Periodic Isolator Design Enhancement via Vibration Confinement through Eigenvector Assignment and Piezoelectric Circuitry

Abstract

The objective of this research is to investigate the feasibility of utilizing eigenvector assignment and piezoelectric circuitry for enhancing vibration isolation performance of periodic isolators. For a classical periodic structure, stop bands are created due to material discontinuity so that wave propagation of external excitation can be suppressed within the stop band frequency range. While effective, such a method cannot always create wide enough stop bands such that all disturbance frequencies are covered. In this study, the eigenvector assignment technique and piezoelectric circuitry are utilized to reduce the transmissibility of the isolator modes near the boundary of the stop bands, and therefore widen the effective frequency range of vibration suppression of the periodic isolator. The principle of eigenvector assignment is to alter the mode shapes of the system so that the modal components corresponding to the concerned coordinates are as small as possible. By applying the eigenvector assignment method on the spatially tailored periodic isolator structure, the response amplitude of the attenuated end (the end of the isolator designed to have small vibration) at resonant frequencies near the stop band can be reduced, which enhances the vibration isolation performance in the frequency range of interest. On the other hand, piezoelectric circuits connecting to the isolator structure increase the degrees of freedom of the integrated system, and enlarge the design space for achievable eigenvectors. The eigenvectors of this integrated system are selected such that the modal energy in the concerned coordinates is minimized by using the Rayleigh Principle. The integrated system with assigned eigenvectors will re-distribute vibratory energy of the complete electromechanical system. Small vibration at the attenuated end of the isolator is achieved since the energy is confined in the circuitry and other parts of the isolator. Numerical simulations are performed to evaluate the effectiveness of the proposed method on vibration confinement for isolator designs. An integrated closed-loop system with state estimator is developed to realistically implement the proposed algorithm. It is shown that with the piezoelectric circuitry and eigenvector assignment, the system energy is redistributed and confined in the unconcerned regions, which can greatly enhance the performance of the vibration isolation system.