Natural frequencies of stepped thickness rectangular plates

This paper presents the natural frequencies of stepped thickness square and rectangular plates together with the mode shapes of vibration. The transverse deflection of a stepped thickness plate is written in a series of the products of the deflection functions of beams parallel to the edges satisfying the boundary conditions, and the frequency equation of the plate is derived by the energy method. By use of the frequency equation, the natural frequencies (the eigenvalues of vibration) and the mode shapes are calculated numerically in good accuracy for square and rectangular plates with edges simply supported or elastically restrained against rotation, having square, circular or elliptical stepped thickness, from which the effects of the stepped thickness on the vibration are studied.