Analysis of wave propagation in sandwich beams with parametric stiffness modulations

Propagation of flexural and shear waves in an unbounded sandwich beam is considered. This beam is thought of as a ‘unit width strip’, which is cut from an unbounded sandwich plate in the direction of propagation of a plane flexural or shear wave. The skin plies of such a plate (or, in effect, a beam) are made of a homogeneous material, whereas the core ply is microscopically inhomogeneous. This consists of foam bulk material filled by multiple inclusions whose orientation may be varied in a prescribed manner both in space and in time domains to generate stiffness modulation. At the macro-level, this composition of two ‘standard’ skin plies with a ‘two-phase’ core ply manifests itself as a homogenized smart ‘dynamic’ material having controlled distributed stiffness parameters. Control of the wave motions in a sandwich beam made of this material is then limited to wavelengths, which greatly exceed the characteristic size of cell elements of the micro-structure in the core ply and therefore to comparatively low frequencies. It is shown that asymptotically small stiffness modulations are capable of transforming propagating waves existing in a plate of constant stiffness to non-propagating ones. This mechanism of suppression of wave propagation in sandwich beams always co-exists with suppression of wave propagation due to the presence of internal damping in the material of all plies. The efficiency of the suggested mechanism is therefore estimated by the comparison of decrements of amplitudes of ‘almost’ propagating waves produced by the stiffness modulation and to the internal damping.