Analytical investigation of the acoustic behavior of nanocomposite porous media by using modified nonlocal Biot’s equations

Abstract

In this paper, the modified Biot’s equations based on nonlocal elasticity theory are presented for modeling nanocomposite porous media. The analytical solution of modified Biot’s equations is obtained by using the recently developed potential function method. By doing some mathematical manipulation, the coupled modified Biot’s equations are converted to two decoupled equations. Consequently, the variations of field variables and acoustical properties of a considered nanocomposite foam are studied by changing the nonlocal parameter. The obtained results show that the local Biot’s results are in good agreement with the nonlocal modified Biot’s results for very small values of the nonlocal parameter. In addition, the values of field variables (i.e. pressure) in the thickness direction are decreased by increasing the nonlocal parameter for frequencies below 5000 Hz. Furthermore, by increasing the nonlocal parameter, the differences between local and nonlocal values of field variables and the absorption coefficient increase. Also, the nonlocal parameter has no considerable effect on the absorption coefficient for frequencies lower than 2000 Hz, whereas by increasing the nonlocal parameter the differences between corresponding results of local and nonlocal theories increase for frequencies above 2000 Hz.