Analysis of solid elastic cylinders with internal losses using complete sets of functions

A method to determine the response of a solid, elastic, isotropic cylinder with internal losses and arbitrary length to radius ratio to excitations acting on its surface is presented. The method is based on the use of complete sets of functions and the response to arbitrary excitations can be analysed. It is illustrated for axisymmetric excitations that are anti-symmetric with respect to the plane midway between the ends of the cylinder. Excitations that are symmetric have been considered earlier. [D.D. Ebenezer et al., Forced vibrations of solid elastic cylinders, Journal of Sound and Vibration 282 (2005) 991–1007]. All components of displacement and stress are expressed as a sum of two infinite series that contain terms that are complete in the axial and radial direction, respectively. Therefore, arbitrary boundary conditions can be satisfied. In lossless cylinders, for each chosen set, there are difficulties at those frequencies at which certain functions become zero. Some other complete set of functions can be used at these frequencies. However, this difficulty does not arise for cylinders with losses. Two different sets are used to compute the resonance frequencies of lossless cylinders. The responses of cylinders with internal losses to uniform and concentrated excitations on the flat and curved surfaces are also presented to illustrate the approach. They are in good agreement with results obtained using ATILA—a finite element software package.