VARIATIONAL PRINCIPLES IN DYNAMIC THERMOVISCOELASTICITY
Dual variational principles for steady state wave propagation in three dimensional thermoviscoelastic media are presented. The first one, for the equations of motion, involves only the complex displacement function. The second principle is for the energy equation. The specialized versions of these principles in two-dimensional polar coordinates and then in one dimension are obtained. A one-dimensional example, that of wave propagation in a thermoviscoelastic rod insulated on its lateral surface and driven by a sinusoidal stress at one end, is solved using the Rayleigh-Ritz method. The displacement and temperature functions are expressed as series of polynomials. Successive approximations for the solution are compared with a solution obtained by a method of finite differences, and an estimate of the degree of accuracy as a function of the number of terms taken in the series is obtained. It is found that that as long as the spatial distribution of stress and temperature are sufficiently smooth, rapid convergence to the correct solution is obtained. If the stress is a rapidly oscillating function of the distance along the rod, polynomials are no longer efficient and other test functions must be chosen.
Stanford University PressStanford, CA United States
- Mukherjee, S
- Publication Date: 1972-4
- Features: References;
- Pagination: 28 p.
- TRT Terms: Finite differences; Thermal stability; Thermal stresses; Viscoelasticity
- Subject Areas: Marine Transportation; Materials;
- Accession Number: 00035635
- Record Type: Publication
- Source Agency: Ship Structure Committee
- Files: TRIS
- Created Date: Mar 19 1973 12:00AM