共查询到20条相似文献,搜索用时 62 毫秒
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对模量泡沫铝芯夹层梁的固有振动问题进行了研究。利用双模量的材料应力-应变方程,推导出了双模量材料剪切弹性模量计算公式,证明了双模量梁中性轴位置不受作用在梁上的横向载荷的影响。在考虑剪切变形的基础上,建立了双模量泡沫铝芯夹层梁的强迫振动控制方程,推导出了双模量泡沫铝芯夹层梁固有振动问题的振型函数及固有频率计算公式,并分析了剪切变形及泡沫铝芯夹层的拉压弹性模量对双模量泡沫铝芯夹层梁固有振动频率的影响。研究表明:泡沫铝芯夹层梁固有振动时,其固有振动波形是不连续的,奇数波型与偶数波型之间存在间断点;剪切变形及泡沫铝芯夹层的拉压弹性模量对双模量泡沫铝芯夹层梁固有振动的影响是不能忽略的。 相似文献
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用强迫力法求解弹性支承梁的固有振动 总被引:2,自引:1,他引:1
本文将强迫力法引入弹性支承梁固有振动的计算问题,把具有多个弹性支承的梁按自由粱米处理,而将支承反力看作作用于梁上的强迫力。最后利用各支承点的位移约束条件建立了系统的频率方程和以各支反力为基本未知量的线性方程组. 相似文献
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两端固定音叉的力-频率关系及其非线性 总被引:1,自引:0,他引:1
两端固定音叉结构常被用作石英或硅振梁加速度计的敏感结构。论文的目的是建立两端固定音叉结构的固有频率与受力之间,及差动音叉结构频率差与受力之间的精确关系,研究差动音叉结构量程与非线性之间的联系。以梁的弯曲振动微分方程为基础,推导了在轴向力作用下两端固定的梁的固有振动角频率与轴向力之间的关系,并用多项式拟合;进一步得到差动音叉结构传感器的角频率差与轴向力之间的拟合多项式。梁的力-频率关系和差动音叉结构的力-频率差关系的5次多项式拟合误差分别低于0.0056%和0.0015%,并给出了敏感结构量程与输出非线性度之间的近似公式。这些公式可以为传感器的设计提供依据。 相似文献
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结构地震反应分析的频域传递矩阵法 总被引:1,自引:0,他引:1
本文将传递矩阵法的应用范围由结构的固有振动分析推广到频域内的地震反应分析。文中具体给出了弯剪梁结构的单元传递矩阵的频域形式。用这种频域内的传递矩阵,结合离散傅里叶变换,即可求得多自由度弯剪梁体系的地震反应。同样地,可用这种方法计算各种串联多自由度体系在其它动力荷载下的反应。该方法精度良好且比相应的有限元法节省计算机CPU时间。 相似文献
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变截面梁横向振动固有频率数值计算 总被引:1,自引:0,他引:1
根据边界条件对变截面梁横向振动四阶变系数微分方程降阶, 形成关于挠度和弯矩的二
阶非显式递推变系数微分方程组; 利用有限差分法, 研究了变截面简支梁横向振动固有频率
的数值计算方法及其精度. 理论分析和正交计算的算例表明: 数值计算算法简单, 计算精度
取决于计算步长的数目和梁横截面竖向渐变率, 与梁宽和梁长无关; 对于给定的计算步长或
数目, 可以估算数值计算的精度; 对于给定的精度要求, 可以确定合理的计算步长或数目. 相似文献
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对受非保守载荷的简支梁在后屈曲附近的自由振动进行了研究. 基于可伸长梁的大变形理论,建立了受沿轴线分布切向非保守力作用的简支梁后屈曲附近自由振动的几何非线性模型. 在小振幅和谐振动假设下,简化得到后屈曲梁线性振动的控制方程. 采用打靶法求解振动问题的控制方程,给出了前三阶固有频率与载荷之间的特征关系曲线. 结果表明:非保守载荷作用下梁的振动响应与保守载荷作用下梁的振动响应有着明显不同. 相似文献
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Dong-Liang Sun 《基于设计的结构力学与机械力学》2019,47(1):102-120
Free vibration of nonuniform axially functionally graded Timoshenko beams subjected to combined axially tensile or compressive loading is studied. An emphasis is placed on the effect of tip and distributed axial loads on the natural frequencies and mode shapes for an inhomogeneous cantilever beam including material inhomogeneity and geometric non-uniform cross section. The initial value method is developed to determine the natural frequencies. The method’s effectiveness is verified by comparing our results with previous ones for special cases. Natural frequencies of standing/hanging Timoshenko beams are calculated for four different cross sections. The influences of shear rigidity, taper ratio, gradient index, tip force, and axially distributed loading on the natural frequencies of clamped-free beams are discussed. Material inhomogeneity and geometric non-uniform cross-section strongly affect higher-order vibration frequencies and mode shapes. 相似文献
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Yang Xiaodong Chen Liqun 《Acta Mechanica Solida Sinica》2005,18(4):340-347
The axially moving beams on simple supports with torsion springs are studied. The general modal functions of the axially moving beam with constant speed have been obtained from the supporting conditions. The contribution of the spring stiffness to the natural frequencies has been numerically investigated. Transverse stability is also studied for axially moving beams on simple supports with torsion springs. The method of multiple scales is applied to the partialdifferential equation governing the transverse parametric vibration. The stability boundary is derived from the solvability condition. Instability occurs if the axial speed fluctuation frequency is close to the sum of any two natural frequencies or is two fold natural frequency of the unperturbed system. It can be concluded that the spring stiffness makes both the natural frequencies and the instability regions smaller in the axial speed fluctuation frequency-amplitude plane for given mean axial speed and bending stiffness of the beam. 相似文献
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Axially moving beam-typed structures are of technical importance and present in a wide class of engineering problem. In the present paper, natural frequencies of nonlinear planar vibration of axially moving beams are numerically investigated via the fast Fourier transform (FFT). The FFT is a computational tool for efficiently calculating the discrete Fourier transform of a series of data samples by means of digital computers. The governing equations of coupled planar of an axially moving beam are reduced to two nonlinear models of transverse vibration. Numerical schemes are respectively presented for the governing equations via the finite difference method under the simple support boundary condition. In this paper, time series of the discrete Fourier transform is defined as numerically solutions of three nonlinear governing equations, respectively. The standard FFT scheme is used to investigate the natural frequencies of nonlinear free transverse vibration of axially moving beams. The numerical results are compared with the first two natural frequencies of linear free transverse vibration of an axially moving beam. And results indicate that the effect of the nonlinear coefficient on the first natural frequencies of nonlinear free transverse vibration of axially moving beams. The numerical results also illustrate the three models predict qualitatively the same tendencies of the natural frequencies with the changing parameters. 相似文献
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《应用数学和力学(英文版)》2019,(1)
The asymptotic development method is applied to analyze the free vibration of non-uniform axially functionally graded(AFG) beams, of which the governing equations are differential equations with variable coefficients. By decomposing the variable flexural stiffness and mass per unit length into reference invariant and variant parts, the perturbation theory is introduced to obtain an approximate analytical formula of the natural frequencies of the non-uniform AFG beams with different boundary conditions.Furthermore, assuming polynomial distributions of Young's modulus and the mass density, the numerical results of the AFG beams with various taper ratios are obtained and compared with the published literature results. The discussion results illustrate that the proposed method yields an effective estimate of the first three order natural frequencies for the AFG tapered beams. However, the errors increase with the increase in the mode orders especially for the cases with variable heights. In brief, the asymptotic development method is verified to be simple and efficient to analytically study the free vibration of non-uniform AFG beams, and it could be used to analyze any tapered beams with an arbitrary varying cross width. 相似文献
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轴向运动结构的横向振动一直是动力学领域的研究热点之一.目前大多数的文献只涉及对一种模型的研究,而针对几种模型的对比分析较少.本文对3种典型轴向运动结构(Euler梁、窄板和对边简支对边自由的板)的振动特性进行了对比分析.针对工程中不同的结构参数,本文为其理论研究中选择更加合理的模型提供了参考.通过复模态方法求解了3种模型的控制方程,给出了其相应的固有频率及模态函数.对于板模型,同时考虑了其自由边界的两种刚体位移以及弯扭耦合振动3种情况.通过数值算例给出了3种模型的前四阶固有频率随轴速和长宽比的变化情况,并应用微分求积法对复模态方法得到的解析解进行验证.特别采用三维图的形式分析了不同的轴速、阻尼、刚度和长宽比等参数混合时对3种模型第一阶固有频率的影响,着重研究了窄板和梁的不同的长宽比和轴速混合时对两者的第一阶固有频率的相对误差的影响.结果表明:随着轴速的增大,3种模型的固有频率逐渐减小. 窄板是板的一种简化模型.在各参数值发生变化时,阻尼对第一阶固有频率的影响最小.长宽比很大,轴速很小或为零时,复杂模型可以简化为简单模型. 相似文献
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针对连续Bernoulli-Euler和Timoshenko梁单元的动态刚度矩阵,分析了在使用连续梁单元
进行结构动态特性分析中的数值问题. 基于连续梁单元的运动方程,导出了连续
Bernoulli-Euler和Timoshenko梁单元的动态刚度矩阵. 分析了影响动态刚度矩阵中双曲函
数自变量的各个独立变量及其产生的影响,并给出了初估连续梁单元合理长度的方法. 使用
单一连续Bernoulli-Euler和Timoshenko梁单元的动态刚度矩阵分别进行了悬臂梁频响曲线
的数值求解. 研究表明,在合理选择连续梁单元的长度时,大多数工程结构的动态特性分析
中都不会产生数值问题. 相似文献
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将状态空间法和微分求积法相结合,分析了压电-弹性层合梁的自由振动.
通过微分求积把状态方程在每一个节点处离散,进而求得解答. 选用不同的节点数目,
分析了方法的收敛性. 计算结果与相关文献的结果能较好地符合. 该方法
对于分析压电-弹性层合梁的工程振动问题非常方便. 相似文献