Added nonlinear damping of homogenized fluid-saturated microperforated plates in Forchheimer flow regime

Abstract

Microperforated plates (MPP) are commonly used in the field of acoustics for sound absorption purposes. Recent research in the area of structural dynamics revealed that they also provide additional viscous damping in the low-frequency range because of fluid–solid interactions in the microperforation boundary layers, mainly through viscous friction mechanisms. It is now established that the vibratory behavior of these systems can be modeled using a homogenization procedure that produces a pair of coupled partial differential equations (PDEs) collectively governing the dynamics of both a structural plate and a fictitious virtual fluid plate. It has been observed that the added damping achieves its maximum at a characteristic frequency governed in particular by the size of the perforations. It is also known that these systems, which can be implemented in hostile environments such as aircraft turbines, involve nonlinear mechanisms for large mechanical and/or acoustic excitations. Two causes of nonlinearities can be distinguished: (i) one associated with a high amplitude harmonic speed of the fluid in the perforations, and (ii) one associated with large harmonic structural deformations. The two causes can combine under strong excitation. The present paper focuses exclusively on the first cause of nonlinearity. As the fluid velocity increases inside the perforations, resistive and inertial phenomena arise within the perforations, influencing the structural response. These effects can be partly captured analytically by the Forchheimer correction, materialized by an additional quadratic nonlinear damping term in the PDE governing the dynamics of the fictitious fluid plate. The system of equations is solved numerically, and sensitivity analyses are carried out on the added damping to the excitation level. The proposed model is validated by experiments conducted on an equivalent cantilevered MPP. Analytical and experimental results show that the added viscous damping depends on the relative fluid–solid velocity. The added damping effect can, depending on the perforation diameter, reach a maximum for a critical value of the relative fluid–solid velocity, with all other independent parameters fixed. In the nonlinear framework, the added damping is a function of space and depends not only on the perforation diameter as in the linear framework, but also on the relative fluid–solid velocity, and is defined as a function of space.