Vibration behavior of a microperforated plate within an acoustic nonlinear framework

Microperforated plates (MPP) can add substantial damping in the low-frequency range. MPP are known to dissipate energy through thermo-viscous interactions between shearing adjacent fluid layers near the perforation solid walls. Under linear operating conditions, a previous work carried out by the authors showed that the added damping reaches a maximum at a characteristic frequency which solely depends on the perforation parameters. However, MPP is also suitable in environments subject to high levels of mechanical excitation and, consequently, high fluid velocity within the perforations. Two types of nonlinearities should then be considered: (1) an acoustic nonlinearity induced by high fluid velocity, and (2) a nonlinearity induced by large structural displacements. This work only explores the former. The acoustic nonlinearity is modelled by the Forchheimer resistivity correction, a function of the fluid-solid relative velocity in the perforations, introduced into the equations subsequently solved numerically. Experimental measurements using a laser vibrometer on a perforated cantilever beam validate the proposed model. Results show that, under high excitation levels and at the characteristic frequency, the maximum added damping can reach a maximum, depending on the MPP parameters, at a critical value of the relative fluid-solid velocity.