Forced Transverse Vibration of a Solid Viscoelastic Cylinder Bonded to a Thin Casing

Abstract

The amplitude versus frequency-response spectra of stress and displacement components within a solid viscoelastic cylinder bonded to a thin elastic casing are obtained when arbitrary normal and tangential stresses are applied to the outer surface of the casing. Special consideration is given to assemblies whose cores are made either of a Voigt material or a Maxwell material. A quantitative comparison of the bond stress amplitude spectrum at the lowest circumferential wave number reveals for both Voigt and Maxwell cores, and for small values of retardation time and relaxation time, respectively, that the amplitude ratio between the radial bond stress and the lateral pressure decreases with increasing values of the time constant. As the time constants get larger, the resonant amplitude increases for the Maxwell material, and decreases for the Voigt material. The Voigt core essentially behaves like an elastic solid at small values of its retardation time, and like a viscous fluid at large values of its retardation time. The Maxwell core essentially behaves like a nonviscous fluid at small values of its relaxation time and like an elastic solid at large values of its relaxation time.