Sound Radiation Mitigation of Geometrically Nonlinear Plates Subjected to Subsonic Airflow

Abstract

This paper gives a theoretical analysis to obtain and reduce the acoustic pressure generated from plates with geometric nonlinearities subjected to subsonic airflow and external excitation. von-Kármán assumptions are applied considering the nonlinear terms in strain-displacement relations. Airflow passing through the plate is considered as an incompressible, irrotational, and inviscid flow. Galerkin’s method is employed to acquire the governing equations of time-dependent coefficients. Multiple Time Scale Method (MTSM) is then used to obtain the response of the plate. Suppressing undesirable vibration is carried out using an optimal tuned mass damper (TMD) system and an analytical solution is proposed based on Laplace transform and Adomian Decomposition Method (ADM). The acoustic pressure received from the plate is calculated by solving the Rayleigh integral using Boundary Element Method (BEM). A parametric study is carried out, and the effects of the flow speed, the aspect ratio, the thickness of the plate, the material of the plate, the forcing frequency, and the effectiveness of the designed TMD system on the sound pressure are examined. According to the results, using the TMD system reduces the amplitudes of the plate vibrations and, consequently, reduces the acoustic pressure around the vibrating plate. In this study, the passive control strategy leads to a significant decrease in the sound pressure level (about 35%) in some airflow speeds. Results show good efficiency in the control strategy. It is also found that the acoustic pressure generated from steel plates is significantly larger than that generated from aluminum plates. Moreover, increasing the aspect ratio and the plate thickness reduces the acoustic pressure. On the other hand, the external excitations with lower frequencies and the airflows with higher densities can generate lower sound pressures around the plate.