On Saint-Venant's principle in linear elastodynamics

✍ Scribed by S. Chirită; R. Quintanilla

• Publisher: Springer Netherlands
• Year: 1996
• Tongue: English
• Weight: 665 KB
• Volume: 42
• Category: Article
• ISSN: 0374-3535
• DOI: 10.1007/bf00041790

✦ Synopsis

We investigate the spatial behaviour of the steady state and transient elastic processes in an anisotropic elastic body subject to nonzero boundary conditions only on a plane end. For the transient elastic processes, it is shown that at distance x3 > ct from the loaded end, (c is a positive computable constant and t is the time), all the activity in the body vanishes. For x3 < ct, an appropriate measure of the elastic process decays with the distance from the loaded end, the decay rate of end effects being controlled by the factor (1 -~). Next, it is shown that for isotropic materials, in the case of a steady state vibration, an analogue of the Phragm6n-LindelOf principle holds for an appropriate cross-sectional measure. One immediate consequence is that in the class of steady state vibrations for which a quasi-energy volume measure is bounded, this measure decays at least algebraically with the distance from the loaded end.