J. S. Tomar, D. C. Gupta and V. Kumar, “Free Vibrations of Non-Homogeneous Circular Plate of Variable Thickness Resting on Elastic Foundation,” Journal of Engineering Design, Vol. 1, No. 3, 1983, pp. 49-54.

has been cited by the following article:

• TITLE: Vibration of Visco-Elastic Parallelogram Plate with Parabolic Thickness Variation

  AUTHORS: Arun Kumar Gupta, Anuj Kumar, Yogesh Kumar Gupta

  KEYWORDS: Vibration, Parallelogram Plate, Visco-Elastic Mechanics, Parabolic Thickness, Aspect Ratio

  JOURNAL NAME: Applied Mathematics, Vol.1 No.2, July 22, 2010

  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