Forced vibrations and resonance wave scattering on impurity in 1D discretelattice with nearest- and next-nearest-neighbors interaction

Vibrations of a discrete linear atomic chain with nearest- and next-nearest -neighbor interaction consist of two parts corresponding to localized and e xtended vibrations. The vibrations under external force action are studied. It is shown that localized vibrations with discrete frequencies lying in t he continous spectrum can arise and the condition for their existence is de rived. The wave scattering from a point impurity is analysed. Resonance ref lection of the doublepartial waves with frequencies belonging to the quasil ocalized spectrum is described. (C) 2000 Elsevier Science B.V. All rights r eserved.