Abstract
The main objective of the present investigation is to study the vibration of visco-elastic parallelogram plate whose thickness varies parabolically. It is assumed that the plate is clamped on all the four edges and that the thickness varies parabolically in one direction i.e. along length of the plate. Rayleigh-Ritz technique has been used to determine the frequency equation. A two terms deflection function has been used as a solution. For visco-elastic, the basic elastic and viscous elements are combined. We have taken Kelvin model for visco-elasticity that is the combination of the elastic and viscous elements in parallel. Here the elastic element means the spring and the viscous element means the dashpot. The assumption of small deflection and linear visco-elastic properties of “Kelvin” type are taken. We have calculated time period and deflection at various points for different values of skew angles, aspect ratio and taper constant, for the first two modes of vibration. Results are supported by tables. Alloy “Duralumin” is considered for all the material constants used in numerical calculations
Highlights
The materials are being developed, depending upon the requirement and durability, so that these can be used to give better strength, flexibility, weight effectiveness and efficiency
Free vibrations of non-homogeneous circular plate of variable thickness resting on elastic foundation are discussed by Tomar, Gupta and Kumar [7]
A simple model presented here is to study the effect of parabolic thickness variation on vibration of viscoelastic parallelogram plate having clamped boundary conditions on all the four edges
Summary
The materials are being developed, depending upon the requirement and durability, so that these can be used to give better strength, flexibility, weight effectiveness and efficiency. Ansari and Sharma [4] have analyzed vibration analysis of non-homogenous circular plate of non linear thickness variation by differential quadrature method. Free vibrations of non-homogeneous circular plate of variable thickness resting on elastic foundation are discussed by Tomar, Gupta and Kumar [7]. Ansari and Sharma [9] discussed the vibration of non-homogeneous circular Mindlin plates with variable thickness. Gupta, Kumar and Gupta [13] studied the vibration of visco-elastic parallelogram plate of linearly varying thickness. A simple model presented here is to study the effect of parabolic thickness variation on vibration of viscoelastic parallelogram plate having clamped boundary conditions on all the four edges. Time period and deflection function at different point for the first two modes of vibration are calculated for various values of taper constant, aspect ratio and skew angle and results are presented in tabular form
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