Free vibrations of annular plates of variable thickness

Abstract

The s t ructure of disks used in s team and gas turbines is frequently modeled by an elastic annular plate, whose thickness varies symmetr ica l ly with respect to the center [1]. Determination of the natural frequencies and modes of vibrations in these plates is a ra ther complex problem, the precise solution of which cannot be obtained for a thickness that varies a rb i t ra r i ly using elementary or speeiaI famil iar functions. In the case of ax isymmetr ie vibration modes and a linear thickness variation that decreases with increasing distance from the center , the problem is accurate ly solved in power ser ies [2-4], which have also been used in integrating vibration equations and in the case of a thickness that var ies parabolicalty [5]. Various approximate methods for solution of the problem of vibrations of annular plates of variable thickness were developed in [6-9], and a solution was also obtained with allowance for displacements and rotational inertia [7]. Until now, however, the l i terature has provided extremely limited numerical results of determination of the natural-vibrat ion f r e quencies of plates of variable thickness by both precise and approximate methods.