共查询到18条相似文献,搜索用时 171 毫秒
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研究了超临界速度下,两端固定的轴向运动梁静平衡位形及其分岔,以及横向非线性振动前两阶的固有频率.在超临界范围,轴向运动梁的静平衡位形由直线和对称曲线组成.基于轴向运动梁横向振动的非线性积分-偏微分控制方程,给出了固定边界条件下非平凡静平衡位形的解析表达式,讨论了梁的物理参数对轴向运动临界速度的影响.对于非平凡静平衡位形,经坐标变换,建立超临界轴向运动梁连续陀螺系统的标准控制方程.结合有限差分法以及离散傅立叶变换研究了超临界状态下梁横向振动的前两阶固有频率.并将数值结果与局部线性化后的Galerkin截断结果相比较. 相似文献
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纵向与横向振动耦合作用下轴向运动梁的非线性振动研究 总被引:4,自引:3,他引:1
利用增量谐波平衡法(IHB法)研究轴向运动梁在纵向与横向振动耦合作用下的非线性振动,尤其是在横向第1,2固有频率之比1/2接近1:3情况下的内部共振。首先利用哈密顿原理建立非惯性参考系下轴向运动梁的振动微分方程,采用分离变量法分离时间变量和空间变量并利用Galerkin方法离散运动方程。再利用IHB法进行非线性振动的分析。典型算例获得了纵向振动与横向振动耦合时非线性振动复杂的频幅响应曲线,探讨了耦合情况下对系统振动的影响,揭示了很多复杂而有趣的非线性现象。 相似文献
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随机横桥向激励下斜拉索面内耦合振动特性研究 总被引:1,自引:1,他引:0
研究了横桥向零均值高斯白噪声随机激励下斜拉索面内耦合振动特性.基于牛顿运动定律及Galerkin模态截断原理,考虑拉索的垂度、大位移引起的几何非线性及初始静平衡特性,推导了拉索空间三维非线性随机振动平衡微分方程,采用等价随机线性化法推出了14维拉索面内、面外横向振动状态向量一阶均方微分方程组,利用Runge-Kutta数值积分法求解该方程组的均方根响应特性.研究表明,当拉索承受面外横向激励超过一定值时,由于耦合振动项的耦合作用,拉索面内横向振动也将被激起,发生面内耦合振动所需的临界激励均方值随着拉索阻尼比的增大而增大,在此运动状态下,即使激励为平稳荷载,拉索振动也将呈现非平稳特性.最后,采用Lyaponov指数判断系统在耦合振动过程中的稳定性特性,分析了阻尼比对稳定性的影响. 相似文献
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近年来,非线性能量阱作为一种高效的被动控制手段受到国内外学者广泛关注。本文采用Galerkin截断法(GTM)预报弹性边界约束轴向载荷梁结构动力学响应,研究非线性能量阱对梁结构振动行为影响规律。在Galerkin截断法中,选取具有线性边界条件轴向载荷Euler-Bernoulli梁模态函数作为权函数和试函数,之后利用Galerkin条件建立梁结构振动系统的残差方程,结合4阶龙格-库塔算法对上述残差方程进行求解。采用谐波平衡法对Galerkin截断法所得结果进行验证并研究了Galerkin截断法截断数对结果稳定性的影响。在此基础上,研究外部激励位置、非线性能量阱参数对该梁结构系统动力学响应、减振性能的影响规律。结果表明,外部激励位置与非线性能量阱参数对梁结构动力学响应影响显著。适当的非线性刚度、阻尼参数能够有效抑制梁结构端点处的振动响应幅值。 相似文献
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针对含裂纹平板的振动与疲劳问题,研究含裂纹平板耦合动力学建模方法。首先在变形相似性原则下通过力学平衡原理推导出含裂纹项的平板振动方程,进而基于应力关系式形成裂纹项的表达式。在此基础上,利用Galerkin法将含裂纹板简化成单自由度振动系统,根据Berger经验方法产生方程的非线性项构建含裂纹板的非线性振动模型。最后通过算例探讨含裂纹板的动力学特性,协同Paris方程研究含裂纹平板动力学与裂纹扩展的耦合行为。研究结论表明,阻尼大小和激励力的变化对含裂纹板的振动特性及裂纹扩展规律具有显著影响。所提出的含裂纹平板耦合动力学建模方法,考虑了振动与裂纹扩展的耦合效应,为飞行器板结构抗振动疲劳设计提供理论依据。 相似文献
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A formulation for the free vibration analysis of functionally graded (FG) spatial curved beams is presented by taking into account the effects of thickness-curvature. The governing equation is based on the first-order shear deformation theory (FSDT) and Ritz method is employed to obtain the natural frequencies. The curved beams presented are in the form of the cylindrical helical spring. The material distribution is in the direction of the curvature of the curved beam. The results for isotropic planar curved beams are validated with the known data in the literature. The effects of helix pitch angle, number of turns and boundary conditions on frequency parameters of spatial curved beams are investigated. 相似文献
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This study aims to investigate the nonlinear forced vibration of functionally graded (FG) nanobeams. It is assumed that material properties are gradually graded in the direction of thickness. Nonlocal nonlinear Euler–Bernoulli beam theory is used to derive nonlocal governing equations of motion. The linear eigenmodes of FG nanobeams are used to transform a partial differential equation of motion into a system of ordinary differential equations via the Galerkin method. The multiple scale method is used to find the governing equations of the steady-state responses of FG nanobeams excited by a distributed harmonic force with constant intensity. It is also assumed that the working frequency is close to three times greater than the lowest natural frequency. Based on the equation governing the linear natural frequencies of FG nanobeams, the influence of the small scale parameter, material composition, and stiffness of the foundation on the linear relationship among natural frequencies is studied. Results show that superharmonic response or a combination of resonances may occur as well as a subharmonic response depending on the power-law index and stiffness of the foundation. Then the governing equations of a steady-state response of FG nanobeams for four possible solutions are obtained depending on the value of the small scale parameter. It is shown that the simplest response of FG nanobeams is a subharmonic response or superharmonic response. The equations governing the frequency–response curves are obtained and the effects of the power-law index and small scale parameter on them are discussed. 相似文献
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基于弹性板的几何非线性动力平衡方程,首先建立了一个坐标变换将梯形板域变换到正方形域,并将控制方程及其相应的边界条件变换到该正方形域内,然后通过引入中间变量将控制方程降阶,并利用问题的数学物理关系将边界条件进一步简化,在正方形域内对板的控制方程应用伽辽金法使问题变为时间域的非线性动力方程,最后应用参数摄动法得到了梯形板的几何非线性自由振动和动力响应,所得计算结果可供工程设计人员参考。 相似文献
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Nonlinear free vibration of simply supported FG nanoscale beams with considering surface effects (surface elasticity, tension and density) and balance condition between the FG nanobeam bulk and its surfaces is investigated in this paper. The non-classical beam model is developed within the framework of Euler–Bernoulli beam theory including the von Kármán geometric nonlinearity. The component of the bulk stress, σzz, is assumed to vary cubically through the nanobeam thickness and satisfies the balance conditions between the FG nanobeam bulk and its surfaces. Accordingly, surface density is introduced into the governing equation of the nonlinear free vibration of FG nanobeams. The multiple scales method is employed as an analytical solution for the nonlinear governing equation to obtain the nonlinear natural frequencies of FG nanbeams. Several comparison studies are carried out to demonstrate the effect of considering the balance conditions on free nonlinear vibration of FG nanobeams. Lastly, the influences of the FG nanobeam length, volume fraction index, amplitude ratio, mode number and thickness ratio on the normalized nonlinear natural frequencies of the FG nanobeams are discussed in detail. 相似文献
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通过直接求解单对称均匀Timoshenko薄壁梁单元弯扭耦合振动的运动偏微分方程,导出了其自由振动时的动态传递矩阵,同时采用结合频率扫描法的二分法求解频率特征方程,并讨论了剪切变形和转动惯量对弯扭耦合Timoshenko薄壁梁的固有频率的影响.数值结果验证了本文方法在其适用范围内的精确性和有效性. 相似文献
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形状记忆合金纤维正交各向异性层合矩形板的非线性弯曲振动 总被引:3,自引:0,他引:3
研究了形状记忆合金(SMA)纤维混杂复合材料大挠度层合板的非线性自由与受迫振动特性。基于描述SMA力学行为的Brinson理论以及层合板材料性能预测的混合率, 建立了SMA纤维混杂复合材料大挠度层合板的本构方程, 基于对称层合各向异性弹性板的非线性理论, 建立了以横向挠度和应力函数表示的板的横向振动方程和相容方程。采用Galerkin近似解法将振动方程化为时间变量的含有三次非线性项的Duffing型常微分方程, 采用谐波平衡法(HBM)获得系统的固有频率方程和强迫振动稳态频率响应方程。数值计算表明: 非线性板自由振动频率比与激励温度的关系具有与线性板相同的特征, 马氏体相向奥氏体相转变阶段温度对板的振动频响特性曲线的影响最显著, 同时也讨论了SMA纤维含量、 板的纵横比以及自由振动幅值对板的非线性频率比的影响。 相似文献