Axi-symmetric dynamic response of circular plates with arbitrary elastic boundary restraints

The dynamic response of circular plates to axi-symmetric time-dependent loads is studied. The plate is analyzed according to classical plate theory, neglecting rotatory inertia and shear strains. The solution is obtained for a plate with axi-symmetric but arbitrary linear elastic restraints at the outer boundary. The edge restraints are with respect to both rotational and transverse motions. Particular attention is directed to a study of the effect of the transverse restraint on the maxima of the response. As a practical example, numerical results are presented for a plate subjected to an N-shaped pressure wave resulting from a sonic boom.