Vibration behavior of a microperforated plate within an acoustic nonlinear framework
Résumé
Microperforated plates (MPP) can add a substantial damping in low-frequency range. These structures 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 depending only on the perforation parameters. However, MPP is also suitable in environments subject to high levels of mechanical excitation and, consequently, high fluid-velocity inside perforations. Two types of nonlinearities can then be captured: an acoustic nonlinearity induced by high fluid-velocity, and a nonlinearity induced by high fluid-velocity along with large structural displacement. This work only explores the former nonlinearity. 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 of motion worked out in the previous work by the authors. The resulting system of equations is solved numerically. Experimental measurements using a laser vibrometer on a perforated cantilever beam validate the proposed model. Results show that at the characteristic frequency, the maximum added damping can reach a maximum at a critical value of the relative fluid-solid velocity under high excitation level.
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