Waves in a cylindrical shell with a viscous fluid

The paper considers the propagation property of torsional waves and longitudinal and transverse waves in a viscoelastic cylindrical shell which is infinite in length and contains a viscous fluid. The amplitudes of oscillations are considered to be small, which allows us to record the basic relationships of the membrane and fluid in the linear theory of continuum mechanics. Having performed some uncomplicated operations, we obtain a system of first order differential equations with complex coefficients, which can be solved by combining the orthogonal shooting method with Muller's method in complex arithmetic. Numerical results for complex values of the phase velocity of the wave number are obtained.