Study On Low Frequency Band Gap Property Of 1D Three-element Solid-fluid Phononic Crystaland Application To Acoustic One-way Transmission

Phononic crystals are periodic acoustic artificial structures with acoustic/elastic bandgap characteristics.Acoustic waves will be inhibited in some frequency ranges or incidence angle ranges while propagating in phononic crystals which are known as frequency selective transmission and direction selective transmission of phononic crystals.The bandgap properties of phononic crystals can be used in many acoustic manipulation fields,such as acoustic filter,acoustic insulation and acoustic one-way transmission.At present,the studies of phononic crystal band gaps mainly focus on Bragg scattering type or local resonance type phononic crystals.Although the band gap of Bragg scattering phononic crystal has a wider band,the corresponding wavelength is much smaller than the structure size,which is not conducive to the miniaturization of designed structure.Local resonance type phononic crystals can achieve phononic band gap in a very low frequency region,but the narrow band range has brought some limitations.In addition to Bragg scattering band gaps,Ei.Hassouani pointed out that transmission zero band gaps exist in 1D solid-fluid phononic crystals.These band gaps are distributed over the whole frequency region,which means that transmission zero band gaps have great potential application value in the field of sub-wavelength acoustic manipulation.However,the low-frequency transmission zero band gap angle range is single and very narrow.In addition,a subwavelength acoustic one-way transmission device can be constructed by using the zero-point transmission bandgap.However,due to the limitation of the angular width,it is hard to achieve wide-angle acoustic unidirectional transmission.Therefore,to improve its practicability,the low-frequency band gap characteristics of 1D three-dimensional solid-fluid phononic crystals and the application of acoustic unidirectional transmission are studied in this paper.In addition to the introduction of Chapter 1 and the summary and prospect of Chapter 5,the specific work is as follows:In Chapter 2,the basic theory of acoustic wave propagation in isotropic homogeneous medium is introduced.The transfer matrix of acoustic wavepropagation in 1D three-element solid-fluid phononic crystal with finite period is derived in detail.The calculation method of transmission coefficient is proposed.Based on Bloch theorem,the numerical calculation method of band structure is established.The corresponding relationship between band structure and transmission spectrum of acoustic wave through 1D three-dimensional solid-fluid phononic crystal are analyzed.In Chapter 3,the band structure of infinite periodic structure and the transmission spectrum of finite periodic structure are calculated,respectively.It is found that the three-element structure always has double bandgaps.On this basis,the effects of material and structural parameters on the angular width and position of the double-band gap are analyzed by using control variable method.It is also found that the formation of double band gaps is sensitive to the sound velocities of shear and longitudinal waves,and it is difficult to separate the band gaps by changing the mass density of solid layer.In addition,the transmission spectra of cascaded two-element solid-fluid phononic crystals and finite-length three-element solid-fluid phononic crystal are compared.In Chapter 4,in view of the narrow and single incident angle range of the current transmission-zero bandgap-based acoustic unidirectional transmission devices,this chapter designs a sub-wavelength,broadband and multi-angle acoustic unidirectional transmission device based on the wavefront control of the acoustic grating and the low-frequency bandgap characteristics of 1D three-dimensional fluid-solid phononic crystals.The basic idea and main steps of finite element method are introduced.The method of constructing finite element model of one-way transmission structure is introduced in detail.Combining the energy band structure and the acoustic grating equation,the mechanism of reverse cut-off and forward conduction for one-way transmission of acoustic wave is described,and the acoustic pressure and displacement distributions of forward and reverse cut-off for one-way transmission are analyzed.Furthermore,the relationship between the forward and reverse transmittance of acoustic wave and its angle is calculated,the angular width of one-way transmission is analyzed,and the frequency bandwidth is calculated.Inaddition,based on the effect of structure and material attributes on the low frequency band gap,the effective control of the one-way transmission angle range of acoustic wave is realized.