Dynamic response of a long case-bonded viscoelastic cylinder

Time-dependent pressures are applied in an encased viscoelastic cylinder and on the surface of the case. The resulting dynamic response of the cylinder-case system is the subject of a theoretical analysis. The viscoelastic material of the cylinder is assumed to be incompressible and a forced vibration is therefore excited without initial wave effects. The cylinder is viscoelastic in shear, showing short-time elastic behavior and delayed elasticity. The displacement, the circumferential stress, and the radial stress are investigated. If a time-dependent pressure is applied to the case, the radial bond stress at the cylinder-case interface is periodic and shows tensile peaks for high values (˜10⁴) of the ratio of Young's modulus of the shell to the rubbery shear modulus of the cylinder. The stresses are damped exponentially to the compressive quasi-static solution. Analytical solutions are presented for step loading and standard linear viscoelastic shear behavior. A numerical procedure using measured values of the relaxation function is indicated. The solutions are relevant to a compressible cylinder for times long compared to the passage-time of a dilatational wave.