Nonlinear Free Vibration of a Cable Against a Straight Obstacle

2002 ◽  
Author(s):  
Seon Han ◽  
Mark Grosenbaugh
Keyword(s):  
Free Vibration ◽  
Elastic Foundation ◽  
Nonlinear Effect ◽  
Penalty Method ◽  
Transverse Displacement ◽  
Cable Model ◽  
Nonlinear Free Vibration

The purpose of this study is to investigate the nonlinear effect of gravity on the free vibration of a cable against a straight obstacle. The cable model is expressed in terms of nonlinearly coupled transverse and axial displacements. The penalty method is used to simulate the obstacle, which is equivalent to inserting a stiff elastic foundation. The first symmetric frequencies are obtained when the depth of the obstacle is 1/2 and 1/3 of the initial transverse displacement. The effects of varying amplitude and equilibrium curvature are investigated.

Free Vibration and Buckling Analysis of Functionally Graded Plates Resting on Elastic Foundation Using Higher Order Theory

2018 ◽  
Vol 18 (04) ◽  
pp. 1850049 ◽  
Author(s):  
Smita Parida ◽  
Sukesh Chandra Mohanty
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Elastic Foundation ◽  
Volume Fraction ◽  
Plate Theory ◽  
Higher Order ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Transverse Displacement ◽  
Pasternak Elastic Foundation

This paper deals with the free vibration and buckling analysis of functionally graded material (FGM) plates, resting on the Winkler–Pasternak elastic foundation. The higher order shear deformation plate theory (HSPT) is adopted for the realistic variation of transverse displacement through the thickness, using the power law distribution to describe the variation of the material properties. Both the effects of shear deformation and rotary inertia are considered. In the present model, the plate is discretised into [Formula: see text] eight noded serendipity quadratic elements with seven nodal degrees of freedom (DOFs). The validation study is carried out by comparing the calculated values with those given in the literature. The effects of various parameters like the Winkler and Pasternak modulus coefficients, volume fraction index, aspect ratio, thickness ratio and different boundary conditions on the behaviour of the FGM plates are studied.

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