Design Of Phononic Crystal Structures For Low-frequency Vibration And Noise Reduction And Topologically Protected Acoustic Transmission

Conventional acoustic materials are limited by scale and material properties,which cannot control low-frequency elastic waves through small-sized structures.As a class of artificial periodic structures consisting of highly freely designed units,phononic crystals have many extraordinary physical and acoustic properties that conventional materials do not possess,such as subwavelength bandgap,negative refraction,and topologically protected waveguide.It has potential applications in the fields of vibration and noise reduction,acoustic field control,and the design of new acoustic functional devices.In this thesis,we designed and optimized the target phononic crystals and conducted Finite Element simulations to investigate phononic crystals’ two most important properties,i.e.,bandgap and waveguide properties.To address the applications of locally resonant phononic crystals in the field of lowfrequency vibration and noise reduction,a two-component phononic crystal model is designed to obtain a subwavelength low-frequency wide bandgap while ensuring structural stability.A model is designed to optimize the substrate structure of the typical two-component phononic crystals by adding two types of holes to reduce the equivalent stiffness of the substrate and selecting metallic lead as the scatterer of the model to further reduce the intrinsic frequencies of the local resonance modes.The phononic crystals are periodically arranged in space in the form of a cubic lattice with three-dimensional periodicity.Then,the model’s band structures and vibration attenuation properties were investigated,and the equivalent material parameters were calculated.It is found that(1)the model has an ultra-wide low-frequency threedimensional bandgap of up to 133.68 %,confirming that the addition of holes can effectively widen the bandgap and reduce the opening frequency of the bandgap.(2)The three-dimensional bandgap of the same model is significantly better than the two-dimensional bandgap,and the main mode of the bandgap opening is the torsional local resonance mode.(3)Under the longwave approximation,the structure’s equivalent mass density corresponding to the bandgap’s range is calculated to be negative,indicating that the bandgap arises from the anti-phase resonance between the scatterers and the substrate.(4)The transmission loss results of a 5-layer semi-infinite structure composed of the unit cells indicate that it can efficiently attenuate elastic waves in the bandgap frequency range.(5)The bandgap width and opening frequency can be effectively tuned by changing the geometrical parameters of the component materials and the additional holes.The proposed three-dimensional two-component multihole locally resonant phononic crystals have reference value in the design of low-frequency vibration and noise reduction structures and their lightweight optimization.The structural design and the topological properties of the phononic crystals waveguides based on the valley Hall effect are investigated.By comparing the three types of currently existing acoustic topological boundary states,the acoustic valley Hall effect is screened as a method for topological phononic crystal structure design,valley Dirac degeneracies,and topological edge state formation.A hexagonal lattice valley phononic crystal model consisting of a triangular-shaped conformal resonator and connecting beams is proposed for the widely used plate-type structure in engineering applications.It is found that(1)due to the protection of spatial inversion symmetry of the hexagonal lattice,there are deterministic Dirac degeneracies in the band structures of the phononic crystals,and the number of degeneracies depends on the number of low-order vibrational mode types of the thin plate.(2)In particular,when a triangular resonators design is used,two independent Dirac degeneracies exist simultaneously below the conventional Bragg scattering degeneracy,generated by the out-ofplane translational and torsional vibrations of resonators at different positions in the rhombic unit cell,respectively.(3)When the heights of the triangular resonators are different,the spatial inversion symmetry of the structure is broken and the Dirac cone opens to form two topological bandgaps containing boundary state passbands.(4)Unlike most of the current topological phononic crystals,which only have a single boundary state band,the proposed structure can obtain two boundary state passbands simultaneously in the subwavelength range.(5)Equivalent material calculations show that the structure exhibits negative equivalent mass density in both bandgap frequency ranges,i.e.,both belong to local resonance.(6)Due to the strong spatial inversion symmetry breaking,the calculated values of the valley Chern numbers of the upper and lower bands of the two topological bandgaps deviate from the theoretical value of ± 0.5.This phenomenon is directly related to whether the topological boundary states can connect the bulk bandgaps or not,while it has less influence on the topological nature of the boundary states.Through full-domain simulation of the elastic wave transmission effect of the waveguide structure composed of this topological phononic crystal,it is found that the elastic waves corresponding to the two frequency bands are immune to the large corner backscattering and single defects existing in the waveguide path,and have topological protection properties.In addition,the band tunability of topological phononic crystals under the condition of an external circuit is investigated,and the formation principle of electromechanical coupling mode is analyzed,which enriches the theoretical basis of the phononic crystal waveguide structure in frequency real-time regulation.