Optimization of vibration energy localization in quasi-periodic structures

A mechanical periodic structure in presence of component perturbations can be a seat of a localization of vibration energy. In fact, it is well known that mistuned components have larger response levels than those of perfect components. This results in a localized energy, which can be tapped via harvesting devices. In this study, the dynamic behavior of a quasi-periodic system consisting in weakly connected linear oscillators is investigated. The main objective is to optimize the mistuning parameter, the coupling stiffness and the damping coefficient in order to functionalize the imperfection, which leads to the maximization of the localized vibration energy.

LOCALIZED MODES OF A COMPRESSION WAVE IN TWO-DIMENSIONAL SOLID–SOLID PHONONIC CRYSTALS

We have studied the compression (P) wave band structures at a low frequency in two-dimensional solid–solid phononic crystals. The plane-wave expansion method based on the decomposition of elastic waves was used. The pressure field distribution of P-wave localized modes at Γ points in the lowest bands, including multiple flat bands of systems comprising different configurations, were analyzed. The results show that a lower symmetry of the scatterer are an effective method to enhance the localization of vibration modes. The property has potential applications in the design of waveguides.

Localization of Vibration Propagation in Two-Dimensional Systems With Multiple Substructural Modes

Localization of vibration propagation in randomly disordered weakly coupled two-dimensional cantilever-mesh-spring arrays, in which multiple substructural modes are considered for each cantilever, is studied in this paper. A method of regular perturbation for a linear algebraic system is applied to determine the localization factors, which are defined in terms of the angles of orientation and characterize the average exponential rates of growth or decay of the amplitudes of vibration in the given directions. Iterative formulations are derived to determine the amplitudes of vibration of the cantilevers. In the diagonal directions, a transfer matrix formulation is obtained. For a given direction of orientation, the localization behavior is similar to that of a one-dimensional cantilever-spring-mesh chain. The effect of the stiffnesses and the disorder in the stiffnesses of the cantilevers on the localization behavior of the system is investigated.

Localization of Vibration in Disordered Multi-Span Beams With Damping

The combined effects of disorder and structural damping on the dynamics of a multi-span beam with slight randomness in the spacing between supports are investigated. A wave transfer matrix approach is chosen to calculate the free and forced harmonic responses of this nearly periodic structure. It is shown that both harmonic waves and normal modes of vibration that extend throughout the ordered, undamped beam become spatially attenuated if either small damping or small disorder is present in the system. The physical mechanism which causes this attenuation, however, is one of energy dissipation in the case of damping but one of energy confinement in the case of disorder. The corresponding rates of spatial exponential decay are estimated by applying statistical perturbation methods. It is found that the effects of damping and disorder simply superpose for a multi-span beam with strong interspan coupling, but interact less trivially in the weak coupling case. Furthermore, the effect of disorder is found to be small relative to that of damping in the case of strong interspan coupling, but of comparable magnitude for weak coupling between spans. The adequacy of the statistical analysis to predict accurately localization in finite disordered beams with boundary conditions is also examined.