Damped Vibrations of Parabolic Tapered Non-homogeneous Infinite Rectangular Plate Resting on Elastic Foundation

In the present paper, damped vibrations of non-homogeneous infinite rectangular plate of parabolically varying thickness resting on elastic foundation has been studied. Following Lévy approach, the equation of motion of plate of varying thickness in one direction is solved by quintic spline method. The effect of damping, elastic foundation and taperness is discussed with permissible range of parameters. The frequency parameter Ω decreases as damping parameter Dk increases and it decreases faster in clamped-simply supported as compared to clamped-clamped boundary conditions. It was also observed that in the presence of damping parameter Dk the frequency parameter Ω decreases continuously with increasing value of taper parameter for both the boundary conditions but variations were found in the absence of damping parameter.