Nonlinear dynamics and optimization of a vibration reduction system with time delay

This paper reveals the dynamical properties of a nonlinear vibration reduction system with time delay feedback control and quasi-zero stiffness structure. The stable and unsta-ble regions of the trivial solution of the system in the parameter plane of time delay and feedback gain are given. The amplitude-frequency responses and force transmissibility of the system under harmonic excitation are determined. The optimized parameters are obtained by using genetic algorithm. The complicated oscillations are explored, such as chaotic motions and multi-periodic orbits. Afterwards, the displacement and the energy of the primary structure and the force transmitted to the base are discussed under the shock excitation and random excitation respectively. The influences of time delay on the dynamical behaviors and reduction performance are shown.(c) 2023 Elsevier B.V. All rights reserved.