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The free vibrations of a circular plate having elastic constraints variable according to the angular co-ordinate are investigated. The non-uniform translational and rotational stiffness of the constraints are expanded in a Fourier series; it is assumed that the system presents a symmetry axis. The mode shapes are expanded in a Fourier-Bessel series by using the Rayleigh-Ritz method. The eigenfunctions of the free-edge circular plate vibrating in vacuum are assumed as admissible functions. This choice allows one to compute the potential energy of the plate using the kinetic energy of single modes of free-edge plates. The effect of the in-plane load is included and internal constraints are studied. By using the same technique, the free vibrations of a circular plate resting on an annular, non-uniform, Winkler foundation are investigated. Numerical results are given for the cases studied already, in order to validate the proposed method, and for bolted (or riveted) plates fixed by different numbers of bolts.
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