Plate and Rod Vibrations With Initial Stress

The influence of a homogeneous state of initial stress on the frequency of three-dimensional vibrations of plates and rods is considered. A linear constitutive relation is used and only terms to first power of initial stress are retained in all results. General frequency equations are found and various limiting cases are considered. Membrane and string tension terms appear in the bending modes indicating possible instabilities. In all other limiting cases, frequencies are modified only slightly by the presence of initial stress.