixed Boundary Condition

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Zhoulian Zheng ◽  
Jianjun Guo ◽  
Weiju Song ◽  
Xiaoting He ◽  
Faming Lu ◽  
...  
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Circular Membrane ◽  
Nonlinear Free Vibration ◽  
Frequency Method ◽  
Initial Displacement ◽  
Small Deflection ◽  
Deflection Theory ◽  
Polar Orthotropic

This paper presents the nonlinear free vibration analysis of axisymmetric polar orthotropic circular membrane, based on the large deflection theory of membrane and the principle of virtual displacement. We have derived the governing equations of nonlinear free vibration of circular membrane and solved them by the Galerkin method and the Bessel function to obtain the generally exact formula of nonlinear vibration frequency of circular membrane with outer edges fixed. The formula could be degraded into the solution from small deflection vibration; thus, its correctness has been verified. Finally, the paper gives the computational examples and comparative analysis with the other solution. The frequency is enlarged with the increase of the initial displacement, and the larger the initial displacement is, the larger the effect on the frequency is, and vice versa. When the initial displacement approaches zero, the result is consistent with that obtained on the basis of the small deflection theory. Results obtained from this paper provide the accurate theory for the measurement of the pretension of polar orthotropic composite materials by frequency method and some theoretical basis for the research of the dynamic response of membrane structure.

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