Vibration Of Visco-Elastic Rectangular Plate Research Articles

Thermal Effect on Vibration of Clamped Visco-Elastic Rectangular Plate with Parabolic Thickness Variation in Both Directions

The analysis presented here is to study the effect of thermal gradient on the vibration of visco-elastic rectangular plate (having clamped boundary condition on all the four edges) of variable thickness whose thickness varies parabolically in both directions. The effect of linear temperature variation has been considered. A frequency equation of plate has been obtained by Rayleigh-Ritz technique with two terms of deflection function. The assumption of small deflection and linear visco-elastic properties of ‘Kelvin’ type are taken. Deflection and time period corresponding to the first two modes of vibrations for clamped plate have been computed for various combinations of aspect ratio, thermal constants, and taper constants. Numerical computations have been performed for an alloy ‘Duralium’ and the results obtained are depicted graphically.

Thermal effect on vibration of clamped visco-elastic rectangular plate with parabolic thickness variation in both directions

The analysis presented here is to study the effect of thermal gradient on the vibration of visco-elastic rectangular plate (having clamped boundary condition on all the four edges) of variable thickness whose thickness varies parabolically in both directions. The effect of linear temperature variation has been considered. A frequency equation of plate has been obtained by Rayleigh-Ritz technique with two terms of deflection function. The assumption of small deflection and linear visco-elastic properties of ‘Kelvin’ type are taken. Deflection and time period corresponding to the first two modes of vibrations for clamped plate have been computed for various combinations of aspect ratio, thermal constants, and taper constants. Numerical computations have been performed for an alloy ‘Duralium’ and the results obtained are depicted graphically.

Transverse vibration of viscoelastic rectangular plate with linearly varying thickness and multiple cracks

Based on the thin-plate theory and the two-dimensional viscoelastic differential constitutive relation, the differential equations of motion of the viscoelastic plate with linearly varying thickness and an arbitrary number of all-over part-through cracks are established, and the expressions of the additional rotation angle induced by the cracks are deduced. We assume that it is elastic in dilatation, but postulate the Kelvin–Voigt laws for distortion, the complex eigenvalue equations of the viscoelastic plate with linearly varying thickness and multiple cracks are derived by the differential quadrature method. The general eigenvalue equations of the viscoelastic plate with multiple cracks under different boundary conditions are calculated. The effects of various geometric parameters, dimensionless delay time and dimensionless crack parameters on the transverse vibration characteristics of a viscoelastic plate containing multiple all-over part-through cracks are analyzed.

Vibration of visco-elastic rectangular plate with linearly thickness variations in both directions

The analysis presented here is to study the effect of linear thickness variations in both directions on vibration of visco-elastic rectangular plate having clamped boundary conditions on all the four edges. Using the separation of variables method, the governing differential equation has been solved for vibration of visco-elastic rectangular plate. An approximate but quite convenient frequency equation is derived by using Rayleigh–Ritz technique with a two-term deflection function. Logarithmic decrement, time period and deflection at different points for the first two modes of vibration are calculated for various values of taper constants and aspect ratio.