磁电弹性声带隙材料结构中的弹性波传播与局部化研究
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摘要
弹性波在周期结构中的传播以及由此而引发的关于声带隙材料(声子晶体)的研究是近年来力学、物理学以及材料科学的热点问题之一。由于声子晶体本身所具有的禁带特性,使得这类结构在隔振、隔音、降噪、声波导与声滤波器等工程技术领域具有广泛的应用前景。以压电材料为代表的智能材料的广泛应用,以及结构中存在随机失谐时而引起的弹性波局部化现象,使得弹性波在智能声带隙材料中的传播及局部化问题的研究具有重要意义。本文系统地研究了弹性波在压电、磁电弹性声带隙材料中的传播以及系统存在随机失谐情况下弹性波的局部化行为。具体完成的主要研究工作如下:
研究了二维压电声子晶体中散射体形状以及矩形点阵长宽比对带隙结构的影响。根据固体物理学中的平面波展开法,得到了弹性波的带隙结构。提出了以往关于光子晶体以及纯弹性声子晶体中,散射体形状不同时禁带宽度与填充比之间的关系,在压电散射体情况下存在局限性。验证了纯弹性声带隙材料中矩形点阵结构的带隙行为,在压电系统中同样存在。
发展了用于研究二维压电声带隙材料的平面波展开法,解决了三维压电周期结构中弹性波的传播问题。给出了此类系统中模态耦合情况下的广义特值方程,并在第一Brillouin区内进行求解,从而得到带隙结构。同时,针对简单立方、体心立方以及面心立方三种典型三维点阵结构,系统地研究了其禁带特性。分析了散射体填充率以及压电效应对带隙行为的影响。
设计和研究了压电/压磁以及磁电弹性声带隙材料的弹性波禁带特性,给出了求解该类问题的分析方法。根据结构的周期性以及Bloch定理,得到了力-电-磁场耦合情况下的弹性动力学广义特征值方程。对比了散射体在不同点阵结构情况下的禁带特性。同时,研究了具有Kagome点阵的磁电弹性声带隙材料中弹性波的禁带性能,分析了压电性与压磁性对带隙结构的影响。
研究了随机失谐压电声带隙材料中Rayleigh表面波的传播与局部化问题。根据结构表面力场与电场的边界条件,通过迭代求解得到了Rayleigh表面波沿深度方向的衰减系数。给出了结构的传递矩阵以及局部化因子的表达式。分析了结构尺寸与弹性系数随机失谐对Rayleigh表面波传播与局部化行为的影响。同时,研究了含有初应力的压电杆状声带隙材料中弹性波的传播与局部化问题。给出了结构中局部化因子与局部化长度的表达式。分析了结构随机失谐以及初应力对波的传播与局部化特性的影响。
研究了热效应情况下随机失谐层状三组元声带隙材料中SH波的传播与局部化问题。根据相邻单胞边界处的连续条件,推导了结构中弹性波的传递矩阵,给出了结构中局部化因子的表达式。分析了弹性波入射角、厚度比、材料常数失谐、热效应对波的传播与局部化特性的影响,讨论了含橡胶层声带隙材料的禁带特性。
研究了二维声带隙材料中存在随机失谐情况时弹性波的传播与局部化问题。以往关于二维声带隙材料缺陷态的研究多局限于点缺陷与线缺陷这样的确定性缺陷问题,带隙结构可以准确地描述这类特性。但对于二维随机缺陷问题,由于问题的复杂性和不确定性,求解确定性缺陷问题的方法已不再适合。所以,需要寻求一种适合研究二维随机缺陷声带隙材料的方法。结合平面波展开法、传递矩阵方法以及矩阵特征值方法,给出了二维声子晶体中局部化因子的表达式。验证了局部化因子同样可以表征二维声带隙材料的带隙结构,并可有效地描述随机失谐声带隙材料中波的传播特性。分析了随机失谐量以及散射体填充率对弹性波局部化行为的影响。与含有随机分布气泡的液体中声波的局部化问题相比,观察到了类似的物理现象,比较了二者的区别。
In recent years, there is a lot of work on the elastic wave propagation in periodic structures which becomes a hot topic on band gap materials (phononic crystals) in mechanics, physics and material science. With the stop band characteristics, these structures can be extensively applied in vibration isolation technology, sound isolation, noise suppression, sound wave-guide and sound filter. Due to the wide use of piezoelectric materials and the random disorder in periodic structures which results in the wave localization, it is important to investigate the elastic wave propagation and localization in intelligent band gap materials. In this thesis, the elastic wave propagation in piezoelectric and magnetoelectroelastic band gap materials and localization in randomly disorder systems are studied systematically. The primary obtained results are as follows:
The effects of scatterer shapes and lattice constant ratios for rectangular lattice on the band gap structures of the two-dimensional piezoelectric phononic crystals are studied. Based on the plane wave expansion method in solid physics, the band gap structures of elastic waves are derived. The limitation of the relation between the band gap widths and the filling fractions with different scatterer shapes are pointed out for piezoelectric scatterers, which is valid for the photonic crystals and pure elastic systems. The influences of the lattice constant ratio for rectangular lattices on the band gap characteristics in the pure phononic crystals are also exist in the piezoelectric periodic structures with rectangular lattices.
The plane wave expansion method for the two-dimensional piezoelectric acoustic band gap materials is developed and used to investigate the wave propagation in three-dimensional piezoelectric periodic structures. The generalized eigenvalue equation is presented for this case with coupling modes and the band gap structures can be obtained in the first Brillouin zone. At the mean time, the stop band characteristics are studied systematically by considering three typical kinds of lattices (i.e. sc, bcc and fcc). The effects of the filling fraction and piezoelectricity on the band gap properties are analyzed.
The piezoelectric/piezomagnetic and magnetoelectroelastic band gap materials are designed and studied and the analytical method for this problem is presented. Based on the periodicity and the Bloch theory, the generalized eigenvalue equation of elastic dynamics is provided by considering the mechanical-electro-magneto coupling into account. The stop band characteristics for different lattices are compared. Simultaneously, the band gap characteristics of magnetoelectroelastic band gap materials with Kagome lattices are investigated and the effects of the piezoelectricity and piezomagneticity on the band gap structures are analyzed.
The propagation and localization characteristics of Rayleigh surface waves in randomly disordered piezoelectric band gap materials are studied. With the surface boundary condition of the mechanical and electrical fields, the decaying rate of Rayleigh surface waves along the depth direction can be iteratively obtained. The expressions of the transfer matrix and the localization factor are presented. The effects of the random disorder of the structural length and the material constant on the localization behaviors of Rayleigh surface waves are analyzed. Simultaneously, the propagation and localization of elastic waves in randomly disordered piezoelectric rod band gap materials with initial stress are studied. The expressions of the localization factor and the localization length are presented. The effects of the random disorder and initial stress on the wave propagation and localization characteristics are analyzed.
The SH waves propagation and localization in randomly disordered layered three-component band gap materials with thermal effects are studied. According to the continuous condition between the consecutive unit cells, the transfer matrix is derived and the expression of the localization factor is presented. The influences of the elastic wave incident angel, thickness ratio, material constant and thermal effects on wave propagation and localization characeristics are analyzed. The stop band characteristics of band gap materials with rubber are discussed.
The elastic wave propagation and localization behaviors in two-dimensional band gap materials with random disorder are studied. The studies on the two-dimensional band gap materials with defects are mainly focoused on the point and linear defects which can be considered as the determined ones. The stop band characteristics can be described by the band gap structures. However, this method will not be suitable when these defects become random. Based on the plane wave expansion, transfer matrix and matrix eigenvalue methods, the localization factor is presented for two-dimensional phononic crystals. The localization factor is also an effective way to describe the band gap structures of two-dimensional band gap materials. The randomness and filling fraction on the elastic wave localization behaviors are analyzed. Compared with the case of the acoustic wave localization in liquid media with random bubble, similar phenomena can also be observed for this system and the difference between them is illustrated.
研究了二维压电声子晶体中散射体形状以及矩形点阵长宽比对带隙结构的影响。根据固体物理学中的平面波展开法,得到了弹性波的带隙结构。提出了以往关于光子晶体以及纯弹性声子晶体中,散射体形状不同时禁带宽度与填充比之间的关系,在压电散射体情况下存在局限性。验证了纯弹性声带隙材料中矩形点阵结构的带隙行为,在压电系统中同样存在。
发展了用于研究二维压电声带隙材料的平面波展开法,解决了三维压电周期结构中弹性波的传播问题。给出了此类系统中模态耦合情况下的广义特值方程,并在第一Brillouin区内进行求解,从而得到带隙结构。同时,针对简单立方、体心立方以及面心立方三种典型三维点阵结构,系统地研究了其禁带特性。分析了散射体填充率以及压电效应对带隙行为的影响。
设计和研究了压电/压磁以及磁电弹性声带隙材料的弹性波禁带特性,给出了求解该类问题的分析方法。根据结构的周期性以及Bloch定理,得到了力-电-磁场耦合情况下的弹性动力学广义特征值方程。对比了散射体在不同点阵结构情况下的禁带特性。同时,研究了具有Kagome点阵的磁电弹性声带隙材料中弹性波的禁带性能,分析了压电性与压磁性对带隙结构的影响。
研究了随机失谐压电声带隙材料中Rayleigh表面波的传播与局部化问题。根据结构表面力场与电场的边界条件,通过迭代求解得到了Rayleigh表面波沿深度方向的衰减系数。给出了结构的传递矩阵以及局部化因子的表达式。分析了结构尺寸与弹性系数随机失谐对Rayleigh表面波传播与局部化行为的影响。同时,研究了含有初应力的压电杆状声带隙材料中弹性波的传播与局部化问题。给出了结构中局部化因子与局部化长度的表达式。分析了结构随机失谐以及初应力对波的传播与局部化特性的影响。
研究了热效应情况下随机失谐层状三组元声带隙材料中SH波的传播与局部化问题。根据相邻单胞边界处的连续条件,推导了结构中弹性波的传递矩阵,给出了结构中局部化因子的表达式。分析了弹性波入射角、厚度比、材料常数失谐、热效应对波的传播与局部化特性的影响,讨论了含橡胶层声带隙材料的禁带特性。
研究了二维声带隙材料中存在随机失谐情况时弹性波的传播与局部化问题。以往关于二维声带隙材料缺陷态的研究多局限于点缺陷与线缺陷这样的确定性缺陷问题,带隙结构可以准确地描述这类特性。但对于二维随机缺陷问题,由于问题的复杂性和不确定性,求解确定性缺陷问题的方法已不再适合。所以,需要寻求一种适合研究二维随机缺陷声带隙材料的方法。结合平面波展开法、传递矩阵方法以及矩阵特征值方法,给出了二维声子晶体中局部化因子的表达式。验证了局部化因子同样可以表征二维声带隙材料的带隙结构,并可有效地描述随机失谐声带隙材料中波的传播特性。分析了随机失谐量以及散射体填充率对弹性波局部化行为的影响。与含有随机分布气泡的液体中声波的局部化问题相比,观察到了类似的物理现象,比较了二者的区别。
In recent years, there is a lot of work on the elastic wave propagation in periodic structures which becomes a hot topic on band gap materials (phononic crystals) in mechanics, physics and material science. With the stop band characteristics, these structures can be extensively applied in vibration isolation technology, sound isolation, noise suppression, sound wave-guide and sound filter. Due to the wide use of piezoelectric materials and the random disorder in periodic structures which results in the wave localization, it is important to investigate the elastic wave propagation and localization in intelligent band gap materials. In this thesis, the elastic wave propagation in piezoelectric and magnetoelectroelastic band gap materials and localization in randomly disorder systems are studied systematically. The primary obtained results are as follows:
The effects of scatterer shapes and lattice constant ratios for rectangular lattice on the band gap structures of the two-dimensional piezoelectric phononic crystals are studied. Based on the plane wave expansion method in solid physics, the band gap structures of elastic waves are derived. The limitation of the relation between the band gap widths and the filling fractions with different scatterer shapes are pointed out for piezoelectric scatterers, which is valid for the photonic crystals and pure elastic systems. The influences of the lattice constant ratio for rectangular lattices on the band gap characteristics in the pure phononic crystals are also exist in the piezoelectric periodic structures with rectangular lattices.
The plane wave expansion method for the two-dimensional piezoelectric acoustic band gap materials is developed and used to investigate the wave propagation in three-dimensional piezoelectric periodic structures. The generalized eigenvalue equation is presented for this case with coupling modes and the band gap structures can be obtained in the first Brillouin zone. At the mean time, the stop band characteristics are studied systematically by considering three typical kinds of lattices (i.e. sc, bcc and fcc). The effects of the filling fraction and piezoelectricity on the band gap properties are analyzed.
The piezoelectric/piezomagnetic and magnetoelectroelastic band gap materials are designed and studied and the analytical method for this problem is presented. Based on the periodicity and the Bloch theory, the generalized eigenvalue equation of elastic dynamics is provided by considering the mechanical-electro-magneto coupling into account. The stop band characteristics for different lattices are compared. Simultaneously, the band gap characteristics of magnetoelectroelastic band gap materials with Kagome lattices are investigated and the effects of the piezoelectricity and piezomagneticity on the band gap structures are analyzed.
The propagation and localization characteristics of Rayleigh surface waves in randomly disordered piezoelectric band gap materials are studied. With the surface boundary condition of the mechanical and electrical fields, the decaying rate of Rayleigh surface waves along the depth direction can be iteratively obtained. The expressions of the transfer matrix and the localization factor are presented. The effects of the random disorder of the structural length and the material constant on the localization behaviors of Rayleigh surface waves are analyzed. Simultaneously, the propagation and localization of elastic waves in randomly disordered piezoelectric rod band gap materials with initial stress are studied. The expressions of the localization factor and the localization length are presented. The effects of the random disorder and initial stress on the wave propagation and localization characteristics are analyzed.
The SH waves propagation and localization in randomly disordered layered three-component band gap materials with thermal effects are studied. According to the continuous condition between the consecutive unit cells, the transfer matrix is derived and the expression of the localization factor is presented. The influences of the elastic wave incident angel, thickness ratio, material constant and thermal effects on wave propagation and localization characeristics are analyzed. The stop band characteristics of band gap materials with rubber are discussed.
The elastic wave propagation and localization behaviors in two-dimensional band gap materials with random disorder are studied. The studies on the two-dimensional band gap materials with defects are mainly focoused on the point and linear defects which can be considered as the determined ones. The stop band characteristics can be described by the band gap structures. However, this method will not be suitable when these defects become random. Based on the plane wave expansion, transfer matrix and matrix eigenvalue methods, the localization factor is presented for two-dimensional phononic crystals. The localization factor is also an effective way to describe the band gap structures of two-dimensional band gap materials. The randomness and filling fraction on the elastic wave localization behaviors are analyzed. Compared with the case of the acoustic wave localization in liquid media with random bubble, similar phenomena can also be observed for this system and the difference between them is illustrated.
引文
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