Optimising open porous foam for acoustical and vibrational performance

A computational method for designing optimal arrangements of multilayer noise and vibration treatments in general and porous open cell foam in particular is discussed. The method uses finite element solutions to Biotʹs equations for poroelastic materials and provides data to evaluate cost functions and gradients. The porous material is parameterised using scaling laws linking the microscopic properties to the classical parameters, i.e. averaged elasticity, flow resistivity and characteristic viscous and thermal lengths. The cost function is either in terms of weight or in terms of the pressure response in a finite cavity, complemented with constraints on the other. However, care must be taken when choosing the cost function, as this will greatly affect the outcome of the optimisation. Observations made during the optimisation process indicate a limited number of minima within the parameter range of interest as well as beneficial continuity around these minima, thus enabling a meaningful optimisation. The results suggest that if alterations of the microscopic properties of the foam are made, the foam may be adapted to specific environmental conditions and thereby achieve improved acoustic behaviour as well as reduced weight.