共查询到18条相似文献,搜索用时 140 毫秒
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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。 相似文献
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基于广义胡克定律及混和变量弹性波方程,解析求得各层介质内位移、应力传递矩阵,给出了直角坐标系下各向异性层状介质中弹性波的传播矩阵解法.该方法适用于非轴对称各向异性和点源作用,较好地解决了数值计算中有效数字精度损失问题.数值结果表明,计算效率、准确性及稳定性均较好. 相似文献
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非均匀损伤介质中波传播的数值解 总被引:2,自引:0,他引:2
对弹性波在非均匀损伤介质中的传播理论进行了研究。通过将非均匀损伤区域离散成分层均匀的区域,结合相邻区域交界面处的连续条件,推导出了以右行波、左行波为状态向量的波动方程和传递矩阵。对几种非均匀损伤介质中波的传播进行了实例数值计算,并和其解析解的结果进行了比较,讨论了弹性波在非均匀损伤介质中传播的一般性质。 相似文献
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阶梯压电层合梁的波动动力学特性 总被引:2,自引:0,他引:2
采用行波理论系统地研究了压电阶梯梁的自由振动分析以及强迫响应的分析方法. 基于分布
参数理论研究了压电阶梯梁的波传播特性,忽略柔性梁横向剪切和转动惯量的影响,给出了
梁的轴向和横向的简谐波解. 将压电阶梯梁离散化为单元,考虑压电片的刚度和质量的影响,
建立了节点散射模型. 应用位移连续和力平衡条件,推导了节点的波反射和波传递矩阵,在
此基础上,引入波循环矩阵的概念,给出波循环矩阵、波传递系数矩阵的确定方法. 应用波
循环矩阵可以有效地计算结构的固有频率. 另外,应用波传递系数研究了压电陶瓷作动器位
置对其驱动能力的影响. 得出两个主要结论:1)作动器靠近悬臂梁固定端将有较强的驱动
能力,悬臂梁边界反射行波产生弯曲消失波有利于增大压电波的模态传递系数;2)模态传
递系数与固有频率的灵敏度密切相关,波传递系数越大, 对应该处固有频率变化灵敏度越大.
另外,数值算例表明了行波方法比有限元方法具有更高的计算精度. 相似文献
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能量法具有将求解微分方程边值问题转化为泛函极值问题的优点,故而在结构动力学分析中被广泛使用, 近年来也被引入到周期结构带隙计算中. 然而,由于周期结构边界条件相对复杂,采用传统能量法(如Rayleigh-Ritz法)分析时位移函数构造难度大;且由于位移函数中包含波数项,扫描波数计算带隙的过程中质量、刚度矩阵需不断重算, 导致计算量较大. 鉴于此,本文对传统能量法进行改进,通过引入人工弹簧来模拟包含周期边界在内的各类边界条件,可将边界约束转化为人工弹簧的弹性势能,故而各能量分部中仅有周期边界弹性势能包含波数项,扫描波数时仅需重新计算与其对应的刚度矩阵,其余的质量、刚度矩阵只需要计算一次, 继而显著降低了计算量. 研究结果表明,本文方法准确、可靠, 且相较于传统能量法, 本文方法的计算效率更高,随着结构质量、刚度矩阵的维度增大, 或者扫描波数点数的增多,本文方法计算效率优势更加明显. 此外, 人工弹簧模型使用灵活、便捷,可进一步地拓展到更为复杂的周期性组合结构带隙分析中. 相似文献
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Li Fengming Wang Yuesheng Chen Ali 《Acta Mechanica Solida Sinica》2006,19(1):50-57
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. 相似文献
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Active control of bending waves in a periodic beam by the Timoshenko beam theory is concerned. A discussion about the possible wave solutions for periodic beams and their control by forces is presented. Wave propagation in a periodic beam is studied. The transfer matrix between two consecutive unit cells is obtained based on the continuity conditions. Wave amplitudes are derived by employing the Bloch-Floquet theorem and the transfer matrix. The influences of the propagating constant on the wave amplitudes are considered. It is shown that vibrations are still needed to be suppressed in the pass-band regions. Wave-suppression strategy described in this paper is employed to eliminate the propagating disturbance of an infinite periodic beam. A minimum wave-suppression strategy is compared with the classical wave-suppression strategy. 相似文献
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Qing-Xu Fu Long Zhong Jian-Fei Lu 《Archive of Applied Mechanics (Ingenieur Archiv)》2013,83(7):1039-1059
In this contribution, wave localization in a disordered periodic viaduct (DPV) undergoing out-of-plane vibration is investigated. The DPV is assumed to be composed of infinite spans with each span deviating from the standard span slightly. Each span is supposed to be composed of two longitudinal beams and a pier linked by three springs. By using the governing equations for the pier and beams as well as the joint conditions at the beam-beam-pier junction, the transfer matrix for each span of the viaduct undergoing out-of-plane vibration is derived. Based on the derived transfer matrix for each span, the wave transfer matrices for the spans of the DPV are obtained. According to the Wolf’s algorithm, the Lyapunov exponents for the wave motion of the DPV are calculated. With the proposed model, the influences of the pier-height and beam-length disorders on the wave localization are examined. Also, the interactive effect of the damping and disorders on the wave localization in the DPV is investigated. Moreover, by the wave transfer matrix method, the wave conversion phenomenon in the DPV is studied. 相似文献
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A systematic approach to the study of normal modes and frequencies of disordered periodic rods is presented within a new transfer matrix framework proposed earlier by the authors. The normal frequency structure and mode localization of multiply-disorder periodic rods are investigated. The Monte Carlo and the perturbation method are applied to study the effects of material parameter uncertainties on normal modes and frequencies of randomly-disordered periodic rods. Some intricate aspects are investigated statistically, and it is shown that for this strongly-coupled elastic system, multiple and/or random disorders lead to more localized modes in or near stop-bands in a more complex way. In addition, high frequency wave localization is a typical feature of such a strongly-coupled but randomly-disordered periodic rod system. 相似文献
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《Acta Mechanica Solida Sinica》2017,(2)
The localization factor is used to describe the band structures for P wave propagating normally in the nanoscaled nearly periodic layered phononic crystals. The localization factor is calculated by the transfer matrix method based on the nonlocal elastic continuum theory.Three kinds of nearly periodic arrangements are concerned, i.e., random disorder, quasiperiodicity and defects. The influences of randomly disordered degree of the sub-layer's thickness and mass density, the arrangement of quasi-periodicity and the location of defect on the band structures and cut-off frequency are analyzed in detail. 相似文献
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《International Journal of Solids and Structures》2005,42(24-25):6457-6474
The two-dimensional wave propagation and localization in disordered periodic layered 2-2 piezoelectric composite structures are studied by considering the mechanic-electric coupling. The transfer matrix between two consecutive sub-layers is obtained based on the continuity conditions. Regarding the variables of mechanical and electrical fields as the elements of the state vector, the expression of the localization factors in disordered periodic layered piezoelectric composite structures is derived. Numerical results are presented for two cases—disorder of the thickness of the polymers and disorder of the piezoelectric and elastic constants of the piezoelectric ceramics. The results show that due to the piezoelectric effects, the characteristics of the wave localization in disordered periodic layered piezoelectric composite structures are different from those in disordered periodic layered purely elastic ones. The wave localization is strengthened due to the piezoelectricity. And the larger the piezoelectric constant is, the larger the wave localization factors are. It is found that slight disorder in the piezoelectric or elastic constants of the piezoelectric ceramics can lead to more prominent localization phenomenon. 相似文献
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Yize Wang Fengming Li Kikuo Kishimoto Yuesheng Wang Wenhu Huang 《Acta Mechanica Solida Sinica》2008,21(6):529-535
The elastic wave localization in disordered periodic piezoelectric rods with initial stress is studied using the transfer matrix and Lyapunov exponent method. The electric field is approximated as quasi-static. The effects of the initial stress on the band gap characteristics are investigated. The numerical calculations of localization factors and localization lengths are performed. It can be observed from the results that the band structures can be tuned by exerting the suitable initial stress. For different values of the piezoelectric rod length and the elastic constant, the band structures and the localization phenomena are very different. Larger disorder degree can lead to more obvious localization phenomenon. 相似文献
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Transfer matrix approach of vibration isolation analysis of periodic composite structure 总被引:1,自引:0,他引:1
Wang Yong Huang Qibai Zhou Minggang Xu Zhisheng 《Archive of Applied Mechanics (Ingenieur Archiv)》2007,77(7):461-471
The transmission properties of elastic waves propagating in a three-dimensional composite structure embedded periodically
with spherical inclusions are analyzed by the transfer matrix method in this paper. Firstly, the periodic composite structures
are divided into many layers, the transfer matrix of monolayer structure is deduced by the wave equations, and the transfer
matrix of the entire structure is obtained in the case of boundary conditions of displacement and stress continuity between
layers. Then, the effective impedance of the structure is analyzed to calculate its reflectivity and transmissivity of vibration
isolation. Finally, numerical simulation is carried out; the experiment results validate the accuracy and feasibility of the
method adopted in the paper and some useful conclusions are obtained.
Project (No. 50075029) supported by the National Natural Science Foundation of China. 相似文献