Vibration Confinement via Optimal Eigenvector Assignment and Piezoelectric Networks

Abstract

The underlying principle for vibration confinement is to alter the structural vibration modes so that the corresponding modal components have much smaller amplitude in concerned area than in the remaining part of the structure. In this research, the state-of-the-art in vibration confinement technique is advanced in two correlated ways. First, a new eigenstructure assignment algorithm is developed to more directly suppress vibration in regions of interest. This algorithm is featured by the optimal selection of achievable eigenvectors that minimizes the eigenvector components at concerned region by using the Rayleigh Principle. Second, the active control input is applied through an active-passive hybrid piezoelectric network. With the introduction of circuitry elements, which are much easier to implement than changing or adding mechanical components, the state matrices can be reformed and the design space for eigenstructure assignment can be greatly enlarged. To maximize the system performance, a simultaneous optimization/optimal eigenvector assignment approach to decide the passive and active parameters concurrently is outlined. The merits of the proposed system and scheme are demonstrated and analyzed using numerical examples.