ON SAINT-VENANTS PRINCIPLE IN LINEAR ELASTODYNAMICS

We investigate the spatial behaviour of the steady state and transient elastic processes in an anisotropic elastic body subject to nonzero b oundary conditions only on a plane end. For the transient elastic proc esses, it is shown that at distance x(3) > ct from the loaded end, (c is a positive computable constant and t is the time), all the activity in the body vanishes. For x(3) < ct, an appropriate measure of the el astic process decays with the distance from the loaded end, the decay rate of end effects being controlled by the factor (1 - x3/ct). Next, it is shown that for isotropic materials, in the case of a steady stat e vibration, an analogue of the Phragmen-Lindelof principle holds for an appropriate cross-sectional measure. One immediate consequence is t hat in the class of steady state vibrations for which a quasi-energy v olume measure is bounded, this measure decays at least algebraically w ith the distance from the loaded end.