P. Schiavone et C. Constanda, OSCILLATION PROBLEMS IN THIN PLATES WITH TRANSVERSE-SHEAR DEFORMATION, SIAM journal on applied mathematics, 53(5), 1993, pp. 1253-1263
In this paper, the authors present a modern theory of thin elastic pla
tes with transverse shear deformation where the disturbance is represe
nted by a train of harmonic waves. Dirichlet- and Neumann-type problem
s are formulated together with appropriate radiation conditions (in th
e case of the exterior domain). The paper shows that uniqueness for ex
terior problems is guaranteed fora range of flexural waves. In the int
erior problems, the presence of eigenfrequencies means that there is n
o general uniqueness result. The paper also indicates how correspondin
g results can be proved for micropolar plates.