Wave Propagation in Prestressed Curved Rods

Abstract

The vibration and harmonic wave propagation in prestressed curved rods is theoretically studied. The equations of spatial elastic rods subjected to a generally deformation-dependent loading are employed and are specialized to prestressed planar circular arch equations. Torsional-lateral and extensional-flexural modes of motion of prestressed circular arches and rings are then investigated. The dispersion relations for each mode of motion are determined and are plotted for certain values of loading parameter. The loading considered in these problems consists of dead force, hydrostatic pressure, and centrally directed pressure loading.