LAUSR

Abstract An approach is proposed in which the form of the partial waves in the decomposition of the displacement field is chosen in such a way that boundary conditions on the outer surfaces of a layered structure are matched exactly. So found basis functions are further used to solve for the remaining boundary conditions. Explicit analytic expressions for the vibration spectrum and normalized amplitudes of a free plate in the long wavelength regime are derived and their behavior in the full space of material parameters is discussed. Thus, it is found that properties of the fundamental flexural mode change in a strongly non-monotonous way. In particular, by increasing the thickness of added layer one may observe the same propagation velocity for up to three different values of layer thicknesses ratio. Existence of an important criterion based on the relative signs taken by the amplitudes on the outer surfaces in this regime is revealed. It allows to establish a clear correspondence between symmetric and antisymmetric solutions for a single layer and those for a bilayered plate. It is suggested that the criterion is not limited to case of two layers. Branches of the spectrum are classified accordingly and their evolution from long to short wavelength is discussed. Analysis of a specific example which includes volume and surface modes (Rayleigh and Stoneley) is presented. The results demonstrate the efficiency of the proposed scheme and possible extensions are suggested.