共查询到19条相似文献,搜索用时 62 毫秒
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旋涡诱发振动中的次谐,超谐和主共振问题 总被引:1,自引:0,他引:1
陆启韶 《非线性动力学学报》1993,1(1):15-25
本文利用尾流-结构振子模型去研究弹性结构的旋涡诱发振弱和强的相互作用下的共振动力学特性。我们借助于多重尺度法和范式方法,得到次谐、超谐和主共振周期运动和呼种定量和定性结果。 相似文献
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分析了非线性Winkler地基上矩形薄板在车辆移动荷载作用下的非线性动力特性。考虑地基反力的存在,基于Hamilton能量变分原理,建立了车辆、板、地基耦合系统非线性振动的控制微分方程;并将方程进行了量纲归一化处理,构造了满足周边自由矩形薄板全部边界条件的试探函数;运用伽辽金法和谐波平衡法对耦合系统控制方程进行了求解,讨论了板参数、地基参数、车辆系统参数等变化对耦合系统板振动幅频曲线的影响。结果表明:该耦合系统振动的频率都随板振幅的增大而增大;当板振动的幅值一定时,系统振动频率随着板厚、地基反应模量、车辆运行速度、车体刚度的增大而增大,但随着车体质量的增大而减小。因此,适当增加地基的反应模量可优化地基板的振动,并且从行车舒适性角度考虑,适当控制车速和车体刚度是有益的。 相似文献
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以载流导线激发的磁场中轴向运动梁为研究对象,同时考虑外激励力作用,推导出梁的磁弹性非线性振动方程.通过位移函数的设定和伽辽金积分法,将非线性振动方程离散为常微分方程组.采用多尺度法得到系统的近似解析解.应用Matlab 和Mathematica 软件求解幅频响应方程,并对稳态解进行稳定性判定.通过具体算例得到前两阶假设模态的响应幅值随不同参数的变化规律.结果发现:系统在内共振条件下发生超谐波共振时,二阶假设模态幅值明显小于一阶;随着外激励的增大,多值解区域范围明显缩小;随着电流强度增加,振动幅值减小,表明载流导线能够起到控制共振的作用. 相似文献
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《应用力学学报》2016,(1)
基于已建立的弹性地基上不可伸长梁的非线性动力学模型,利用梁的量纲归一化运动方程和多尺度方法求得梁2次超谐共振的幅频响应方程和位移的二次近似解。进而,运用梁的幅频响应曲线对其超谐共振响应特性进行研究,同时分析了弹性地基模型、Winkler参数、外激励幅值、边界条件等对该共振响应的影响效应。结果表明:弹性地基模型中剪切参数的引入增大了梁2次超谐共振响应的幅值和多值区域;弹性地基Winkler参数的增加会抑制系统的共振响应,但同时会增加系统动力响应的软弹簧特性;在外激励幅值较小的情况下,系统共振响应未展现出明显的非线性特征;边界约束对弹性地基剪切参数作用于梁2次超谐共振响应的效应有显著影响,可在一定程度上改变系统响应幅值及多值区域。 相似文献
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对均布荷载作用下一次超静定梁的弹塑性加载和变形全过程进行了改进分析.根据受力变形特点,均布荷载作用下一次超静定梁的加载过程可分为4个阶段,分别是弹性阶段、固支端附近塑性变形区扩展阶段、固支端保持为塑性铰而固支端附近塑性变形区卸载阶段、固支端保持为塑性铰而梁中部塑性变形区产生并扩展直至中部某点形成塑性铰阶段.在弹性阶段,位移与外荷载是线性比例关系,在第2、第4两个阶段,位移与外荷载是复杂的非线性关系,而在第3阶段,位移与外荷载是线性关系但不是比例关系.针对现有研究中位移计算存在的错误,给出了产生塑性铰后的第3、4两个阶段全过程任意点的位移计算公式,给出了跨中位置点各阶段荷载终值对应的位移.给出的位移公式具有一定的结构设计应用价值. 相似文献
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采用解析方法研究了置于线性弹性地基上的Euler-Bernoulli梁在均匀升温载荷作用下的临界屈曲模态跃迁特性;分别在两端不可移简支和夹紧边界条件下,给出了弹性梁屈曲模态跃迁点的地基刚度值以及屈曲载荷值的精确表达式,并分析了模态跃迁特点.结果表明:随着地基刚度参数值的增大临界屈曲模态通过跃迁点从低阶次向高阶次跃迁;两端简支梁的模态跃迁具有突变特性,而两端夹紧梁的模态跃迁则是一个缓慢变化过程,它是通过端截面的弯矩或曲率的正负号改变实现的. 相似文献
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V. D. Kubenko Yu. M. Pleskachevskii É. I. Starovoitov D. V. Leonenko 《International Applied Mechanics》2006,42(5):541-547
The natural vibration of an elastic sandwich beam on an elastic foundation is studied. Bernoulli’s hypotheses are used to
describe the kinematics of the face layers. The core layer is assumed to be stiff and compressible. The foundation reaction
is described by Winkler’s model. The system of equilibrium equations is derived, and its exact solution for displacements
is found. Numerical results are presented for a sandwich beam on an elastic foundation of low, medium, or high stiffness
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Translated from Prikladnaya Mekhanika, Vol. 42, No. 5, pp. 57–63, May 2006. 相似文献
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轴向运动梁非线性振动内共振研究 总被引:19,自引:2,他引:19
采用多元L-P方法分析轴向运动梁横向非线性振动的内共振,首先根据哈密顿原理建立轴向运动梁的横向振动微分方程,然后利用Galerkin方法分离时间和空间变量,再采用多元L-P方法进行求解,推导了内共振条件下频率-振幅方程的求根判别式,理论分析发现内共振与强迫力的振幅有关,而且可以从理论上决定这一界乎不同内共振的强迫力振幅的临界值,典型算例获得了轴向运动梁横向非线性振动内共振复杂的频率一振幅响应曲线,揭示了很多复杂而有趣的非线性振动特有的现象,多元L-P方法的数值结果,在小振幅时与IHB法的结果一致。 相似文献
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The subharmonic resonance and bifurcations of a clamped-clamped buckled beam under base harmonic excitations are investigated. The nonlinear partial integrodifferential equation of the motion of the buckled beam with both quadratic and cubic nonlinearities is given by using Hamilton's principle. A set of second-order nonlinear ordinary differential equations are obtained by spatial discretization with the Galerkin method. A high-dimensional model of the buckled beam is derived, concerning nonlinear coupling. The incremental harmonic balance (IHB) method is used to achieve the periodic solutions of the high-dimensional model of the buckled beam to observe the nonlinear frequency response curve and the nonlinear amplitude response curve, and the Floquet theory is used to analyze the stability of the periodic solutions. Attention is focused on the subharmonic resonance caused by the internal resonance as the excitation frequency near twice of the first natural frequency of the buckled beam with/without the antisymmetric modes being excited. Bifurcations including the saddle-node, Hopf, perioddoubling, and symmetry-breaking bifurcations are observed. Furthermore, quasi-periodic motion is observed by using the fourth-order Runge-Kutta method, which results from the Hopf bifurcation of the response of the buckled beam with the anti-symmetric modes being excited. 相似文献
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In this study, the vibrations of multiple stepped beams with cubic nonlinearities are considered. A three-to-one internal resonance case is investigated for the system. A general approximate solution to the problem is found using the method of multiple scales (a perturbation technique). The modulation equations of the amplitudes and the phases are derived for two modes. These equations are utilized to determine steady state solutions and their stabilities. It is assumed that the external forcing frequency is close to the lower frequency. For the numeric part of the study, the three-to-one ratio in natural frequencies is investigated. These values are observed to be between the first and second natural frequencies in the cases of the clamped-clamped and clamped-pinned supports, and between the second and third natural frequencies in the case of the pinned-pinned support. Finally, a numeric algorithm is used to solve the three-to-one internal resonance. The first mode is externally excited for the clamped-clamped and clamped-pinned supports, and the second mode is externally excited for the pinned-pinned support. Then, the amplitudes of the first and second modes are investigated when the first mode is externally excited. The amplitudes of the second and third modes are investigated when the second mode is externally excited. The force-response, damping-response, and .frequency- response curves are plotted for the internal resonance modes of vibrations. The stability analysis is carried out for these plots. 相似文献
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Static and free vibration analyses of straight and circular beams on elastic foundation are investigated. The Timoshenko beam theory is adopted in the derivation of the governing equation. Ordinary differential equations in scalar form obtained in the Laplace domain are solved numerically using the complementary functions method. The static and free vibration analyses of beams on elastic foundation are analyzed through various examples. 相似文献
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The vibration suppression analysis of a simply-supported laminated composite beam with magnetostrictive layers resting on visco-Pasternak’s foundation is presented.The constant gain distributed controller of the velocity feedback is utilized for the purpose of vibration damping.The formulation of displacement field is proposed according to Euler-Bernoulli’s classical beam theory(ECBT),Timoshenko’s first-order beam theory(TFBT),Reddy’s third-order shear deformation beam theory,and the simple sinu... 相似文献
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为建立混凝土路面结构受力分析计算模型,以Winkler弹性地基梁模型为基础,推导出了弹性地基双层梁理论的表达式;给定边界条件,利用MATLAB软件获得了无限长弹性地基梁在集中力作用下的挠度表达式。将混凝土路面结构简化为弹性地基上的双层梁,当车辆荷载作用于混凝土路面时,在集中载荷的作用下,建立了面层与基层的微分平衡方程。应用广义“初参数”法,得到了双层梁位移和应力的解析解。通过算例,对面层及基层的变形和应力进行了分析,结果表明:增大面层、基层的轴惯性矩和地基的弹性常数,可以有效地减少面层和基层的变形量,降低最大应力数值,但抗弯刚度对基层和面层的弯矩受力影响不大。最后将结果与ANSYS分析结果进行了比较,佐证了解的可靠性,研究结果可为混凝土路面结构设计提供依据。 相似文献