Study On Nonlinear Acoustic Field In Saturated Porous Media

With the rapid development of modern science and technology,the importance of nonlinear acoustics has become increasingly prominent,which has attracted extensive attention from the academic community and attracted more and more scholars to devote themselves to it.For a long time,linear acoustics has been used to study the excitation,propagation,reception and scattering of acoustic waves in media.The application of this theory is only suitable to the case of small amplitude acoustics waves.That is,if the particle velocity is much less than the acoustic velocity,the particle displacement is much smaller than the wavelength of the acoustic waves,the density increment of the medium is much smaller than the static density,the second order trace in the acoustic equation is ignored,linearization approximation is done for nonlinear wave equation,and then finally we have a familiar linear wave equation,so linear acoustics deals with small amplitude acoustic problems.But when we solve some practical problems encountered in production,the assumed conditions of small amplitude waves will be no longer valid.When acoustic wave with large intensity or frequency,at this point,the nonlinear term in the acoustic wave equation can't be ignored,or it will appear a series of nonlinear phenomenon which linear acoustics theory cannot explain.How to deal with the nonlinear problem involved behind the phenomenon,this goes to the non-linear theory.So we can say,nonlinear acoustics is the study of the medium of finite amplitude sound wave propagation problems.Based on the nonlinear acoustic wave theory,the acoustic propagation of finite-amplitude acoustic waves in fluid-saturated porous media and soft solids are studied in this thesis.Therefore,the main content of this thesis can be divided into two parts.The research work in this thesis might have an important scientific value for petroleum exploration and seabed ecological resources exploration.The nonlinear acoustic field in saturated porous media is studied this thesis.First,learning from Tong et al.'s work,the strain energy formula was given to further study the properties of nonlinear acoustic field in saturated porous media.Second,compared with the complete form of strain energy formula given by Grinfeld and Norris,the strain energy function of saturated porous media proposed by Tong et al(2017)ignores one nonlinear term produced by the coupling of solid-phase strain and liquid-phase strain,so the fluid-solid coupling term is introduced to modify the latter,then this thesis studies the nonlinear acoustic field in porous media,focus on the analysis and discussion the basis and necessity of the introducing the fluid-solid coupling nonlinear parameter.In the three-dimensional case,with the developed strain energy formula from Tong et al.,and the Lagrangians is applied to derive the governing equation of the saturated porous media.In order to investigate the nonlinear acoustic characteristics in porous media,plane wave is introduced,the nonlinear acoustic field equations excited by linear P wave and S wave are derived in one-dimensional case.The formula for calculating the fluid-solid coupling nonlinear parameter is given.Results show that nonlinear term introduced does not affect the nonlinear acoustic field excited by one-dimensional P-wave,but it does affect the nonlinear acoustic field excited by one-dimensional S-wave.The effect of fluid-solid coupling parameter on acoustic field excited by one-dimensional S-wave in saturated porous media is investigated by numerical simulation.Results show that the introduced nonlinear term of fluid-solid coupling has obvious influence on the nonlinear acoustic field excited by one-dimensional shear wave source,which shows that the nonlinear effect of fluid-solid coupling cannot be ignored.Finally,on the basis of the complete modified strain energy formula,the cubic order nonlinear wave equations excited by one-dimensional linear shear wave source in saturated porous media is derived,and investigate the properties of high-order nonlinear acoustic field in saturated porous media through numerical calculation.The amplitudes of quadratic order nonlinear and cubic order nonlinear field are calculated.Through the comparison of the quadratic order nonlinear acoustic field and nonlinear acoustic field consideration the cubic order changed with distance,it is observed the cubic order nonlinear acoustic field should be considered at several cases.In addition,in order to carry out the shock wave of porous medium,the thesis simply introduces the work by Zabolotskaya et al(2004)in soft solid medium such as simulation of nonlinear shear wave,and the derivation and simulation that the nonlinear acoustic field excited by one-dimensional finite amplitude shear wave in soft solid medium is paralleled in the fourth chapter in this thesis.