Schiavone, P.; Constanda, C. Oscillation problems in thin plates with transverse shear deformation. (English) Zbl 0785.73048 SIAM J. Appl. Math. 53, No. 5, 1253-1263 (1993). Summary: The authors present a modern theory of thin elastic plates with transverse shear deformation where the disturbance is represented by a train of harmonic waves. Dirichlet- and Neumann-type problems are formulated together with appropriate radiation conditions (in the case of the exterior domain). The paper shows that uniqueness for exterior problems is guaranteed for a range of flexural waves. In the interior problems, the presence of eigenfrequencies means that there is no general uniqueness result. The paper also indicates how corresponding results can be proved for micropolar plates. Cited in 15 Documents MSC: 74H45 Vibrations in dynamical problems in solid mechanics 74K20 Plates 74G30 Uniqueness of solutions of equilibrium problems in solid mechanics 74H25 Uniqueness of solutions of dynamical problems in solid mechanics 35J55 Systems of elliptic equations, boundary value problems (MSC2000) Keywords:bending of plates; stationary oscillations; train of harmonic waves; radiation conditions; eigenfrequencies; micropolar plates PDFBibTeX XMLCite \textit{P. Schiavone} and \textit{C. Constanda}, SIAM J. Appl. Math. 53, No. 5, 1253--1263 (1993; Zbl 0785.73048) Full Text: DOI