Free vibrations of annular sector cantilever plates. Part 1: out-of-plane motion

An analysis of the flexural vibrations of an annular sector plate is performed by means of a variational approximation procedure. The plate is fixed on one straight edge and free on the other three. The annular plate is assumed to have polar orthotropy in the analysis, although calculations are performed only for the isotropic case. The problem is treated by first obtaining the exact solution for flexural waves in the annular sector plate by satisfying the flexural equation of motion for the plate with the circumferential edges free. In this exact solution, new radial functions are obtained from a Frِbenius type expansion. The solution results in a set of dispersion curves. A number of the resulting waves are used in what remains of the variational equation, in which all conditions occur as natural conditions. Roots of the resulting transcendental equation are calculated, which yield the eigensolutions and associated eigenfrequencies. The results compare very well with those from FEM calculation, which shows that this procedure is very accurate. It also provides an understanding in terms of the waves that make up the vibration, which is not provided by any of the other methods.