Elastic waves in a medium with a block structure

Abstract

In [i, 2], the propagation of pulses and vibrations in elastic media of plecewise-homogeneous structure was considered, using one-dimenslonal wave equations to describe the motion of structural elements. A series of features which are present in nonsteady processes in composite systems of regular structure end disappear in the equivalent homogeneous models of the long-wave approximation have been discovered.One-dlmenslonal models, as used in [i, 2], are suitable for the description of the dynamic state of the medium under the action of real perturbation sources of special form, for which the direct wave can be regarded as plane.Below, the wavegulde properties of a medium of block structure is analyzed on the basis of a two-dimensional model (plane formulation): the blocks --rigid bodies of rectangular cross section --interact through intervening elastic layers. In the case of antiplane deformation, an analogous structure was considered in [3], where the steady problem of semiinfinlte-crack motion in the layer between blocks was investigated.

Resonant waves and localization phenomena in lattices

“…(b) Three-layered package (S = 3). In the standing mode with the second frequency ω 2 = 4 + γ , the inner layer remains immobile, while the two outer layers oscillate in contra-phase with identical (in absolute value) magnitudes: the ratio of amplitudes (u m,n,1 /u m,n,2 /u m,n,3 (20,20,3) are depicted in figure 4 (there Q 1 = 3 sin ω 2 t and Q 2 = Q 3 = 0, where the factor 3 is set in Q 1 for easy comparison of quantitative results with those obtained for the single lattice).…”

“…To the best of the authors' knowledge, a dynamic anisotropy of transient wave patterns in combination with resonant-like process was originally observed in [20], where the response of structures modelling block rock massifs to the harmonic excitations was numerically studied. There, an unexpected result was detected in the SCL: the action of the frequency of the point harmonic force that is resonant for the MSL results in the development of growing oscillations in certain selected directions, while the oscillations in other directions are practically locked into the source vicinity.…”

Wave localization in stratified square-cell lattices: The antiplane problem

“…Subsequently, a set of nonstationary dynamic problems was analyzed by united numerical and analytical approaches allowing steady-and unsteady-state processes to be simultaneously studied (see, e.g., [8][9][10]18] related to 1D problems and [20][21][24][25][26][27][28][29][30] -to 2D problems).…”

Propagation of a low-frequency wave component in a model of a block medium

“…The discrete structure of the material at various scale levels was taken into account in the solution of problems of dynamic crack propagation in [3,4]. A two-dimensional model for the dynamics of a discrete medium consisting of rigid rectangular blocks in contact through thin elastic layers was examined in [5]. It was assumed that layers between the blocks consisted of two parts, each of which was a surface layer of a block weakened by defects and hence loaded to a greater degree than the core of the block.…”