Periodic excitation of a finite linear viscoelastic solid

Abstract

The response of a finite three-dimensional standard linear viscoelastic solid to periodic excitation is investigated. The theory is specialized for a circular cylindrical body that is bonded to a rigid base at one end and shaken by a prescribed oscillation of a circular rigid plate that is bonded concentrically to the other end. A practical relevance of the theory is the design of vibration absorbers that are made of blocks of viscoelastic materials. Four types of motion of the driving plate are treated: (1) a simple harmonic translation of the plate perpendicular to its plane; (2) an angular oscillation of the plate about its normal axis of symmetry; (3) a simple harmonic translation of the plate in its plane; and (4) an angular oscillation of the plate about a diameter. The theory provides the displacements, stresses, and natural frequencies of the body for the four types of motion. In addition, the mean power input and driving force or driving moment applied to the plate are obtained. Computer programs have been written for the solutions of finite difference approximations of the governing equations. Sample results of the computations are included.