Drgania i Zginanie Płyt Kołowych o Zmiennej Sztywności

In this paper consideration is given to the problem of bending and vibration of a circular isotropic plate with small bendings and circular-symmetrically varying mass and rigidity of bending. Plates freely supported and fixed along the edge are also considered, together with plates with a free edge subjected to an arbitrary load harmonically varying with time. Further, the method of procedure with inhomogeneous boundary conditions is described, and the solution is generalized for a plate with arbitrarily variable rigidity and mass in the case of free support along the edge.
The solution of the differential equation for vibration and bending of the circular plate is given by the double Fourier-Bessel series, based on a set of eigenfunctions of the differential equation for the free vibrations of a uniform circular plate with constant rigidity of bending, which is a product of the cosine function and a linear combination of the Bessel functions of the first kind. Using the orthogonalization method the solution of the problem was brought to an infinite set of algebraic nonhomogeneous linear equations. Solution of this set gives the coefficients of the Fourier-Bessel series. The solution obtained may in a simple manner be reduced to the known forms in the case of a uniform plate with constant rigidity. Concrete examples are given, illustrating the practical application of the general solution presented.