D. V. Bambill, C. A. Rossil, P. A. A. Laura and R. E. Rossi, “Transverse Vibrations of an Orthotropic Rectangular Plate of Linearly Varying Thickness and with a Free Edge,” Journal of Sound and Vibration, Vol. 235, No. 3, 2000, pp. 530-538.

has been cited by the following article:

• TITLE: Effect of Non-Homogeneity on Thermally Induced Vibration of Orthotropic Visco-Elastic Rectangular Plate of Linearly Varying Thickness

  AUTHORS: Arun Kumar Gupta, Pooja Singhal

  KEYWORDS: Non-Homogeneous, Orthotropic, Visco-Elastic, Variable Thickness, Rectangular Plate, Vibration, Thermal Gradient

  JOURNAL NAME: Applied Mathematics, Vol.1 No.4, October 29, 2010

  ABSTRACT: The analysis presented here is to study the effect of non-homogeneity on thermally induced vibration of orthotropic visco-elastic rectangular plate of linearly varying thickness. Thermal vibrational behavior of non-homogeneous rectangular plates of variable thickness having clamped boundary conditions on all the four edges is studied. For non–homogeneity of the plate material, density is assumed to vary linearly in one direction. Using the method of separation of variables, the governing differential equation is solved. An approximate but quite convenient frequency equation is derived by using Rayleigh-Ritz technique with a two-term deflection function. Time period and deflection at different points for the first two modes of vibration are calculated for various values of temperature gradients, non- homogeneity constant, taper constant and aspect ratio. Comparison studies have been carried out with non-homogeneous visco-elastic rectangular plate to establish the accuracy and versatility.