Vibration of variable thickness plates with edges elastically restrained against translation and rotation

The vibration analysis of variable thickness plates in one direction with edges elastically restrained against both rotation and translation is investigated using the finite strip transition matrix technique. The boundary conditions in the variable thickness direction are satisfied identically and the boundary conditions in the other direction are approximated. The validity of the purposed technique has been established through convergence analysis and comparison studies. In all cases considered, excellent agreement with other results from literature has been obtained. The effect of the elastic restraint coefficients is studied and the results are illustrated as three dimensional surface contours for two opposite edges (simply supported) and in tabulated form for two opposite edges (clamped). In both cases, the other two edges are elastically restrained against both translation and rotation. Also, the effect of taper ratio variation for such plates is included.