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.

Large amplitude free vibration of simply supported antisymmetric cross-ply plates

AIAA Journal ◽  
1991 ◽  
Vol 29 (5) ◽  
pp. 784-790 ◽  
Author(s):  
Gajbir Singh ◽  
G. Venkateswara Rao ◽  
N. G. R. lyengar
Keyword(s):  
Free Vibration ◽  
Large Amplitude ◽  
Simply Supported

On Asymptotic Analysis for Large Amplitude Nonlinear Free Vibration of Simply Supported Laminated Plates

2009 ◽  
Vol 131 (5) ◽  
Author(s):  
S. K. Lai ◽  
C. W. Lim ◽  
Y. Xiang ◽  
W. Zhang
Keyword(s):  
Differential Equation ◽  
Free Vibration ◽  
Nonlinear Differential Equation ◽  
Large Amplitude ◽  
Analytical Approximation ◽  
Laminated Plates ◽  
Thin Plates ◽  
Nonlinear Free Vibration ◽  
Simply Supported ◽  
Analytical Approximations

An analytical approximation is developed for solving large amplitude nonlinear free vibration of simply supported laminated cross-ply composite thin plates. Applying Kirchhoff’s hypothesis and the nonlinear von Kármán plate theory, a one-dimensional nonlinear second-order ordinary differential equation with quadratic and cubic nonlinearities is formulated with the aid of an energy function. By imposing Newton’s method and harmonic balancing to the linearized governing equation, we establish the higher-order analytical approximations for solving the nonlinear differential equation with odd nonlinearity. Based on the nonlinear differential equation with odd and even nonlinearities, two new nonlinear differential equations with odd nonlinearity are introduced for constructing the analytical approximations to the nonlinear differential equation with general nonlinearity. The analytical approximations are mathematically formulated by combining piecewise approximate solutions from such two new nonlinear systems. The third-order analytical approximation with better accuracy is proposed here and compared with other numerical and approximate methods with respect to the exact solutions. In addition, the method presented herein is applicable to small as well as large amplitude vibrations of laminated plates. Several examples including large amplitude nonlinear free vibration of simply supported laminated cross-ply rectangular thin plates are illustrated and compared with other published results to demonstrate the applicability and effectiveness of the approach.

Using phase field and third-order shear deformation theory to study the effect of cracks on free vibration of rectangular plates with varying thickness

2020 ◽  
Vol 71 (7) ◽  
pp. 853-867
Author(s):  
Phuc Pham Minh
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Phase Field ◽  
Deformation Theory ◽  
Plate Thickness ◽  
Shear Deformation Theory ◽  
Rectangular Plates ◽  
Equilibrium Equations ◽  
Third Order ◽  
Free Vibration Frequency

The paper researches the free vibration of a rectangular plate with one or more cracks. The plate thickness varies along the x-axis with linear rules. Using Shi's third-order shear deformation theory and phase field theory to set up the equilibrium equations, which are solved by finite element methods. The frequency of free vibration plates is calculated and compared with the published articles, the agreement between the results is good. Then, the paper will examine the free vibration frequency of plate depending on the change of the plate thickness ratio, the length of cracks, the number of cracks, the location of cracks and different boundary conditions

A Study on Structural System Identification and Damage Detection for Free Vibration Response Using the Wavelet Transform

2015 ◽  
Vol 752-753 ◽  
pp. 1029-1034
Author(s):  
Asnizah Sahekhaini ◽  
Pauziah Muhamad ◽  
Masayuki Kohiyama ◽  
Aminuddin Abu ◽  
Lee Kee Quen ◽  
...  
Keyword(s):  
Free Vibration ◽  
Damage Detection ◽  
Vibration Response ◽  
Structural System ◽  
Modal Parameter ◽  
Modal Parameter Identification ◽  
Complex Morlet Wavelet ◽  
Structural System Identification ◽  
Free Vibration Response ◽  
Energy Components

This paper presents a wavelet-based method of identification modal parameter and damage detection in a free vibration response. An algorithm for modal parameter identification and damage detection is purposed and complex Morlet wavelet is chosen as an analysis wavelet function. This paper only focuses on identification of natural frequencies of the structural system. The method utilizes both undamaged and damage experiment data of free vibration response of the truss structure system. Wavelet scalogram is utilizes for damage detection. The change of energy components for undamaged and damage structure is investigated from the plot of wavelet scalogram which corresponded to the detection of damage.

Free vibration of simply supported and clamped elliptical plates

1992 ◽  
Vol 158 (2) ◽  
pp. 383-386 ◽  
Author(s):  
K.L. Prasad ◽  
A. Venkateshwar Rao ◽  
B. Nageswara Rao
Keyword(s):  
Free Vibration ◽  
Simply Supported
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