Large-amplitude free vibration of tapered hinged beams

AIAA Journal ◽  
1978 ◽  
Vol 16 (1) ◽  
pp. 88-90 ◽  
Author(s):  
Gangan Prathap ◽  
T. K. Varadan
Keyword(s):  
Free Vibration ◽  
Large Amplitude ◽  
Hinged Beams

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.

Simple Formula to Study the Large Amplitude Free Vibrations of Beams and Plates

2008 ◽  
Vol 75 (1) ◽  
Author(s):  
G. Venkateswara Rao ◽  
K. Meera Saheb ◽  
G. Ranga Janardhan
Keyword(s):  
Free Vibration ◽  
Large Amplitude ◽  
Simple Formula ◽  
Space Variable ◽  
Linear Time ◽  
Amplitude Ratio ◽  
Compressive Load ◽  
Maximum Amplitude ◽  
Free Vibrations ◽  
Structural Members

A simple formula to study the large amplitude free vibration behavior of structural members, such as beams and plates, is developed. The nonlinearity considered is of von Karman type, and after eliminating the space variable(s), the corresponding temporal equation is a homogeneous Duffing equation. The simple formula uses the tension(s) developed in the structural members due to large deflections along with the corresponding buckling load obtained when the structural members are subjected to the end axial or edge compressive load(s) and are equal in magnitude of the tension(s). The ratios of the nonlinear to the linear radian frequencies for beams and the nonlinear to linear time periods for plates are obtained as a function of the maximum amplitude ratio. The numerical results, for the first mode of free vibration obtained from the present simple formula compare very well to those available in the literature obtained by applying the standard analytical or numerical methods with relatively complex formulations.

Large Amplitude Free Vibration of Shallow Spherical Shell on a Pasternak Foundation

1993 ◽  
Vol 115 (1) ◽  
pp. 70-74 ◽  
Author(s):  
D. N. Paliwal ◽  
V. Bhalla
Keyword(s):  
Free Vibration ◽  
Spherical Shell ◽  
Large Amplitude ◽  
Free Vibrations ◽  
Numerical Results ◽  
Shallow Spherical Shell ◽  
Pasternak Foundation ◽  
New Approach ◽  
Foundation Parameters ◽  
Clamped Edges

Large amplitude free vibrations of a clamped shallow spherical shell on a Pasternak foundation are studied using a new approach by Banerjee, Datta, and Sinharay. Numerical results are obtained for movable as well as immovable clamped edges. The effects of geometric, material, and foundation parameters on relation between nondimensional frequency and amplitude have been investigated and plotted.

Sign in / Sign up

Export Citation Format

Share Document