Absorption and trapping of vibration energy by complex resonators

Abstract

This presentation examines conditions that can enhance apparent damping of a master structure due to its coupling with a complex resonator that does not exhibit classical dissipation properties. The model uses a set of multistage parallel oscillators within which energy is trapped. The method presented here for predicting the apparent damping is based on evaluation of the asymptotic response of the master structure utilizing the Hilbert transform. The result is a functional relationship between the frequency distribution within the system and the resulting apparent damping. This study leads to a nonclassical dynamic absorber, consisting of a multistage parallel oscillators, in terms of its absorption and trapping characteristics. The energy is absorbed from the master at a rate determined by the apparent damping and trapped for a given time interval as measured by the return time. The theoretical results suggest optimal configurations to decrease the absorption time and to increase the trapping time (up to an infinite delay). The results of numerical simulations performed on complex vibro-acoustic systems support the proposed theoretical approach. [Research sponsored by INSEAN and NSF.]