Finite element Modeling of smart foam for active vibration and noise control applications

A new finite element model for elastic porous materials is introduced. The term "elastic" stems from the fact that the motion of the solid phase is encountered for, resulting in the propagation of the acoustic waves in both the solid and fluid phases. A 3-dimentional analysis is essential to fully describe the dynamic behavior and wave types propagating in the porous materials. When using numerical modeling techniques several difficulties arise due to the 3-dimensional nature of the model. Such difficulties are the high computational effort required for accurately modeling the porous material and the difficulty in coupling this material smoothly to any 2-dimensional flexible structure without introducing a coupling matrix. Therefore, a 2-dimensional finite element model for the porous materials is introduced, where it takes advantage of the 1st order shear deformation theory assumptions first introduced by Mindlin for modeling thick plates. Comparing the newly developed 2-dimensional model for partially reticulated polyurethane foam with the original 3-dimentional model based on the 3D elasticity theory has revealed good results when the thickness-to-width ratio doesn't exceed the limits posed by Mindlin for accurate representation of thick plates. The 2-dimensional model was experimentally verified by developing a new type of smart foam, which by attaching to a flexible plate coupled with an acoustic cavity showed good match between the numerical and experimental results.