Vibrations of Elastic Surface Systems Carrying Dynamic Elements

Abstract

The set of problems where shells, plates, or membranes carry discrete dynamic systems at discrete points on their surface is treated in a general manner. Interaction of each discrete dynamic system with the surface system is assumed to be in direction of the normal to the surface only. General solution equations are given. To apply these general equations to a specific problem, the eigenfunctions and eigenvalues of the surface system alone and the displacement impedances of the discrete dynamic systems at their point of attachment are required. The eigenfunction and eigenvalue equations of a system consisting of a circular cylindrical shell carrying a dynamic absorber, which is also connected with a second spring to ground, are obtained as specific examples.