Adaptive Control of Nonlinear Free Vibration of Shallow Shell Using Piezoelectric Actuators

AIAA Journal ◽  
2011 ◽  
Vol 49 (3) ◽  
pp. 472-488 ◽  
Author(s):  
Minseock Park ◽  
Adam Przekop ◽  
Thongchai Phairoh ◽  
Jen-Kuang Huang ◽  
Chuh Mei
Keyword(s):  
Adaptive Control ◽  
Free Vibration ◽  
Shallow Shell ◽  
Piezoelectric Actuators ◽  
Nonlinear Free Vibration

Nonlinear Free Vibration for Cross-Ply Laminated Damaged Plates with Piezoelectric Actuators

2006 ◽  
Vol 324-325 ◽  
pp. 479-482
Author(s):  
Yu Fang Zheng ◽  
Yi Ming Fu ◽  
Kai Qi
Keyword(s):  
Free Vibration ◽  
Harmonic Balance ◽  
Piezoelectric Actuators ◽  
Laminated Plates ◽  
Governing Equations ◽  
Nonlinear Free Vibration ◽  
Response Curves ◽  
Method Of Harmonic Balance ◽  
Amplitude Frequency Response ◽  
Damage Theory

On the basis of the anisotropic damage theory and piezoelectric theory, the nonlinear free vibration governing equations for cross-ply laminated damaged plates with piezoelectric actuators are established. The Galerkin procedure furnishes an infinite system of equations for time functions which are solved by the method of harmonic balance. In the numerical results, the influences of damage parameters and piezoelectric effect on the nonlinear amplitude-frequency response curves of the laminated plates are discussed, which results reveal the inherent features about the coupled mechanics and electricity.

NONLINEAR FREE VIBRATION OF A MODERATELY THICK DOUBLY CURVED SHALLOW SHELL OF ELLIPTICAL PLAN-FORM

2009 ◽  
Vol 06 (04) ◽  
pp. 615-632 ◽  
Author(s):  
S. M. CHORFI ◽  
A. HOUMAT
Keyword(s):  
Free Vibration ◽  
Harmonic Balance ◽  
Shallow Shell ◽  
Geometrical Nonlinearity ◽  
Harmonic Balance Method ◽  
The Finite Element Method ◽  
Nonlinear Free Vibration ◽  
Mode Method ◽  
Convergence Study ◽  
Doubly Curved

The p-version of the finite element method is used in conjunction with the blending function method to investigate the nonlinear free vibration of a doubly curved shallow shell of elliptical plan-form. The effects of transverse shear deformations, rotary inertia, and geometrical nonlinearity are taken into account. The harmonic balance method is used to derive the equations of free motion. The resultant nonlinear equations are solved iteratively using the linearized updated mode method. The efficiency of the method is demonstrated through convergence study and comparison with published results. The effects of geometric parameters such as thickness, ellipse aspects, and curvatures on the backbone curves of a clamped doubly curved shallow shell of elliptical plan-form are studied. It is shown that the increase or decrease of the hardening behavior is dependent upon these parameters.

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