Towards Chaos in Vibrating Damaged Structures—Part I: Theory and Period Doubling Cascade

Abstract

The aim of the present paper is to evaluate the complex oscillatory behavior, i.e., the transition toward deterministic chaos, in damaged nonlinear structures under excitation. In the present paper (Part I), we show the developed theoretical approach and how it allows us to capture not only the super-harmonic and offset components (predominant for moderate nonlinear systems) but also the subharmonics of the structural dynamic response, describing complex and highly nonlinear phenomena, like the experimentally observed period doubling. Moreover, a period doubling cascade with a route to chaos seems to emerge from our considerations.