简单周期结构波传播主动控制研究

研究了在梁结构插入压电材料的周期结构波传播的一般规律。以梁的弯曲波传播方程的解析解为基础，进一步分析了简单周期结构的波传播的一些固有特性。并在此基础上，以压电材料作为作动器，采用主动控制方法研究了调整结构传播波的带通、带阻的频率范围可行性和有效性。     

周期性加筋板中的波传播特性

本文利用周期性结构的交互变分原理分析加筋板的波传播特性。并引进升阶谱有限元以提高计算精度，验证了该方法在高频区域的有效性。最后，分析了加筋板的长宽比，加筋状态及边界条件对结构波传播的影响。     

结构中弹性波传播的可视化方法

由于结构中弹性波传播的复杂性，其场量(位移、应变、速度)表达式往往为繁杂、冗长的数学表达式，表达式本身不能直观、形象地表征结构中弹性波的传播特征．本文以杆中纵波传播为例，基于Matlab开发了弹性波传播特征的可视化程序，将杆中纵波传播特性以一种动态、直观、形象的形式展现出来．     

一种可以反射p波的土层结构

本文将光子晶体的概念应用于土层结构设计，并利用传输矩阵法计算了p波在土层结构中的传播特性。结果表明，这种土层结构可以全部反射特定频率范围内入射的p波，从而可以减少p波对地上建筑的破坏。此外，还考察了土层的物理特性对反射频带的影响。     

梯度材料层状结构中的Love波

研究了功能梯度材料层状结构中Love波的传播特性．对覆盖层中的剪切弹性模量沿厚度方向为指数函数和幂函数变化的两种函数形式,利用WKB方法分别求得了波传播问题的近似解析解,通过计算分析,得到了Love波在功能梯度材料层中传播的一些规律．     

细观结构固体层中孤立波的传播及相互作用特性

利用直接微扰方法.确定了孤立波的放大或衰减与孤立波的初始幅度以及介质的结构参数之间的关系.然后利用线性化技术构造出一种二阶精度的稳定差分格式,并对孤立波在细观结构固体层中传播特性进行了数值模拟,特别对细观结构固体层中传播的不同幅度的孤立波的相互作用进行了详细的数值模拟,从而得到在适当条件下细观结构固体层中孤立波传播时即可以衰减、放大又可以稳定传播,且相互作用不影响这种传播特性.     

桁架材料弹性波带隙特性分析

研究了弹性波在周期性桁架材料中的传播特性,并根据桁架材料的周期性特点和杆纵向振动模态,给出了基于单胞的桁架材料弹性波色散(dispersion)方程。分析了1维和2维问题的色散特性,研究了相应的弹性波带隙性质;以CAE分析软件为工具平台对桁架材料的带隙特性进行了数值仿真实验,给出了基于谐响应和特征频率变化特征的仿真实验方法。仿真实验确认了所分析的桁架材料的带隙特性,同时说明所用的仿真实验方法是可行的。     

含单排周期微裂纹平板结构中的弹性波传播

受损伤固体中含有的微裂纹或微孔洞往往具有周期性，对含周期性缺陷结构中的弹性波分析是力学研究中的重要课题，它直接关系到结构的强度和使用寿命。目前对损伤固体中弹性波散射与透射研究结果主要是弹性动力学平面问题。1995年。Scarpetta和Sumbatyan采用解析法研究了平面波在双周期裂纹弹性介质中的传播问题。并推出显式分析结果。本文基于弹性动力学理论，分析研究了含有单排横向周期裂纹的平板中弯曲波的反射与透射问题。给出了含单排裂纹时反射波与透射波系数的数值结果。对于多排裂纹情况，可采用具有退化核第一类Fredholm积分方程方法分析求解，在求解中给出相应的无量纲数，例如无量纲波数、裂纹尺寸比等。本文分析结果可望能在工程振动控制中应用。     

一维格子结构动力分析的传递矩阵法

本文将传递矩阵法推广应用于分析一维格子结构的波传播和动力响应特性。一个格子结构的元件可分为主元件和次元件,传递矩阵沿主元件形成并考虑次元件的作用。文中通过例子说明形成一个周期单元传递矩阵的方法,指出利用传递矩阵计算无限或半无限长格子结构波传播的传播常数及有限长格子结构固有频率和频率响应函数的方法。作为数例,文中计算了一维平面格子结构的传播常数和频率响应函数。     

晶体在冲击作用下产生的相干THz波辐射理论模型与数值模拟

建立宏观电动力学模型,理论预测冲击作用下极性晶体中偶极振荡产生的THz波段的电磁辐射,分析这种电磁辐射的相干性,它预示着一种新型的相干THz波辐射源。通过傅立叶分析和相位叠加方法,数值模拟冲击波在离子晶体中传播时诱导的相干THz波辐射,结果发现,10THz左右的电磁辐射相干长度接近mm量级,若增加晶体沿冲击波方向的尺度,预计相干长度会进一步增长,并且辐射频率的分布具有周期性。分析冲击脉冲形状、晶体横向和纵向周期性对辐射谱的影响。通过数值模拟结果发现,晶格沿冲击波传播方向的周期性是冲击晶体辐射THz波具有相干性最本质的原因,用这种相干THz波辐射谱可以分析冲击作用下物质在原子尺度上的物理特性。     

Symplectic analysis for wave propagation in one-dimensional nonlinear periodic structures

The wave propagation problem in the nonlinear periodic mass-spring structure chain is analyzed using the symplectic mathematical method. The energy method is used to construct the dynamic equation, and the nonlinear dynamic equation is linearized using the small parameter perturbation method. Eigen-solutions of the symplectic matrix are used to analyze the wave propagation problem in nonlinear periodic lattices. Nonlinearity in the mass-spring chain, arising from the nonlinear spring stiffness effect, has profound effects on the overall transmission of the chain. The wave propagation characteristics are altered due to nonlinearity, and related to the incident wave intensity, which is a genuine nonlinear effect not present in the corresponding linear model. Numerical results show how the increase of nonlinearity or incident wave amplitude leads to closing of transmitting gaps. Comparison with the normal recursive approach shows effectiveness and superiority of the symplectic method for the wave propagation problem in nonlinear periodic structures.     

Wave propagation in double helical rods

The propagation of waves in helical rods has been studied extensively. However, studying the wave propagation in double helical rods have received less attention although this can be useful in multiple fields of science and engineering. Obtaining an analytical model for a double helical rod is challenging since the curvature and tortuosity are not constant. Thus, resolving the wave behaviour analytically is nearly impossible. In this paper, wave propagation in a double helical rod will be studied using the wave and finite element method which is a technique that can be used to model homogeneous and periodic one and two dimensional structures based on the periodic structure theory. For modelling a double helical rod, the finite element model of a single turn is processed using Bloch waves. The dispersion curves and wavemodes are obtained and the similarities and differences of waves in helical and double helical rods are highlighted.     

Bloch theorem with revised boundary conditions applied to glide and screw symmetric,quasi-one-dimensional structures

Bloch theorem is useful for analyzing wave propagation in periodic systems. It has been widely used to determine the energy bands of various translationally-periodic crystals and with the advent of nanoscale structures like nanotubes, it has been extended to account for additional symmetries using group theory. However, this extension is restricted to Hamiltonian systems with analytical potentials. For complex problems, as for engineering structures, the periodic unit cells are often discretized and the Bloch method is restricted to translational periodicity.The goal of this paper is to generalize the direct and transfer-matrix propagation Bloch method to structures with glide and screw symmetries by deriving appropriate boundary conditions. Dispersion relations for a set of reduced problems are compared to results from the classical method, when available. It is found that (i) the dispersion curves are easier to interpret, (ii) the computational cost and error are reduced, and (iii) revisited Bloch method is applicable to structures as the Boerdijk–Coxeter helix that do not possess purely-translational symmetries for which the classical method is not applicable.     

非饱和土-结构动力响应的多耦合周期性有限元法

真实的地基土体-隧道系统中土体及结构性质往往沿线路纵向变化.为考虑土体与结构沿纵向的变化特性,提出了一种非饱和土-结构系统动力响应分析的多耦合周期性有限元法.首先基于非饱和土的实用波动方程,采用Galerkin法推导了单节点5个自由度的非饱和土ub-pl-pg格式有限元表达式,相比于单节点9个自由度的ub-v-w格式有...     

Wave propagation in circular cylindrical shells with periodic axial curvature

The propagation of longitudinal and flexural waves in axisymmetric circular cylindrical shells with periodic circular axial curvature is studied using a finite element method previously developed by the authors. Of primary interest is the coupling of these wave modes due to the periodic axial curvature which results in the generation of two types of stop bands not present in straight circular cylinders. The first type is related to the periodic spacing and occurs independently for longitudinal and flexural wave modes without coupling. However, the second type is caused by longitudinal and flexural wave mode coupling due to the axial curvature. A parametric study is conducted where the effects of cylinder radius, degree of axial curvature, and periodic spacing on wave propagation characteristics are investigated. It is shown that even a small degree of periodic axial curvature results in significant stop bands associated with wave mode coupling. These stop bands are broad and conceivably could be tuned to a specific frequency range by judicious choice of the shell parameters. Forced harmonic analyses performed on finite periodic structures show that strong attenuation of longitudinal and flexural motion occurs in the frequency ranges associated with the stop bands of the infinite periodic structure.     

WAVE LOCALIZATION IN RANDOMLY DISORDERED PERIODIC PIEZOELECTRIC RODS

The wave propagation in periodic and disordered periodic piezoelectric rods is studied in this paper. The transfer matrix between two consecutive unit cells is obtained according to the continuity conditions. The electromechanical coupling of piezoelectric materials is considered. According to the theory of matrix eigenvalues, the frequency bands in periodic structures are studied. Moreover, by introducing disorder in both the dimensionless length and elastic constants of the piezoelectric ceramics, the wave localization in disordered periodic structures is also studied by using the matrix eigenvalue method and Lyapunov exponent method. It is found that tuned periodic structures have the frequency passbands and stopbands and localization phenomenon can occur in mistuned periodic structures. Furthermore, owing to the effect of piezoelectricity, the frequency regions for waves that cannot propagate through the structures are slightly increased with the increase of the piezoelectric constant.     

Wave dispersion and dissipation performance of locally resonant acoustic metamaterials using an internal variable model

Engineering structures for different dispersion and dissipation levels of wave propagation use internal variable models, which may enhance the performance of acoustic metamaterials (AMMs). In this study, the wave dispersion and dissipation performance of AMMs is studied using an anelastic displacement fields (ADF) model. A symmetric state-space method based on Floquet-Bloch’s theorem for a nonviscously damped unit cell is developed. The study also constructs Bloch’s eigenvalue problems built from the symmetric state-space formulation to obtain the wavevector-dependent damped frequency and damping ratio for wave propagation analysis of periodic structures. The effects of wave dispersion and dissipation on the performance of AMMs are studied by using two numerical examples of mass-in-mass lattice systems containing multiple resonators. It is shown that nonviscous damping increases the wave dispersion performance of AMM. It is also shown that the metadamping phenomenon enhances the wave dissipation performance of AMM. It is demonstrated that the new method in symmetric form is applicable for performance analysis of periodic phononic crystal.     

The SEA Approach to Vibration Localization in a Nearly Periodic Structure

Abstract

The phenomenon of vibration localization occurring in a nearly periodic structure was investigated through a statistical energy analysis (SEA) approach. The phenomenon has been examined mostly through a wave propagation approach, where a localization factor was often employed to evaluate the strength of vibration localization. The wave propagation approach properly predicted the factor close to Monte Carlo calculations in nearly periodic structures for both weak and strong couplings. In this analytical study, the localization factor was derived from the SEA approach for a nearly periodic structure monocoupled with a weak coupling. The SEA approach sequentially breaks the structure into two-oscillator blocked substructures and proposes a way of determining the vibration localization factor with equations of energy balance. This article shows that the SEA approach is quite appropriate for calculating the vibration localization factor compared to the wave propagation approach.     

The mutual variational principle of free wave propagation in periodic structures

By taking infinite periodic beams as examples, the mutual variational principle for analyzing the free wave propagation in periodic structures is established and demonstrated through the use of the propagation constant in the present paper, and the corresponding hierarchical finite element formulation is then derived. Thus, it provides the numerical analysis of that problem with a firm theoretical basis of variational principles, with which one may conveniently illustrate the mathematical and physical mechanisms of the wave propagation in periodic structures and the relationship with the natural vibration. The solution is discussed and examples are given. Supported by Doctorate Training Fund of National Education Commission of China     

失谐周期结构中弹性波与振动的局部化

基于弹性波传递矩阵方法，研究了失谐周期结构中弹性波与振动的局部化问题．给出了结构中弹性波传递矩阵的一般表达式，采用奇异值分解方法，分别计算了谐和与失谐周期结构中的局部化因子，并对其进行了分析讨论．对周期结构中波传播与振动局部化的分析方法可用于结构的优化设计．