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Singhal P.,P.C.E.T. | 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.


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.


Here, thermal gradient effect on vibration of non-homogeneous orthotropic rectangular plate having bi-direction linearly thickness variations is studied. The non-homogeneity is assumed to arise due to the variation in the density of the plate material. Rayleigh Ritz method is used to evaluate the fundamental frequencies and deflection function. The two-dimensional thickness variation is taken as the Cartesian product of linear variations along the two concurrent edges of the plate. Yet the method used for the solution of present problem provides an approximate solution but it is quite convenient and authentic one. A two-term deflection function is used. Frequency corresponding to first mode of vibration is calculated for clamped plate for different values of temperature gradient, taper constants and non-homogeneity constant. In special cases, comparisons have been made with results that are available in the literature. © Springer Science+Business Media B.V. 2009.


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).


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.


Gupta A.K.,Ms College | Singhal P.,Ms College
Acta Technica CSAV (Ceskoslovensk Akademie Ved) | Year: 2013

The effect of non-homogeneity on thermally induced vibration of orthotropic visco-elastic rectangular plate of linearly varying thickness is presented. The plate is characterized by the clamped boundary conditions on all the four edges. For visco-elastic materials, basic elastic and viscous elements are combined. We have assumed the Kelvin model for visco-elasticity, which is a combination of elastic and viscous elements connected in parallel. For non-homogeneity of the plate material, density is assumed to vary parabolically. Using the separation of variables method, the governing differential equation has been solved for vibration of non-homogeneous orthotropic visco-elastic rectangular plate. An approximate frequency equation is derived by using Rayleigh-Ritz technique with a two-term deflection function. Results are calculated for time period and deflection at different points, for the first two modes of vibration, for various values of temperature gradients, non-homogeneity constant, taper constant and aspect ratio and shown by graphs. © 2013 Institute of Thermomechanics AS CR, v.v.i.


Gupta A.K.,MS College | Sharma P.,MS College
JVC/Journal of Vibration and Control | Year: 2012

Plates of variable thickness are widely used in modern technology nowadays in various engineering fields, such as marine engineering, aeronautical fields, nuclear reactors etc. The present paper is a study of linear thermal gradient on the vibration of trapezoidal plates with parabolically varying thickness. The Rayleigh Ritz technique is used to get the required frequency equation. In the present investigation, the effect of various factors, i.e. thermal gradient, taper constant and aspect ratio are studied to calculate the frequencies corresponding to the first two modes of vibration and are presented in tabular and graphical form. © 2010 The Author(s) Reprints and permissions.


Gupta A.K.,Ms College | Mamta,Ms College
International Journal of Acoustics and Vibrations | Year: 2014

The fourth order differential equation, governing the transverse motion of an elastic rectangular plate of a nonlinear thickness variation with a thermal gradient, has been analysed on the basis of classical plate theory employing the Quintic spline interpolation technique. An algorithm for computing the solution of this differential equation is presented for the case of equal intervals. The effect of the thermal gradient, together with taper constants on the natural frequencies of vibration, is illustrated for the first three modes of vibration for C-S-C-S and S-S-S-S rectangular plates.


De K.K.,Ms College | Pal R.,Panjab University | Kumar C.N.,Panjab University | Raju T.S.,IISER
2015 International Conference on Microwave, Optical and Communication Engineering, ICMOCE 2015 | Year: 2015

Using phase amplitude ansatz method and standard linear stability analysis, we have investigated modulational instability (MI) for the ultrashort pulse propagation in cascaded quadratic-cubic-quintic nonlinear media. Propagation of wave has been described beyond the slowly varying envelope approximation (SVEA). Controlling the generation of frequency side-bands and hence desired pulse, through engineering of different parameters are being explored. © 2015 IEEE.


The present paper deals with the free transverse vibration of orthotropic thin trapezoidal plate of parabolically varying thickness in x-direction subjected to linear temperature distribution in x-direction through a numerical method. The deflection function is defined by the product of the equations of the prescribed continuous piecewise boundary shape. Rayleigh-Ritz method is used to evaluate the fundamental frequencies. The equations of motion, governing the free transverse vibrations of orthotropic thin trapezoidal plates, are derived with boundary condition CSCS. Frequency corresponding to the first two modes of vibration is calculated for the orthotropic thin trapezoidal plate having CSCS edges for different values of thermal gradient, taper constant, and aspect ratio. The proposed method is applied to solve orthotropic thin 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 the first two modes of vibrations. Copyright © 2014 A. K. Gupta and S. Sharma.

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