THE STATE-VECTOR APPROACH TO THE WAVE AND POWER FLOW-ANALYSIS OF THE FORCED VIBRATIONS OF A CYLINDRICAL-SHELL .1. INFINITE CYLINDERS IN VACUUM

The vibration induced by a time harmonic point excitation on an elastic circular cylindrical shell in vacuum and the power flow associated with it are analyzed by using a state vector technique. The forced vibration of the shell is identified by integrating a system of first-order differential equations satisfied by the state vector having ten components, five of them representing forces and moment resultants, and the other five representing linear and angular velocities at a shell location. The solution is expressed as a linear combination of "waveguide modes," solutions of the source-free problem, periodic in the circumferential coordinate, which are either attenuating or propagating in the longitudinal direction. The shell model here used is based on the assumptions of a negligible normal radial stress and of a velocity vector varying linearly within the shell thickness and includes shear deformation and rotary inertia effects. The shell two-dimensional (2-D) intensity vector has a simple expression in terms of the components of the state vector. Propagating modes having different azimuthal numbers are orthogonal; the total power flow through the shell cross section is the sum of the individual power flows associated with each waveguide mode. Several numerical examples of vibrational velocity response to point forces and uniform rings of forces, having different directions, are presented. For a point force the longitudinal power flow associated with combinations of waveguide modes is calculated in the frequency range from (close to) zero to above the first ring resonance. The intensity vector is also calculated at various points of the shell.