The paper addresses the wave motions in an unbounded sandwich plate with and without heavy fluid loading in a plane problem formulation. A plate is composed by two identical isotropic skin plies and by an isotropic core ply. Several alternative theories for stationary dynamics of such a plate are derived, including a formulation in the framework of a theory of elasticity applied for a core ply. The 'in-phase' and the 'anti-phase' wave motions (with respect to transverse deflections of skins) of a sandwich plate are analysed independently upon each other. Dispersion curves obtained by a use of the 'elementary' theories are compared with those obtained by a use of the 'exact' theory (which involves a theory of elasticity in description of the wave motion in a core ply) for a plate without fluid loading. It is shown that these simplified models are capable to give a complete and accurate description of all propagating waves in not too high frequency range, which is sufficient in practical naval and aerospace engineering. In the case of heavy fluid loading, similar analysis is performed for the 'anti-phase' wave motions of a plate. Two simplified theories as well as the 'exact' one are extended to capture the fluid loading effects. A good agreement between the results obtained in the 'elementary' and the 'exact' problem formulations is demonstrated. The role of fluid's compressibility in generation of propagating waves in a sandwich plate is explored. It is shown that whereas analysis of the wave motions in the case of an incompressible fluid predicts an existence of two propagating waves, only one such a wave exists when a fluid is sufficiently compressible. The threshold magnitude of the ratio of a sound speed in an acoustic medium to a sound speed in a skin's material is found, which separates these two regimes of wave motions for a given set of parameters of the sandwich plate composition.
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