Thermo-Dynamics of Plates and Shells [Paperback]

This monograph is devoted to nonlinear dynamics of thin plates and shells with thermosensitive excitation. Because of the variety of sizes and types of mathematical models in current use, there is no prospect of solving them analytically. However, the book emphasizes a rigorous mathematical treatment of the obtained differential equations, since it helps efficiently in further developing of various suitable numerical algorithms to solve the stated problems.

The present monograph is devoted to nonlinear dynamics of thin plates and shells with termosensitive excitation. Since the investigated mathematical models are of di?erent sizes (two- and three-dimensional di?erential equation) and di?erent types (di?erential equations of hyperbolic and parabolic types with respect to spatial co- dinates), there is no hope to solve them analytically. On the other hand, the proposed mathematical models and the proposed methods of their solutions allow to achieve more accurate approximation to the real processes exhibited by dynamics of shell (plate) - type structures with thermosensitive excitation. Furthermore, in this mo- graph an emphasis is put into a rigorous mathematical treatment of the obtained di?erential equations, since it helps e?ciently in further developing of various su- able numerical algorithms to solve the stated problems. It is well known that designing and constructing high technology electronic - vices, industrial facilities, ?ying objects, embedded into a temperature ?eld is of particular importance. Engineers working in various industrial branches, and part- ularly in civil, electronic and electrotechnic engineering are focused on a study of stress-strain states of plates and shells with various (sometimes hybrid types) da- ing along their contour, with both mechanical and temperature excitations, with a simultaneous account of heat sources in?uence and various temperature con- tions. Very often heat processes decide on stability and durabilÃb