Targeted Energy Transfer in Systems with Periodic Excitations

Abstract

Previous chapters demonstrated that the addition of a relatively lightweight strongly nonlinear attachment to a primary (discrete or continuous) linear structure under shock excitation can drastically modify its transient dynamic response and bring about the TET phenomenon. Hence, it is not unreasonable to expect that similar salient dynamical behavior will be revealed also for the case of external periodic excitation. The transition from shock (broadband) to periodic (narrowband) excitation, however, is not trivial, and the application of nonlinear energy sinks (NESs) to structures under narrowband excitation deserves special consideration. For, example, it is not obvious that the capacity for TET of an NES under conditions of shock excitation of a primary structure can be extended to the case of periodic excitation. This chapter treats exactly this problem.We aim to demonstrate that the steady state response of a primary system under harmonic excitation with an attached NES exhibits not only common steady state and weakly modulated responses, but also a very special type of responses characterized by large modulations of the resulting oscillations; this response type is referred to as Strongly Modulated Response (SMR), and may be regarded as the extension of the TET phenomenon to structures under periodic (narrowband) excitation. Moreover, we demonstrate that SMRs are related to relaxation oscillations of the corresponding averaged dynamical flows (the slow flows of the dynamics), and in fact, one can regard SMRs as a form of repetitive TETs under the action of persistent periodic forcing. The possible application of NESs as strongly nonlinear vibration absorbers for vibration isolation of harmonically forced single- and multi-DOF primary subsystems is then discussed, and it is shown that under certain conditions, the efficiency of the NESs as vibration isolators can far exceed that of properly tuned linear absorbers (or tuned mass dampers — TMDs).