Study On Nonreciprocity And Topological Property Of Tunable Phononic Crystal Slabs

Recently,the nonreciprocity and topological properties of phononic crystals have attracted a lot of attention and research because they can greatly enhance the ability to manipulate sound waves,which has potential applications including vibration and noise reduction,acoustic rectification and acoustic communications.Beam and slab structures with finite thickness are common in engineering.Compared with ideal phononic crystals with infinite size in non-periodic direction,phononic crystal slabs are closer to these actual structures.However,there is lack of research on the nonreciprocity and topological properties of phononic crystal slabs.In addition,the tunability of the system greatly enhances their flexi bility and practical applicability,which can enrich the applications of the corresponding acoustic devices.Therefore,it is of great theoretical and practical significance to study the nonreciprocity and topological properties of tunable phononic crystal slabs.Based on the basic theory of phononic crystal slabs,nonreciprocal theory and topological theory,this paper deeply investigates the nonreciprocity and topological properties of tunable phononic crystal slabs.The results prove that there are tunab le nonreciprocity,topological interface states and topological edge states in our designed phononic crystal slabs.The main work of this paper is as follows:(1)The nonreciprocity of elastic waves is studied in one-dimensional tunable magnetoelastic phononic crystal slabs by the plane wave method.First,the theory of spin and elastic waves in a one-dimensional magnetoelastic phononic crystal slabs with magnetoelastic interaction is derived,and the procedure calculating the band structure by the plane wave method is given.The band structure of magnetoelastic waves shows that there are asymmetric dispersion curve of spin waves in one-dimensional magnetoelastic phononic crystal slabs when the time-reversal and spatial inversion symmetries are broken simultaneously.Due to magnetoelastic interaction,the asymmetric dispersion curve of spin waves leads to the nonreciprocity of elastic waves that is obviously different from the asymmetric propagation of elastic waves in the non-periodic structure.Further,we demonstrate that the time-reversal and spatial inversion symmetry breakings of magnetoelastic system are the necessary factor for nonreciprocal elastic waves in periodic system.In addition,without altering the structure of the system,simply varying the value of the controllable external static magnetic field can tune the frequencies of nonreciprocal elastic waves,which greatly enhances the flexibility of the system.It is worth noting that,different previously proposed nonreciprocal system depending on the nonlinear effect and dynamic elements,this new model is a linear static elastic system,having advantages on high conversion efficiency,miniaturization and stability.(2)The topological interface states for Lamb waves in the one-dimensional tunable magnetoelastic phononic crystal slabs are studied by the finite element method.First,the basic theory of Lamb waves in one-dimensional magnetoelastic phononic crystal slabs composed of alternating nonmagnetic and magnetoelastic layers under an external static magnetic field is derived,and the procedure calculating the band structure by the finite element method is given.The band structure and its topological properties show that a topological phase transition can be induced only by contactlessly and nondestructively tuning the value of the external magnetic field applied on intercell and intracell magnetoelastic layers.Then,it can be observed that topological interface states for Lamb waves appear at the interface between two topologically different magnetoelastic phononic crystal slabs.Furthermore,based on the tunability of the external magnetic field,the existence of topological interface states can be switched and the frequency of topological interface states can be continuously tuned.More importantly,drastically different from the conventional topological phononic crystals that cannot be tuned after machining,the arbitrary positions of topological interface states can be dynamically achieved by varying the external magnetic field without altering the structure.(3)The spin topological edge states for Lamb waves in two-dimensional tunable phononic crystal slabs are studied by the finite element method.First,we construct phononic crystal slabs with movable sandwich cylinders,and give the method to calculate the corresponding band structure.The band structure and its topological properties show that the pseudo-spin orbit coupling effect can be induced by shifting the sandwich cylinders up or down,resulting in a spin topological phase transit ion.Then,it can be demonstrated that spin topological edge states for Lamb waves appear at the interface of the supercell formed by phononic crystal slabs with different topological properties.Furthermore,based on the full wave simulation,the topologically protected unidirectional transmission of Lamb waves and the robustness of spin topological edge states for Lamb waves against defects are observed.Finally,we demonstrate the dynamic tunability of both frequency and topological transport pathways for Lamb waves in the system,which provides the possibility of designing novel tunable functional devices.(4)The valley topological edge states for multi-mode Lamb waves in the same frequency range in two-dimensional tunable phononic crystal slabs are stu died by the finite element method.First,we construct phononic crystal slabs with movable sandwich columns.The band structure and its topological properties show that a valley topological phase transition can be induced by selective removing the sandwich columns.Then,it can be demonstrated that valley topological edge states for multi-mode Lamb waves in the same frequency range appear at the interface of the supercell formed by phononic crystal slabs with different topological properties.Furthermore,based on the full wave simulation,the topologically protected unidirectional transmission of Lamb waves and the robustness of valley topological edge states for Lamb waves against defects are observed.Finally,we demonstrate the dynamic tunability of topological transport pathways for Lamb waves in the system.In summary,this paper systematically investigates the nonreciprocity and topological properties of tunable phononic crystal slabs,the corresponding theory and methods calculating the band structure are derived,and the tunable nonreciprocity of elastic waves,topological interface states for Lamb waves,topological edge states for Lamb waves are demonstrated.The main innovations are summarized as follows: 1)Tunable nonreciprocity of elastic waves is realized in one-dimensional linear agnetoelastic phononic crystal slabs under an external static magnetic field for the first time,which provides important scheme for designing nonreciprocal devices with high conversion efficiency,miniaturization,and high stability;2)With no need of altering the structure,magnetically tunable topological interface states for Lamb waves are achieved by contactlessly,nondestructively and intelligently tuning the value of the external magnetic field in one-dimensional magnetoelastic phononic crystal slabs;3)We present relatively simple tunable phononic crystal slabs exhibiting spin topological edge states for Lamb waves and dynamically tunable topological transport pathways for Lamb waves;4)We present tunable phon onic crystal slabs exhibiting valley topological edge states for multi-mode Lamb waves in the same frequency and tunable topological transport pathways for Lamb waves,which enhances the carrying capacity of acoustic information and the security of transmitting information,broadening practical application.The research in this paper lays an extremely important theoretical basis for vibration and noise reduction in engineering and the development of acoustic functional devices.