Abstract:
It is shown that there exist a large class of nonlinear elastic systems (which includes both dissipative and conservative systems) where localized modes (linear or nonlinear) completely define the large time behavior. For dissipative systems, there are possible generations of unboundedly complicated chaotic attractors. For some conservative (for example, weakly nonlinear) elastic systems, the method developed allows one to construct an algorithm of the integration of the corresponding evolution equations. The phenomenon of vibration and nonstationary wave localization within beams, plates, and shells has been studied using the nonlinear approach.