Effective medium method of slightly compressible elastic media permeated with air-filled bubbles

An effective medium method has been developed for the slightly compressible elastic media permeated with air-filled bubbles,according to the nonlinear oscillation of bubble,which will be happened when compressional wave travels through the porous media.The effective Lame coefficients of the porous medium and the nonlinear elastic wave equation can be deduced,as the micro-unit of effective medium should have the same stress and strain with the micro- unit of porous media.The linearized properties obtained by this method are in good agreement with the results of Gaunaurd's classic theory.Furthermore,the nonlinear coefficient,which is the important property of the porous media, can also be acquired by this method.