Band gaps of 2D phononic crystal with orthotropic cylindrical fillers embedded in the isotropic host are studied in this paper. Two kinds of periodic structures, namely, the square lattice and the triangle lattice, ar...Band gaps of 2D phononic crystal with orthotropic cylindrical fillers embedded in the isotropic host are studied in this paper. Two kinds of periodic structures, namely, the square lattice and the triangle lattice, are considered. For anisotropic phononic crystal, band gaps not only depend on the periodic lattice but also the angle between the symmetry axis of orthotropic material and that of the periodic structure. Rotating these cylindrical fillers makes the angle changing continuously; as a result, pass bands and forbidden bands of the phononic crystal are changed. The plane wave expansion method is used to reduce the band gap problem to an eigenvalue problem. The numerical example is given for YBCO/Epoxy composites. The location and the width of band gaps are estimated for different rotating angles. The influence of anisotropy on band gaps is discussed based on numerical results.展开更多
In this paper, the elastic wave propagation in a two-dimensional piezoelectric phononic crystal is studied by considering the mechanic-electric coupling. The generalized eigenvalue equation is obtained by the relation...In this paper, the elastic wave propagation in a two-dimensional piezoelectric phononic crystal is studied by considering the mechanic-electric coupling. The generalized eigenvalue equation is obtained by the relation of the mechanic and electric fields as well as the Bloch-Floquet theorem. The band structures of both the in-plane and anti-plane modes are calculated for a rectangular lattice by the planewave expansion method. The effects of the lattice constant ratio and the piezoelectricity with different filling fractions are analyzed. The results show that the largest gap width is not always obtained for a square lattice. In some situations, a rectangular lattice may generate larger gaps. The band gap characteristics are influenced obviously by the piezoelectricity with the larger lattice constant ratios and the filling fractions.展开更多
A wavelet-based method was developed to compute elastic band gaps of one-dimensional phononic crystals. The wave field was expanded in the wavelet basis and an equivalent eigenvalue problem was derived in a matrix for...A wavelet-based method was developed to compute elastic band gaps of one-dimensional phononic crystals. The wave field was expanded in the wavelet basis and an equivalent eigenvalue problem was derived in a matrix form involving the adaptive computation of integrals of the wavelets. The method was then applied to a binary system. For comparison, the elastic band gaps of the same one-dimensional phononic crystals computed with the wavelet method and the well- known plane wave expansion (PWE) method are both presented in this paper. The numerical results of the two methods are in good agreement while the computation costs of the wavelet method are much lower than that of PWE method. In addition, the adaptability of wavelets makes the method possible for efficient band gap computation of more complex phononic structures.展开更多
Absolute phononic band gaps can be substantially improved in two-dimensional lattices by using a symmetry reduction approach. In this paper, the propagation of elastic waves in a two-dirnensional hybrid triangular lat...Absolute phononic band gaps can be substantially improved in two-dimensional lattices by using a symmetry reduction approach. In this paper, the propagation of elastic waves in a two-dirnensional hybrid triangular lattice structure consisting of stainless steel cylinders in air is investigated theoretically. The band structure is calculated with the plane wave expansion （PWE） method. The hybrid triangular Bravais lattice is formed by two kinds of triangular lattices. Different from ordinary triangular lattices, the band gap opens at low frequency （between the first and the second bands） regime because of lifting the bands degeneracy at high symmetry points of the Brillouin zone. The location and width of the band gaps can be tuned by the position of the additional rods.展开更多
We present a detailed theoretical study on the acoustic band structure of two-dimensional （2D） phononic crystal. The 2D pho- nonic crystal with parallelogram lattice structure is considered to be formed by rigid sol...We present a detailed theoretical study on the acoustic band structure of two-dimensional （2D） phononic crystal. The 2D pho- nonic crystal with parallelogram lattice structure is considered to be formed by rigid solid rods embedded in air. For the circu- lar rods, some of the extrema of the acoustic bands appear in the usual high-symmetry points and, in contrast, we find that some of them are located in other specific lines. For the case of elliptic rods, our results indicate that it is necessary to study the whole first Brillouin zone to obtain rightly the band structure and corresponding band gaps. Furthermore, we evaluate the first and second band gaps using the plane wave expansion method and find that these gaps can be tuned by adjusting the side lengths ratio R, inclined angle 0 and filling fraction F of the parallelogram lattice with circular rods. The results show that the largest value of the first band gap appears at θ=90° and F--0.7854. In contrast, the largest value of the second band gap is at θ=60° and F=0.9068. Our results indicate that the improvement of matching degree between scatterers and lattice pattern, ra- ther than the reduction of structural symmetry, is mainly responsible for the enhancement of the band gaps in the 2D phononic crystal.展开更多
采用迭代法改进了一维声子晶体带隙特性计算的平面波展开(PWE)算法,以使其适用于组成材料粘弹性所导致的弹性常数随频率非线性变化的特性。将该算法应用于丁腈橡胶(NBR)和钢组成的两种结构尺寸的一维周期结构声子晶体振动带隙的研究中,...采用迭代法改进了一维声子晶体带隙特性计算的平面波展开(PWE)算法,以使其适用于组成材料粘弹性所导致的弹性常数随频率非线性变化的特性。将该算法应用于丁腈橡胶(NBR)和钢组成的两种结构尺寸的一维周期结构声子晶体振动带隙的研究中,理论计算和振动测试结果吻合理想。进一步的理论分析表明,橡胶材料的储能弹性模量随频率的单调增加,使得在保持禁带开始频率不变的同时大大加宽了禁带范围,在3 mm钢/10 mm NBR以及7 mm钢/10 mm NBR两种周期结构一维声子晶体中禁带宽度分别增加了36.4％和34.0％。展开更多
基金supported by the National Natural Science Foundation of China (No.10672019)
文摘Band gaps of 2D phononic crystal with orthotropic cylindrical fillers embedded in the isotropic host are studied in this paper. Two kinds of periodic structures, namely, the square lattice and the triangle lattice, are considered. For anisotropic phononic crystal, band gaps not only depend on the periodic lattice but also the angle between the symmetry axis of orthotropic material and that of the periodic structure. Rotating these cylindrical fillers makes the angle changing continuously; as a result, pass bands and forbidden bands of the phononic crystal are changed. The plane wave expansion method is used to reduce the band gap problem to an eigenvalue problem. The numerical example is given for YBCO/Epoxy composites. The location and the width of band gaps are estimated for different rotating angles. The influence of anisotropy on band gaps is discussed based on numerical results.
基金the National Natural Science Foundation of China (10672017 and 10632020)
文摘In this paper, the elastic wave propagation in a two-dimensional piezoelectric phononic crystal is studied by considering the mechanic-electric coupling. The generalized eigenvalue equation is obtained by the relation of the mechanic and electric fields as well as the Bloch-Floquet theorem. The band structures of both the in-plane and anti-plane modes are calculated for a rectangular lattice by the planewave expansion method. The effects of the lattice constant ratio and the piezoelectricity with different filling fractions are analyzed. The results show that the largest gap width is not always obtained for a square lattice. In some situations, a rectangular lattice may generate larger gaps. The band gap characteristics are influenced obviously by the piezoelectricity with the larger lattice constant ratios and the filling fractions.
基金Supported by the National Natural Science Foundation of China (Grant No. 10632020)
文摘A wavelet-based method was developed to compute elastic band gaps of one-dimensional phononic crystals. The wave field was expanded in the wavelet basis and an equivalent eigenvalue problem was derived in a matrix form involving the adaptive computation of integrals of the wavelets. The method was then applied to a binary system. For comparison, the elastic band gaps of the same one-dimensional phononic crystals computed with the wavelet method and the well- known plane wave expansion (PWE) method are both presented in this paper. The numerical results of the two methods are in good agreement while the computation costs of the wavelet method are much lower than that of PWE method. In addition, the adaptability of wavelets makes the method possible for efficient band gap computation of more complex phononic structures.
基金supported by the National Natural Science Foundation of China(No.10632020).
文摘Absolute phononic band gaps can be substantially improved in two-dimensional lattices by using a symmetry reduction approach. In this paper, the propagation of elastic waves in a two-dirnensional hybrid triangular lattice structure consisting of stainless steel cylinders in air is investigated theoretically. The band structure is calculated with the plane wave expansion （PWE） method. The hybrid triangular Bravais lattice is formed by two kinds of triangular lattices. Different from ordinary triangular lattices, the band gap opens at low frequency （between the first and the second bands） regime because of lifting the bands degeneracy at high symmetry points of the Brillouin zone. The location and width of the band gaps can be tuned by the position of the additional rods.
基金supported by the National Natural Science Foundation of China(Grant No.10974206)
文摘We present a detailed theoretical study on the acoustic band structure of two-dimensional （2D） phononic crystal. The 2D pho- nonic crystal with parallelogram lattice structure is considered to be formed by rigid solid rods embedded in air. For the circu- lar rods, some of the extrema of the acoustic bands appear in the usual high-symmetry points and, in contrast, we find that some of them are located in other specific lines. For the case of elliptic rods, our results indicate that it is necessary to study the whole first Brillouin zone to obtain rightly the band structure and corresponding band gaps. Furthermore, we evaluate the first and second band gaps using the plane wave expansion method and find that these gaps can be tuned by adjusting the side lengths ratio R, inclined angle 0 and filling fraction F of the parallelogram lattice with circular rods. The results show that the largest value of the first band gap appears at θ=90° and F--0.7854. In contrast, the largest value of the second band gap is at θ=60° and F=0.9068. Our results indicate that the improvement of matching degree between scatterers and lattice pattern, ra- ther than the reduction of structural symmetry, is mainly responsible for the enhancement of the band gaps in the 2D phononic crystal.
文摘采用迭代法改进了一维声子晶体带隙特性计算的平面波展开(PWE)算法,以使其适用于组成材料粘弹性所导致的弹性常数随频率非线性变化的特性。将该算法应用于丁腈橡胶(NBR)和钢组成的两种结构尺寸的一维周期结构声子晶体振动带隙的研究中,理论计算和振动测试结果吻合理想。进一步的理论分析表明,橡胶材料的储能弹性模量随频率的单调增加,使得在保持禁带开始频率不变的同时大大加宽了禁带范围,在3 mm钢/10 mm NBR以及7 mm钢/10 mm NBR两种周期结构一维声子晶体中禁带宽度分别增加了36.4％和34.0％。
基金Project supported by the National Outstanding Youth ScienceFoundation of China (Grant No. 50425206), the National NaturalScience Foundation of China (Grant No. 10647132), the NaturalScience Foundation of Hunan Provincial Education Department(Grant No. 06C652), and the Natural Science Foundation of HunanProvincial Education Department (Grant No. 06C653).
