ABSTRACT
This chapter deals with time-dependent bending of plates with transverse shear deformation. After a brief discussion of preliminary concepts, the formulation of the problem is presented. The chapter shows the formulation of classical dynamic problems with Dirichlet and Neumann boundary conditions for a smooth contour. Then, it focuses on the solvability of the variational problems. The proofs for the interior problems are based on the coerciveness and continuity of a+(u, v) in H°1,p(S+). The problems are then reduced to equations whose operators, by Rellich’s theorem, are compact, and Fredholm theory is applied. The problems are reduced to equations with selfadjoint nonnegative operators, on which spectral arguments are used. Finally, the chapter shows the integral representation of solutions. Here, the properties of the dynamic analogues of the Poincaré-Steklov operators, the continuity and injectivity of the boundary integral operators, and density arguments are made use of.
