No abstract

In this paper, Biot's dynamic poroelasticity theory is applied for deriving theoretical complex dynamic stiffness solutions for fixed lower surface, infinite planar cellular plastic foams with permeable and impermeable upper surfaces. A model using impulse pressure excitation to derive and acquire the acoustic response functions of foams is performed. The derived theoretical dynamic stiffness equations can also be used for predicting the dynamic stiffness of composite foams. The dynamic stiffness of a composite foam can be seen as a series combination of the dynamic stiffness of single planar foams according to their stacking order. Using the derived complex dynamic stiffness equations, frequency response functions of acoustic impedance, reflection coefficient, and sound absorption coefficient are obtained. Experimental results from earlier studies are used to validate the derived frequency response function. The experimental acoustic properties of planar polyurethane foams with the same cellular skeleton at various thicknesses, are compared to the predicted properties. The influences of thickness on the acoustic properties are discussed.

In this paper, a three-dimensional Laplace domain finite element model with four-node tetrahedral porous elements is developed and applied for the investigations. Without the incident acoustic field, the exact acoustical properties of a laterally infinite planar foam, which is backed with a rigid plane, are accurately predicted by assuming the circumferential edge constraints as rollers. It is found that the rigidity of the circumferential edge constraint has a profound effect on the predictions. If the circumferential edge constraints are all fixed, the amplitude of the first sound absorption peak is increased, and the peak is moved to a lower frequency as compared with the exact solutions. Measurements obtained by the two-microphone impedance tube method are bounded by the predictions of samples with roller as well as with fixed constraints. They are much closer to that predicted with fixed edge constraints. Upon increasing the diameter-to-thickness ratio of the sample, the influence of the fixed edge constraint is reduced. The measured acoustic results can be the representatives of the laterally infinite planar foam from which the sample was cut only if the roller edge constraint of the sample is managed or the diameter-to-thickness ratio of the sample is increased.

No abstract

No abstract