Vibration isolator design via energy confinement through eigenvector assignment and piezoelectric networking

Abstract

The objective of this research is to investigate the feasibility of utilizing eigenvector assignment and piezoelectric networking for enhancing vibration isolator design through energy confinement. For a classical periodic isolator structure, the material discontinuity creates stop bands that could suppress the wave propagation of external excitation in a particular frequency range. While effective, such method can not always create wide enough stop bands such that all the disturbance frequencies are covered. In this study, the eigenvector assignment technique and piezoelectric networks are utilized to reduce the transmissibility of the isolator modes near the boundary of the stop bands, and therefore widen the effective frequency range and enhance the performance of the isolator.The eigenvector assignment principle is to alter the mode shapes of the system so that the modal components have smaller amplitude in concerned coordinates than in other parts of the system. By applying the eigenvector assignment method on the spatially tailored periodic isolator structure, the attenuated end (the end of the isolator designed to have small vibration) response amplitude 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 networks connecting to the isolator structure increase the degrees of freedom of the integrated system, and enlarge the design space for achievable eigenvectors. The right eigenvectors of this integrated system are selected such that the modal energy in the concerned area 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. Frequency responses of the different generalized coordinates in the selected frequency range are illustrated. It is shown that with the piezoelectric networking and eigenvector assignment, the system energy is redistributed and confined in the unconcerned areas, which can greatly enhance the performance of the vibration isolation system.

Orthogonal Eigenstructure Control with Non-collocated Actuators and Sensors

“…Consequently, there is no need to define the desirable eigenvectors1 therefore, the problem of closeness of the desired and achievable eigenvectors does not exist. A case study of this method has been presented in (Wu and Wang, 2004). If closeness of achievable and desired eigenvectors happens in unimportant degrees-of-freedom, it may cause unsatisfactory performance Wang, 2003, 2004).…”

Vibration Confinement by Minimum Modal Energy Eigenstructure Assignment

“…Therefore the need for pre-selecting the closed-loop eigenvectors is eliminated and the problem of closeness of the desired and achievable eigenvectors does not exist. A case study of this method has been presented in [14] Pre-determination of the desired eigenvector components can cause unsatisfactory performance if a match between components of the desired and achievable eigenvectors happens in the unimportant degrees of freedom [12,13]. Considering the problem of movement of neighborhood of the closed-loop eigenvalues, an eigenstructure method for constrained state or output feedback has been presented by Slater et al [15].…”

Effect of the Actuators’ Location on Vibration Suppression Using Minimum Modal Energy Eigenstructure Assignment

“…Using the Rayleigh principle optimal eigenvectors can be found. Their method minimizes the ratio of the modal energy at the concerned area to the modal energy of the whole structure using an auxiliary eigenvalue problem [13].…”