2-DIMENSIONAL MODULATION AND INSTABILITIES OF FLEXURAL WAVES OF A THIN-PLATE ON NONLINEAR ELASTIC-FOUNDATION

In the present paper we intend to examine in detail the formation of l ocalized modes and waves mediated by modulational instability in an el astic structure. The elastic composite structure consists of a nonline ar foundation coated with an elastic thin plate. The problem deals wit h flexural waves traveling on the plate. The attention is devoted to t he behavior of nonlinear waves in the small-amplitude limit in view of deducing criteria of instability which produce localized waves. It is shown that, in the small-amplitude limit, the basic equation which go verns the plate deflection is approximated by a two-dimensional nonlin ear Schrodinger equation. The latter equation allows us to study the m odulational instability conditions leading to different zones of insta bility. The examination of the instability provides useful information about the possible selection mechanism of the modulus of the carrier wave vector and growth rate of the instabilities taking place in both (longitudinal and transverse) directions of the plate. The mechanism o f the self-generated nonlinear waves on the plate beyond the birth of modulational instability is numerically investigated. The numerics sho w that an initial plane wave is then transformed, through the instabil ity process, into nonlinear localized waves which turn out to be parti cularly stable. In addition, the influence of the prestress on the nat ure oflocalized structures is also examined. At length, in the conclus ion some other wave problems and extensions of the work are evoked. (C ) 1998 Elsevier Science B,V. All rights reserved.