Linear and nonlinear dynamics of a plate with acoustic black hole, geometric and contact nonlinearity for vibration mitigation

Abstract

A rectangular plate with a wedge profile creating an Acoustic Black Hole (ABH) termination is studied numerically. A particular emphasis is put on combining two different types of nonlinearity in order to improve the passive damping capacity of the ABH by transferring energy to the high-frequency range where it is more efficient. First, the addition of contact points to create a vibro-impact black hole (VI-ABH) is taken into account, following a previous study on beams. The contact nonlinearity allows for a rapid and efficient transfer of energy. Second, the large-amplitude vibrations of the plate in the ABH region where small thickness is reached, is also considered. The geometric nonlinearity is incorporated using a von Kármán plate model, and the regime of wave turbulence is shown to be triggered thus creating an energy flux from the low to the high frequencies. The linear characteristics of the ABH plate are first analyzed. Numerical results show the appearance of overdamped modes gathered in solution branches with constant number of half-waves in the transverse direction of the ABH, seen as a waveguide. The structure of the branches is shown to be more and more prominent when increasing the width of the plate, showing a transition from beam-like to full plate structure, with a fixed value for the fundamental cut-on frequency. The combination of both contact and geometric nonlinearities to improve the ABH effect is then reported. It is shown that the coexistence of both nonlinearities provides better passive damping efficacy.

A metamaterial consisting of an acoustic black hole plate with local resonators for broadband vibration reduction

“…One tested option in this line is that of exploiting non-linearity to transfer energy from low to high frequencies, where the ABH becomes efficient. The effects of geometrical [33], material [34], and contact [35,36] non-linearity have been investigated and experiments have been recently reported in [37]. Using functionally graded [38] and composite [39] materials to build ABH plates has revealed also beneficial.…”

Automobile information modeling based on nonlinear multisensor coupling

“…However, in a multi-sensor system, these remaining components may still contain important sensing information, so it is necessary to minimize the loss of useful information as much as possible. Therefore, for multi-sensor systems with coupling information and other issues, the modeling method must be able to overcome the correlation between independent variables and reflect the nonlinear relationship between independent and dependent variables [2] .…”

Sound radiation and non-negative intensity of a metaplate consisting of an acoustic black hole plus local resonators

“…Therefore, a lot of current research focuses on finding ways to complement the ABH effect to attain broadband vibration reduction in plates. For instance, nonlinear effects are being exploited for that purpose [31][32][33][34][35] as well as optimization techniques [36][37][38][39], which have provided promising results. Periodic distribution of ABHs on plates have proved effective too [40].…”