Sorokin S.

The intended talk is concerned with applicability ranges of the three theories (Kirchhoff theory, Timoshenko theory and elasto-dynamics) to describe time harmonic behaviour of elastic plates with and without heavy fluid loading. Both the free wave propagation in an unbounded plate and the eigenfrequency spectra of plates of finite length are addressed. Although the case of a plate without fluid loading might be regarded as a classical one, some recent publications suggest that there still is an ambiguity in interpretation of, for example, ‘the second Timoshenko spectrum’ and of boundary conditions formulated in Timoshenko theory. To gain a physical insight into the origin of such a misinterpretation and to clarify the subject, the problem of determination of eigenfrequencies is put into the context of analysis of dispersion curves predicted by Timoshenko theory and by solution of the problem in elasto-dynamics. For consistency, the well known issue of validity of Kirchhoff model is also addressed. The findings for an elementary case of the absence of heavy fluid loading are compared with those in the case of a plate with heavy fluid loading. The location of dispersion curves predicted by the three theories (Kirchhoff theory, Timoshenko theory, elasto-dynamics) with fluid-structure interaction effects taken into account is compared with each other. Therefore, validity ranges of the former two are estimated. Some useful observations are made and their physical interpretation is given. To the best of the author’s knowledge, this aspect has not yet been highlighted in the literature. The role of fluid’s compressibility is also explained.