scholarly journals Large amplitude free vibration of magnetoelectroelastic curved panels

2016 ◽  
Vol 23 (6) ◽  
pp. 2606-2615 ◽  
Author(s):  
Alireza shooshtari ◽  
Soheil Razavi
Keyword(s):  
Free Vibration ◽  
Large Amplitude ◽  
Curved Panels

FREE VIBRATION OF CURVED PANELS WITH CUTOUTS

1997 ◽  
Vol 200 (2) ◽  
pp. 227-234 ◽  
Author(s):  
B. Sivasubramonian ◽  
A.M. Kulkarni ◽  
G. Venkateswara Rao ◽  
A. Krishnan
Keyword(s):  
Free Vibration ◽  
Curved Panels

FREE VIBRATION OF LONGITUDINALLY STIFFENED CURVED PANELS WITH CUTOUT

1999 ◽  
Vol 226 (1) ◽  
pp. 41-55 ◽  
Author(s):  
B. SIVASUBRAMONIAN ◽  
G.V. RAO ◽  
A. KRISHNAN
Keyword(s):  
Free Vibration ◽  
Curved Panels

Large Amplitude Forced Vibration Analysis of Stiffened Plates under Harmonic Excitation

2012 ◽  
pp. 26-61
Author(s):  
Anirban Mitra ◽  
Prasanta Sahoo ◽  
Kashinath Saha
Keyword(s):  
Free Vibration ◽  
Forced Vibration ◽  
Large Amplitude ◽  
Vibration Analysis ◽  
Mathematical Formulation ◽  
Free Vibration Analysis ◽  
Harmonic Excitation ◽  
Stiffened Plates ◽  
Backbone Curve ◽  
Forced Vibration Analysis

Large amplitude forced vibration behaviour of stiffened plates under harmonic excitation is studied numerically incorporating the effect of geometric non-linearity. The forced vibration analysis is carried out in an indirect way in which the dynamic system is assumed to satisfy the force equilibrium condition at peak excitation amplitude. Large amplitude free vibration analysis of the same system is carried out separately to determine the backbone curves. The mathematical formulation is based on energy principles and the set of governing equations for both forced and free vibration problems derived using Hamilton’s principle. Appropriate sets of coordinate functions are formed by following the two dimensional Gram-Schmidt orthogonalization procedure to satisfy the corresponding boundary conditions of the plate. The problem is solved by employing an iterative direct substitution method with an appropriate relaxation technique and when the system becomes computationally stiff, Broyden’s method is used. The results are furnished as frequency response curves along with the backbone curve in the dimensionless amplitude-frequency plane. Three dimensional operational deflection shape (ODS) plots and contour plots are provided in a few cases.

Free Vibration of a Large-Amplitude Deflected Plate—Reexamination by the Dynamical Systems Theory

1986 ◽  
Vol 53 (3) ◽  
pp. 633-640 ◽  
Author(s):  
J. Lee
Keyword(s):  
Free Vibration ◽  
Large Amplitude ◽  
Invariant Tori ◽  
Plate Thickness ◽  
Standard Technique ◽  
Simply Supported ◽  
Nonlinear Plate ◽  
Power Spectral ◽  
Mode Truncation ◽  
Energy Components

For a simply supported large-amplitude deflected plate, Fourier expansion of displacement reduces the nonlinear plate equation to a system of infinitely coupled modal equations. To close off this system, we have suppressed all but the four lowest-order symmetric modes. In the absence of damping and forcing, the four-mode truncation can be recasted into a Hamiltonian of 4 DOF. Hence, the free vibration of nonlinear plate can be investigated by the standard technique of Hamiltonian systems. It has been found that subsystems of 2 DOF are practically stable in that the invariant tori remain on a smooth surface up to total energy of 1000, at which modal displacements can be 40 times the plate thickness. On the other hand, the trajectory of 4 DOF system develops chaos at a much lower energy value of 76, corresponding to modal displacements twice the plate thickness. This has been evidenced by many spikes in the power spectral density of displacement time-series and an erratic pattern that modal energy components cut through an energy sphere.

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