Vibration Confinement via Optimal Eigenvector Assignment and Piezoelectric Networks

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.

Vibration Confinement via Optimal Eigenvector Assignment and Piezoelectric Networks

The underlying principle for vibration confinement is to alter the structural modes so that the corresponding modal components have much smaller amplitude in concerned areas than 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 areas 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 is much easier to implement than changing or adding mechanical components, the state matrices can be reformed and the design space in eigenstructure assignment can be greatly enlarged. The merit of the proposed system and scheme is demonstrated and analyzed using a numerical example.

Dynamic Sensitivity of Structures to Cracks

Cracks that develop on machine members and structures influence their dynamic behavior. The Rayleigh principle is used for an estimation of the change in the natural frequencies and modes of vibation of the structure if the crack geometry is known, assuming that the eigenvalue problem for the uncracked structure has been solved in advance. The method reduces the computational effort needed for the full eigensolution of cracked structures and gives acceptable accuracy. It can be extended to higher modes and to decompose degenerate modes found in symmetric structures. To demonstrate the change in the dynamic behavior of linear structures with the crack depth, a cylindrical shaft and a plane frame consisting of prismatic bars were analyzed for dynamic sensitivity to surface cracks.

Cutouts in Shallow Shells

Integral representations of general solutions to the shallow shell equations are obtained by means of the Betti-Rayleigh principle. With the aid of these integral representations the cutout problem of shallow shells is reduced to a system of four coupled integral equations. The cutout can have an arbitrary shape. Cutouts with reinforced edges and other boundary-value problems for shallow shells can be reduced to integral equations by the method developed in the paper.

On the Variational Principle and Lagrange Equations in Studies of Gasdynamic Lubrication

The paper is concerned with the variational formulation in studies of gasdynamic lubrication. It is shown that Reynolds’ equation of lubrication is equivalent to a set of Lagrange equations similar to those in classical dynamics. The Lagrangian and the dissipation-production are defined. Furthermore, based on the Hamiltonian principle for the field of a continuum, the Lagrangian density and the dissipation-production density are established. This formulation includes the incompressible problem, which is obtainable from the Helmholtz-Rayleigh principle of minimum energy-dissipation, as a special case. Hence a unification of the variational methods for both gasdynamic and hydrodynamic lubrication is accomplished.