Boundary Stabilization of Thin Elastic Plates
Author | : John E. Lagnese |
Publisher | : |
Total Pages | : 16 |
Release | : 1987 |
ISBN-10 | : OCLC:227710074 |
ISBN-13 | : |
Rating | : 4/5 (74 Downloads) |
Book excerpt: In this paper we shall consider the question of uniform stabilization of thin, elastic plates through the action of forces and moments on the edge of the plate (or on a part of the edge of the plate). Two particular plate models will be considered: The classical fourth order Kirchoff model, but incorporating rotational inertia, and the sixth order Mindlin-Timoshenko model. The difference in the two models, from a physical point of view, is that the M-T model incorporates transverse shear effects while the Kirchhoff model does not. Actually, the M-T model is a hyperbolic system three coupled second order partial differential equations in two dependent variables. The unknowns, denoted by w, psi, phi are the vertical component w of displacement and angles which are measures of the amount of transverse shear. The three equations are coupled through terms which are multiples of a factor K called the coefficient of elasticity in shear.