Wave Propagation In Fluid-saturated Porous Periodic Structures

Phononic crystals(PCs)are a kind of periodic functional composites.One unique characteristic of PC is to produce band gaps.Acoustic or elastic waves with frequency inside bandgaps cannot propagate in the periodic structures.Therefore,PCs have a broad prospect of engineering applications in noise reduction and shock absorption.The propagation of waves in artificially periodic structures has thus attracted more and more attention.However,most of the existing studies is concerned on PCs composed of single-phase media,and two-phase or multiphase media,such as fluid-saturated porous media composed of both solid and fluid phases,are seldom concerned.In fact,wave theory of fluid-saturated porous medium is always an important branch in the field of dynamics.It is of particular importance in the fields of geotechnical dynamics and seismic engineering.In this paper,around the scientific problems needing to be solved urgently and related to the application of engineering vibration,wave propagation in fluid-saturated porous periodic structures is studied deeply by using theoretical analysis and numerical simulation.The main contents and conclusions include:(1)Taking PCs with single-phase media as examples,the calculation methods of real band structure,complex band structure and frequency response are introduced by using the PDE module in finite element software COMSOL.The related method can be extended to the calculation of the wave behaviors in PCs with two-phase media.(2)According to the Biot theory for porous media,the wave equations in u-w and u-p formats are given.At the same time,analytical solutions to the wave equations in both two formats are given for one-dimensional homogeneous fluid-saturated porous medium,and their equivalence is proved.By using the PDE module,the real band structure(without viscosity),complex band structure and frequency responses of one-dimensional fluid-saturated porous periodic structures,and the effects of viscosity and porosity on wave behaviors are discussed.The results show that the material parameters of pore liquid have significant influences on the complex band structures and frequency responses.The attenuation in the passing bands first increases and then decreases as the viscosity increases,and the attenuation in the Bragg band gaps changes in the opposite way;When the viscosity is negligible,anticrossing band gaps can be formed due to the level repulsion between P1 and P2 waves.The anticrossing band gaps disappear rapidly with the increase of viscosity;With the increase of fluid porosity,the attenuation increases monotonically in passing bands and band gaps;Generally speaking,P2 wave has strong attenuation and is highly influenced by material parameters.P1 wave plays a key role in the transmission of a finite structure.(3)The above work is further extended to two-dimensional transversly isotropic fluid-saturated porous periodic structures.According to wave equation in u-p format and by using PDE module,the real band structure(without viscosity),complex band structure and frequency response of two-dimensional transversly isotropic fluid-saturated porous periodic structure are calculated;the effects of material anisotropy and fluid viscosity on wave behaviors are discussed.The results show that the complete bandgap and wavenumber bandgap can be generated in two-dimensional isotropic periodic structures without viscosity;When the medium is transversely isotropic,the width of the band gap decreases,the modes in the isotropic case can be either separated or degenerated,and a sharp point appear inside the Brillouin zone in the dispersion curve of the evanescent waves;when viscosity is introduced,degenerated states in the complex band structures are separated,and the sharp points in the dispersion curve become rounded;with the increase of viscosity,the transmissions in the passing bands and mode band gap of SV wave decrease,but the transmission increases in complete band gap.