A study of the vibration isolation performance of a limited phononic crystal vibration isolator based on local resonance theory

Abstract

In this study, a limited phononic crystal vibration isolation (LPCVI) model is constructed based on a vibration isolator used in the field of rail transit, and analyses of the characteristics of the bandgap, the vibration isolation effect, and the vibrational energy transfer of the model are presented. In this paper, the Boltzmann integration theory and the Bloch theorem are used to establish a mathematical model that analyzes the band structure based on the viscoelastic damping of the system. Additionally, by comparing the practical finite periodic structure model and the conventional mass-spring-damping vibration isolation model, explicit forms of the vibration isolation coefficients of the models are derived. It is found that when the external excitation frequency is within the forbidden band range, the vibration isolation coefficient of the LPCVI system with a harmonic oscillator is much smaller than that of the vibration isolation system with a general mass-spring. Furthermore, the Newmark-β integration method is adopted to solve the vibration equation of the LPCVI model. The energy input, distribution, and output of the system are obtained when the energy is under excitation in the forbidden band and bandpass frequencies. It is found that the external excitation does both positive and negative works on the vibration isolation system within a certain period under the action of the central frequency excitation of the forbidden band; therefore, the energy cannot be input into the isolation system. This makes it possible to achieve effective vibration isolation at lower frequencies.