二维非局部线弹性平面问题的辛分析

将二维非局部线弹性理论引入到Hamilton体系下,基于变分原理推导得出了二维线弹性理论的对偶方程和相应的边界条件.在分析验证对偶方程的准确性的基础上,该套方法被应用于二维弹性平面波问题的求解.将精细积分与扩展的W-W算法相结合在Hamilton体系下建立了求解平面Rayleigh波的数值算法.从推导到计算的保辛性确保了辛体系非局部理论与算法的准确性.通过对不同算例的数值计算,分析和对比了非局部理论方法与传统局部理论方法的差别,并进一步指出了该套算法的适用性和优势所在.     

声子晶体结构在汽车制动降噪中的理论研究及应用

基于弹性波在声子晶体结构中传播时会产生弹性波带隙,即特定频率范围的弹性波被禁止传播这一特性,为降低高频的制动噪音,将声子晶体这一新结构引入到汽车盘式制动装置中。通过对汽车制动噪音频谱的分析,得到高频噪音比较集中的频段。通过设计专用的二维空气柱/钢体系正方格子声子晶体结构(体积占有率为40%),使高频噪声集中频段(2000~2500Hz)落于声子禁带中,以达到降噪的目的。与传统的制动降噪技术相比,利用声子晶体结构的降噪装置具有频带宽和降噪量大的优越性。通过实验装置验证了声子晶体降噪结构的可行性,在2000~2500Hz范围内,声压的降低幅值最大可达25dB,平均降噪量可达13dB以上,即对汽车刹车减噪起到了明显的效果。     

类石墨烯二维原子晶体的微态理论模型

基于微态(Micromorphic) 连续介质理论,提出了针对类石墨烯二维原子晶体的新力学模型. 该模型以有限大小的布拉维单胞为基元体,考虑基元粒子的宏观位移和微观变形,依据微态理论基本方程,推导了全局坐标系下模型的主导方程. 然后针对布拉维单胞中含有两个原子的类石墨烯晶体,通过分析单胞中声子振动模式与基元体自由度的关系,获得了微态形式下声子色散关系的久期方程,并根据二维晶体声子色散特性对久期方程进行了简化,进而确定了类石墨烯晶体模型的本构方程. 最后,以石墨烯和单层六方氮化硼为例,利用简化的表达式拟合了它们面内声子色散关系数据,计算了模型材料的常数,石墨烯模型的等效杨氏模量、泊松比分别为1.05 TPa 和0.197,氮化硼分别为0.766 TPa 和0.225,均与已有的实验值相符合.     

SH波在局部非均匀声子晶体中的传播

使用传输矩阵法,研究了水平剪切波(SH波)在一维局部材料非均匀声子晶体中的传播。首先使用皮亚诺方程给出了SH波在特定非均匀梯度介质声场的传输矩阵。然后使用传输矩阵和布洛赫定律给出了该声子晶体的禁带结构和传输系数。通过具体计算,发现这种非均匀性能明显影响声子晶体的频散曲线和禁带结构。然后比较了幂指数取不同值时,禁带结构与归一化频率和填充比的关系。发现幂指数不同,声子晶体的禁带不同。     

半无限周期声子晶体的全反射隧穿能带

利用色散法研究了在入射角大于全反射角时弹性波在一维半无限周期声子晶体中的传输特性。结果发现当弹性波大于全反射角入射一维半无限周期声子晶体时出现了两级全反射隧穿导带;并得出了全反射隧穿导带随入射角和周期厚度的响应曲线,分析可知:导带的频率中心随入射角的增加而增加,随周期厚度的增加而降低;导带的频率宽度随入射角的增加而减小,随周期厚度的增加而降低。     

弹性波斜入射声子晶体的传输特性

引入四维波矢的概念,推导出弹性波斜入射到多层介质系统的转移矩阵以及透射系数和反射系数公式.利用这些公式计算了横波和纵波斜入射一维声子晶体时横渡和纵波的透射系数,得出横波斜入射,透射波中的横波和纵波在一定频率范围内都会出现禁带,纵波斜入射时也有类似的结果.透射波中横波与纵波的相互转型随着入射角的增大而越加明显.     

固-液圆柱掺杂声子晶体中弹性波的缺陷模

利用一维固-液圆柱形掺杂声子晶体中弹性波横向受限的条件,推导出弹性波在一维固-液圆柱形掺杂声子晶体中各种模式满足的关系式,研究了各种模式弹性波的特性。利用转移矩阵计算出弹性波的缺陷模随模式量子数以及圆柱半径的变化规律,得到了一些一维固-液结构圆柱形掺杂声子晶体缺陷模的新特征。研究结果表明,缺陷模的频率和半高宽均与模式量子数和圆柱半径有关。     

最优二维固/固声子晶体带隙特性研究

声子晶体是一种具有弹性波带隙特性的周期性复合材料,其带隙特性受单胞拓扑形状的影响.通过拓扑优化技术,能够突破传统设计方法的局限,实现对声子晶体的主动设计.论文基于遗传算法和改进的平面波展开法,通过两阶段的优化过程,得到具有最大相对带隙的二维铜/环氧树脂声子晶体结构,并进一步研究不同带隙最优声子晶体单胞拓扑形状及其带隙特性.结果表明,利用所开发的带隙优化程序,能够得到满足带隙要求的具有全局最优的声子晶体结构;声子晶体最低带隙所对应的单胞是简单晶格结构,其散射体形状简单,而且对应的带隙频率最低,相对带隙最大,对于隔音减振最有实用价值.     

波能耗散的结构阻尼损耗因子度量方法

根据波动理论,用Timoshenko梁理论在高频范围内分析能量的耗散,通过重建作为频率函数的色散关系曲线,得到动力粘弹性模量及材料的损失因子。根据动力系统的固有特征方程与材料弹性特性的关系,研究利用阻尼损耗因子定量描述在高频情况下,波在结构中传播时的能量耗散效应以及结构阻尼损耗因子的表示方法,并通过实验利用波的色散关系估计结构的动力粘弹性模量,理论分析和实验结果表明了这种方法的可行性。     

三相声子晶体能带结构计算的位移-面力映射方法

发展了基于位移-面力映射的方法计算三相声子晶体的能带结构,分析了弹性波在其中传播的特性.由弹性动力学方程出发,利用位移.面力映射,导出波动模态的特征值方程,得到三相局域共振声子晶体反平面剪切波的频散关系(即能带结构).以金-橡胶-环氧树脂体系为例,计算并分析了材料组配、几何尺寸等对频散关系造成的影响.研究结果显示:位移...     

Construction of multi-dimensional isotropic kernels for nonlocal elasticity based on phonon dispersion data

Kernels for non-local elasticity are in general obtained from phonon dispersion relations. However, non-local elastic kernels are in the form of three-dimensional (3D) functions, whereas the dispersion relations are always in the form of one-dimensional (1D) frequency versus wave number curves corresponding to a particular wave direction. In this paper, an approach to build 2D and 3D kernels from 1D phonon dispersion data is presented. Our particular focus is on isotropic media where we show that kernels can be obtained using Fourier–Bessel transform, yielding axisymmetric kernel profiles in reciprocal and real spaces. These kernel functions are designed to satisfy the necessary requirements for stable wave propagation, uniformity of nonlocal stress and stress regularization. The proposed concept is demonstrated by developing some physically meaningful 2D and 3D kernels that will find useful applications in nonlocal mechanics. Relative merits of the kernels obtained via proposed methods are explored by fitting 1D kernels to dispersion data for Argon and using the kernel to understand the size effect in non local energy as seen from molecular simulations. A comparison of proposed kernels is made based on their predictions of stress field around a crack tip singularity.     

Nonlocal shell model for elastic wave propagation in single- and double-walled carbon nanotubes

This paper investigates the transverse and torsional wave in single- and double-walled carbon nanotubes (SWCNTs and DWCNTs), focusing on the effect of carbon nanotube microstructure on wave dispersion. The SWCNTs and DWCNTs are modeled as nonlocal single and double elastic cylindrical shells. Molecular dynamics (MD) simulations indicate that the wave dispersion predicted by the nonlocal elastic cylindrical shell theory shows good agreement with that of the MD simulations in a wide frequency range up to the terahertz region. The nonlocal elastic shell theory provides a better prediction of the dispersion relationships than the classical shell theory when the wavenumber is large enough for the carbon nanotube microstructure to have a significant influence on the wave dispersion. The nonlocal shell models are required when the wavelengths are approximately less than 2.36×10⁻⁹ and 0.95×10⁻⁹ m for transverse wave in armchair (15,15) SWCNT and torsional wave in armchair (10,10) SWCNT, respectively. Moreover, an MD-based estimation of the scale coefficient e₀ for the nonlocal elastic cylindrical shell model is suggested. Due to the small-scale effects of SWCNTs and the interlayer van der Waals interaction of DWCNTs, the phase difference of the transverse wave in the inner and outer tube can be observed in MD simulations in wave propagation at high frequency. However, the van der Waals interaction has little effect on the phase difference of transverse wave.     

Theoretical and numerical investigation of HF elastic wave propagation in two-dimensional periodic beam lattices

The elastic wave propagation phenomena in two-dimensional periodic beam lattices are studied by using the Bloch wave transform. The numerical modeling is applied to the hexagonal and the rectangular beam lattices, in which, both the in-plane （with respect to the lattice plane） and out-of-plane waves are considered. The dispersion relations are obtained by calculating the Bloch eigenfrequencies and eigenmodes. The frequency bandgaps are observed and the influence of the elastic and geometric properties of the primitive cell on the bandgaps is studied. By analyzing the phase and the group velocities of the Bloch wave modes, the anisotropic behaviors and the dispersive characteristics of the hexagonal beam lattice with respect to the wave prop- agation are highlighted in high frequency domains. One im- portant result presented herein is the comparison between the first Bloch wave modes to the membrane and bend- ing/transverse shear wave modes of the classical equivalent homogenized orthotropic plate model of the hexagonal beam lattice. It is shown that, in low frequency ranges, the homog- enized plate model can correctly represent both the in-plane and out-of-plane dynamic behaviors of the beam lattice, its frequency validity domain can be precisely evaluated thanks to the Bloch modal analysis. As another important and original result, we have highlighted the existence of the retro- propagating Bloch wave modes with a negative group veloc- ity, and of the corresponding ＂retro-propagating＂ frequency bands.     

蜂窝材料的弹性波传播特性

通过研究蜂窝材料的弹性波频散关系，分析了其弹性波传播特性. 采用基于小波理论的 分析方法，将材料参数和位移均展开为双正交周期小波基函数的形式，利用Bloch定理将波 动方程转化为特征值方程，求解该方程得到3种典型结构------正方、三角与六角排列的铝 (Al)和聚丙烯(PP)蜂窝材料的频散关系，并进行了比较分析. 结果显示：结构形式的不 同显著地影响其波动特性，而制作材料的不同则没有影响；3种结构形式都不存在完全带隙， 但正方和三角形结构在一定的传播方向范围内存在方向带隙，而六角形结构则在任何方向都 不存在方向带隙；与正方结构相比，三角结构在相同孔隙率下，在更广的传播方向内和更低 的频率下，能产生较宽的方向带隙.     

Waves in Nonlocal Elastic Solid with Voids

In this paper, the governing relations and equations are derived for nonlocal elastic solid with voids. The propagation of time harmonic plane waves is investigated in an infinite nonlocal elastic solid material with voids. It has been found that three basic waves consisting of two sets of coupled longitudinal waves and one independent transverse wave may travel with distinct speeds. The sets of coupled waves are found to be dispersive, attenuating and influenced by the presence of voids and nonlocality parameters in the medium. The transverse wave is dispersive but non-attenuating, influenced by the nonlocality and independent of void parameters. Furthermore, the transverse wave is found to face critical frequency, while the coupled waves may face critical frequencies conditionally. Beyond each critical frequency, the respective wave is no more a propagating wave. Reflection phenomenon of an incident coupled longitudinal waves from stress-free boundary surface of a nonlocal elastic solid half-space with voids has also been studied. Using appropriate boundary conditions, the formulae for various reflection coefficients and their respective energy ratios are presented. For a particular model, the effects of non-locality and dissipation parameter (\(\tau \)) have been depicted on phase speeds and attenuation coefficients of propagating waves. The effect of nonlocality on reflection coefficients has also been observed and shown graphically.     

梯形应力脉冲在弹性杆中的传播过程和几何弥散

在应力波传播过程中,几何弥散效应往往难以避免.对应力波在弹性杆中传播的几何弥散效应进行解析分析,对于基础波动问题研究以及材料动态力学行为表征等课题,显得至关重要.本文简单说明了弹性杆中考虑横向惯性修正的一维 Rayleigh-Love应力波理论,概述了其波动控制方程的变分法推导过程;针对 Hopkinson杆实验中常用的梯形应力加载脉冲,建立了相应的偏微分方程初边值问题的求解模型,并运用 Laplace变换方法研究了脉冲在杆中传播的几何弥散现象;根据留数定理进行 Laplace反变换,给出了杆中不同位置和时刻的应力波的级数形式解析解,分析了计算项数对结果收敛性的影响;将解析计算结果与采用三维有限元数值模拟的计算结果进行对比,两者吻合程度良好,从而证明 Rayleigh-Love横向惯性修正理论可以有效地表征典型 Hopkinson杆实验中的几何弥散效应.在此基础上围绕梯形加载脉冲的弥散效应进行参数研究,定量描述了传播距离、泊松比、脉冲斜率等参数的影响.本文给出的 Rayleigh-Love杆在梯形加载条件下的解析解,揭示了几何弥散效应的本质规律,可以用于实际实验的弥散修正过程.      

Effect of small size on dispersion characteristics of wave in carbon nanotubes

Effect of small size on dispersion characteristics of waves in multi-walled carbon nanotubes is investigated using an elastic shell model. Dynamic governing equations of the carbon nanotube are formulated on the basis of nonlocal elastic theory. The relationship between wavenumber and frequency of wave propagation is obtained from the solution of the eigenvalue equations. The numerical results show that the dispersion characteristics of wave in the multi-walled carbon nanotube are affected by the small size. Effect of small size is not obvious for the smaller wavenumber, and it will arise and increase gradually with the increase of the wavenumber. Effect of the small size will decrease as the inner radius of carbon nanotubes increases. In addition, the explicit expressions of the cut-off frequencies are derived. The results show that the cut-off frequencies cannot be influenced by the small size of carbon nanotubes.     

Hamiltonian systems of propagation of elastic waves and localized vibrations in the strip plate

In this paper, based on Lagrange–Germanian theory of elastic thin plates, applying the method in Hamiltonian state space, the elastic waves and vibrations when the boundary of the two lateral sides of the strip plate are free of traction are investigated, and the process of analysis and solution are proposed. The existence of all kinds of vibration modes and wave propagation modes is also analyzed. By using eigenfunction expansion method, the dispersion relations of waveguide modes in the strip plate are derived, and the comparisons with the dispersion relations directly obtained by the classical theory of thin plates are also presented. At last, the results are analyzed and discussed.