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Sahāranpur, India

Singhal P.,PCET | Gupta A.K.,MS College
International Journal of Acoustics and Vibrations | Year: 2016

The present work analyses the vibration behaviour of non-homogeneous orthotropic visco-elastic rectangular plate of parabolically varying thickness on the basis of classical plate theory when the all edges are clamped and are subjected to linearly thermal variation. For non-homogeneity of the plate material it is assumed that the density of the plate material varies parabolically along the x-direction. For visco-elastic materials, basic elastic and viscous elements are combined. The Kelvin model for visco-elasticity is considered here, which is a combination of elastic and viscous elements connected in parallel. Using the separation of variable method, the governing differential equation has been solved. The time period and deflection corresponding to the first two modes of vibrations of clamped plates have been calculated for different values of thermal gradients, non-homogeneity constants, taper constants, and aspect ratio, with the help of Rayleigh-Ritz techniques, and are shown by graphs. Source


Gupta A.K.,MS College | Saini M.,Jv Jain College | Singh S.,Jv Jain College | Kumar R.,Jv Jain College
JVC/Journal of Vibration and Control | Year: 2014

An analysis is presented of the forced vibrations of non-homogeneous rectangular plate of variable thickness on the basis of classical plate theory. The non-homogeneity of the plate material is assumed to arise due to the variation in density which is assumed to vary linearly. The thickness of the plate also varies linearly. Approximate formulae are proposed for estimating the maximum deflection of a rectangular plate subject to a uniformly distributed harmonic lateral load. Maximum deflection for the different values of the fundamental frequency of vibration is computed for a simply supported-free- simply supported-free plate for various values of taper constant, non-homogeneity constant and aspect ratios. Results are presented in graphical form. © The Author(s) 2012 Reprints and permissions: sagepub.co.uk/ journalsPermissions.nav. Source


Gupta A.K.,MS College | Sharma P.,H.C.T.M.
JVC/Journal of Vibration and Control | Year: 2016

The aim of the present work is to study the free transverse vibrations of non-homogeneous trapezoidal plates of linear thickness variation in the x-direction under thermal gradient effect. The non-homogeneity of the plate is assumed to arise due to parabolic density variation in the y-direction. A two term deflection function has been taken for clamped-simply supported-clamped-simply supported boundary conditions. The Rayleigh-Ritz method is used to obtain a frequency equation for the first two modes of vibration. The effect of non-homogeneity constant, aspect ratios, taper constant and thermal gradient on the frequencies of non-homogeneous trapezoidal plate has been illustrated for the first two modes of vibration. Results are presented in graphical form. Confirmation of results in special cases with authors published one has also been presented. © SAGE Publications. Source


Gupta A.K.,MS College | Sharma S.,MS College
JVC/Journal of Vibration and Control | Year: 2011

In this paper, the thermal effect on vibration of orthotropic trapezoidal plate of linearly varying thickness is studied. The Rayleigh Ritz method is used to evaluate the fundamental frequencies. The deflection function is defined by the product of the equations of the prescribed continuous piecewise boundary shape. Frequency corresponding to the first two modes of vibration is calculated for the trapezoidal plate having clamped-simply supported-clamped-simply supported (C-S-C-S) edges for different values of thermal gradient, taper constant and aspect ratio. The proposed method is applied to solve orthotropic trapezoidal plate of variable thickness with C-S-C-S boundary conditions. Results are shown by figures for different values of thermal gradient, taper constant and aspect ratio for first two modes of vibrations. © 2010 The Author(s). Source


Gupta A.K.,MS College | Sharma S.,MS College
Ain Shams Engineering Journal | Year: 2013

In this paper, thermal effect on vibration of non-homogeneous orthotropic trapezoidal plate of linearly varying thickness is studied through a numerical method. Rayleigh Ritz method is used to evaluate the fundamental frequencies. The deflection function is defined by the product of the equations of the prescribed continuous piecewise boundary shape. Frequency corresponding to first two modes of vibration is calculated for the orthotropic trapezoidal plate having C-S-C-S edges for different values of thermal gradient, taper constant and aspect ratio. The proposed method is applied to solve orthotropic trapezoidal plate of variable thickness with C-S-C-S boundary conditions. Results are shown by figures for different values of thermal gradient, taper constant and aspect ratio for first two modes of vibrations. © 2012 Ain Shams University. Production and hosting by Elsevier B.V. All rights reserved. Source

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