共查询到19条相似文献,搜索用时 437 毫秒
1.
内共振条件下直线运动梁的动力稳定性 总被引:31,自引:4,他引:31
基于Kane方程,建立起了包含有耦合的三次几何及惯性非线性项大范围直线运动梁动力学控制方程.利用多尺度法并结合笛卡尔坐标变换,对所得方程进行一次近似展开,着重对满足一、二阶模态间3:1内共振现象的两端铰支梁参激振动平凡解稳定性进行了详尽的分析,得出了稳定性边界的解析表达式.采用中心流形定理对调制微分方程组进行降维处理,分析了相应Hopf分岔类型并通过数值计算发现了稳定的极限环存在. 相似文献
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研究了梁中的非线性弯曲波的传播特性,同时考虑了梁的大挠度引起的几何非线性效应和
梁的转动惯性导致的弥散效应,利用Hamilton变分法建立了梁中非线性弯曲波的波动方程.
对该方程进行了定性分析,在不同的条件下,该方程在相平面上存在同宿轨道或异宿轨道,
分别对应于方程的孤波解或冲击波解. 利用Jacobi椭圆函数展开法,对该非线性方程进行
求解,得到了非线性波动方程的准确周期解及相对应的孤波解和冲击波解,讨论了这些解存
在的必要条件,这与定性分析的结果完全相同. 利用约化摄动法从非线性弯曲波动方程中导
出了非线性Schr\"{o}dinger方程,从理论上证明了考虑梁的大挠度和转动惯性时梁中存在
包络孤立波. 相似文献
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建立了旋转柔性梁的非线性动力学模型,利用能量法及哈密顿原理导出了耦合的动力学方程,分析了转动惯性、Coriolis力、应力刚化、旋转软化、加速度、横向位移、弯曲刚度等作用效应;通过设置应力刚化及旋转软化等刚度矩阵和编制有限元程序,建立了梁单元有限元模型,对柔性梁在旋转软化状态下的振动模态进行了数值模拟与分析。计算表明:梁的旋转软化导致其沿旋转平面的弯振模态(摆振)频率随转速增大而相对下降,且对第一阶摆振频率的影响最显著,呈现非线性;梁的旋转软化对垂直于旋转平面的弯振频率几乎没有影响,此结果表明了旋转柔性梁动态特性的复杂性,因此在计算旋转柔性梁的振动特性时,必须同时设置平动、转动惯性质量矩阵,才能获得准确结果。此外,梁单元模型与实体单元模型计算结果误差小于等于5%,验证了本文梁单元模型求解方法的准确性。 相似文献
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针对有形状记忆合金的层合梁系统,分析了形状记忆合金层与梁中间基体的厚度比相关参数、激励强度对系统的振动幅频响应的影响。采用形状记忆合金多项式本构模型,建立层合梁的量纲归一化的运动方程,用Galerkin方法离散得到任意阶模态动力学方程,再由平均法求得幅频响应方程。利用奇异性理论计算转迁集和不同类型的幅频响应图。结果表明,一阶模态非线性振动幅频响应可分为类线性和硬特性两种类型。响应为类线性时,厚度比和激励强度在类线性区取值,形状记忆合金层对系统几乎没有减振效果;响应为硬特性时,激励幅值越大,形状记忆合金层越厚,SMA层对系统的减振效果越明显。在不同的激励及SMA层厚度下,二阶和三阶模态非线性振动幅频响应定性相同,其类型可分为:类线性、硬特性、软特性、软硬特性。 相似文献
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本文选用考虑横向剪切效应的退化梁单元,引入几何非线性假设,对具粘弹性阻尼层的夹层梁动响应及其衰减效果进行了研究,得到了一些具有应用价值的结论。 相似文献
10.
《应用力学学报》2021,(2)
螺栓连接的柔性梁既有非线性又有几何非线性,本文针对其动力学建模和振动特性开展了实验与数值研究。首先,搭建了含螺栓连接的柔性大变形梁的实验台架,并开展敲击和正弦激振的实验测试。实验结果表明:螺栓连接的柔性梁较(无螺栓连接的)连续梁的模态频率降低,阻尼增加,呈现出随着激励能量增大,模态频率降低的非线性模态特征。其次,为了建立大变形柔性梁的有效计算模型,采用了动坐标迭代法,并采用改进Iwan模型和库仑摩擦模型刻画连接部件的力学特性。最后,开展了数值计算,通过与实验测试结果对比表明:数值计算结果与实验测试结果误差在7%以内,所建立的柔性连接梁的计算模型能够有效准确地模拟含连接部件柔性梁的非线性模态和动力学响应特征。 相似文献
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Dynamic modeling of a cantilever beam under an axial movement of its basement is presented. The dynamic equation of motion
for the cantilever beam is established by using Kane's equation first and then simplified through the Rayleigh-Ritz method.
Compared with the older modeling method, which linearizes the generalized inertia forces and the generalized active forces,
the present modeling takes the coupled cubic nonlinearities of geometrical and inertial types into consideration. The method
of multiple scales is used to directly solve the nonlinear differential equations and to derive the nonlinear modulation equation
for the principal parametric resonance. The results show that the nonlinear inertia terms produce a softening effect and play
a significant role in the planar response of the second mode and the higher ones. On the other hand, the nonlinear geometric
terms produce a hardening effect and dominate the planar response of the first mode. The validity of the present modeling
is clarified through the comparisons of its coefficients with those experimentally verified in previous studies.
Project supported by the Fundamental Fund of National Defense of China (No. 10172005). 相似文献
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Tang Youqi 《力学学报》2013,45(6):965
研究了轴向加速黏弹性Timoshenko梁的非线性参数振动。参数激励是由径向变化张力和轴向速度波动引起的。引入了取决于轴向加速度的径向变化张力,同时还考虑了有限支撑刚度对张力的影响。应用广义哈密尔顿原理建立了Timoshenko梁耦合平面运动的控制方程和相关的边界条件。黏弹性本构关系采用Kelvin模型并引入物质时间导数。耦合方程简化为具有随时间和空间变化系数的积分-偏微分型非线性方程。采用直接多尺度法分析了Timoshenko梁的组合参数共振。根据可解性条件得到了Timoshenko梁的稳态响应,并应用Routh-Hurvitz判据确定了稳态响应的稳定性。最后通过一系列数值例子描述了黏弹性系数、平均轴向速度、剪切变形系数、转动惯量系数、速度脉动幅值、有限支撑刚度参数以及非线性系数对稳态响应的影响。 相似文献
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We investigate theoretically thenonlinear normal modes of a vertical cantilever beam excited by aprincipal parametric resonance. We apply directly the method ofmultiple scales to the governing nonlinear nonautonomousintegral-partial-differential equation and associated boundary conditions.In the absence of damping, it is shown that the system has nonlinear normal modes, as defined by Rosenberg, even in the presence of the parametric excitation.We calculate the spatial correction to the linear mode shapedue to the effects of the inertia and curvature nonlinearities andthe parametric excitation. We compare the result obtained withthe direct approach with that obtained using a single-mode Galerkindiscretization.The deviation between the two predictions increases as the oscillationamplitude increases. 相似文献
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大范围运动悬臂梁的动力学建模问题对动力学特性分析及控制系统设计具有极其重要的作用. 当前研究多采用一次近似模型,其忽略了由轴向和横向变形所产生的应变能中的耦合项,然而这些项对动力学特性会产生影响. 通过讨论应变能的选取方式,计入了应变能中的耦合项;利用哈密尔顿原理建立结构的耦合振动模型;再借助瑞利—里兹法,以无大范围运动时的振型函数作为基本解组,得到了结构振动广义特征方程并求解. 通过数值算例对比分析,指出考虑应变能耦合项得到的频率与不考虑应变能耦合项得到的频率存在明显差别. 相似文献
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S.N. Mahmoodi S.E. Khadem N. Jalili 《Archive of Applied Mechanics (Ingenieur Archiv)》2006,75(2-3):153-163
The nonlinear equations of motion of planar bending vibration of an inextensible viscoelastic carbon nanotube (CNT)-reinforced
cantilevered beam are derived. The viscoelastic model in this analysis is taken to be the Kelvin–Voigt model. The Hamilton
principle is employed to derive the nonlinear equations of motion of the cantilever beam vibrations. The nonlinear part of
the equations of motion consists of cubic nonlinearity in inertia, damping, and stiffness terms. In order to study the response
of the system, the method of multiple scales is applied to the nonlinear equations of motion. The solution of the equations
of motion is derived for the case of primary resonance, considering that the beam is vibrating due to a direct excitation.
Using the properties of a CNT-reinforced composite beam prototype, the results for the vibrations of the system are theoretically
and experimentally obtained and compared. 相似文献
16.
Non-linear dynamic response of a rotating radial Timoshenko beam with periodic pulse loading at the free-end 总被引:3,自引:0,他引:3
Sunil K. Sinha 《International Journal of Non》2005,40(1):113-149
Consideration is given to the dynamic response of a Timoshenko beam under repeated pulse loading. Starting with the basic dynamical equations for a rotating radial cantilever Timoshenko beam clamped at the hub in a centrifugal force field, a system of equations are derived for coupled axial and lateral motions which includes the transverse shear and rotary inertia effects, as well. The hyperbolic wave equation governing the axial motion is coupled with the flexural wave equation governing the lateral motion of the beam through the velocity-dependent skew-symmetric Coriolis force terms. In the analytical formulation, Rayleigh-Ritz method with a set of sinusoidal displacement shape functions is used to determine stiffness, mass and gyroscopic matrices of the system. The tip of the rotating beam is subjected to a periodic pulse load due to local rubbing against the outer case introducing Coulomb friction in the system. Transient response of the beam with the tip deforming due to rub is discussed in terms of the frequency shift and non-linear dynamic response of the rotating beam. Numerical results are presented for this vibro-impact problem of hard rub with varying coefficients of friction and the contact-load time. The effects of beam tip rub forces transmitted through the system are considered to analyze the conditions for dynamic stability of a rotating blade with intermittent rub. 相似文献
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Global Bifurcations and Chaotic Dynamics in Nonlinear Nonplanar Oscillations of a Parametrically Excited Cantilever Beam 总被引:1,自引:0,他引:1
This paper presents the analysis of the global bifurcations and chaotic dynamics for the nonlinear nonplanar oscillations of a cantilever beam subjected to a harmonic axial excitation and transverse excitations at the free end. The governing nonlinear equations of nonplanar motion with parametric and external excitations are obtained. The Galerkin procedure is applied to the partial differential governing equation to obtain a two-degree-of-freedom nonlinear system with parametric and forcing excitations. The resonant case considered here is 2:1 internal resonance, principal parametric resonance-1/2 subharmonic resonance for the in-plane mode and fundamental parametric resonance–primary resonance for the out-of-plane mode. The parametrically and externally excited system is transformed to the averaged equations by using the method of multiple scales. From the averaged equation obtained here, the theory of normal form is applied to find the explicit formulas of normal forms associated with a double zero and a pair of pure imaginary eigenvalues. Based on the normal form obtained above, a global perturbation method is utilized to analyze the global bifurcations and chaotic dynamics in the nonlinear nonplanar oscillations of the cantilever beam. The global bifurcation analysis indicates that there exist the heteroclinic bifurcations and the Silnikov type single-pulse homoclinic orbit in the averaged equation for the nonlinear nonplanar oscillations of the cantilever beam. These results show that the chaotic motions can occur in the nonlinear nonplanar oscillations of the cantilever beam. Numerical simulations verify the analytical predictions. 相似文献
18.
The purpose of this study is to understand the main differences between the deterministic and random response characteristics of an inextensible cantilever beam (with a tip mass) in the neighborhood of combination parametric resonance. The excitation is applied in the plane of largest rigidity such that the bending and torsion modes are cross-coupled through the excitation. In the absence of excitation, the two modes are also coupled due to inertia nonlinearities. For sinusoidal parametric excitation, the beam experiences instability in the neighborhood of the combination parametric resonance of the summed type, i.e., when the excitation frequency is in the neighborhood of the sum of the first bending and torsion natural frequencies. The dependence of the response amplitude on the excitation level reveals three distinct regions: nearly linear behavior, jump phenomena, and energy transfer. In the absence of nonlinear coupling, the stochastic stability boundaries are obtained in terms of sample Lyapunov exponent. The response statistics are estimated using Monte Carlo simulation, and measured experimentally. The excitation center frequency is selected to be close to the sum of the bending and torsion mode frequencies. The beam is found to experience a single response, two possible responses, or non-stationary responses, depending on excitation level. Experimentally, it is possible to obtain two different responses for the same excitation level by providing a small perturbation to the beam during the test. 相似文献
19.
João C. André 《Nonlinear dynamics》1996,11(3):275-293
In the study of nonlinear vibrations of planar frames and beams with infinitesimal displacements and strains, the influence of the static displacements resulting from gravity effect and other conservative loads is usually disregarded. This paper discusses the effect of the deformed equilibrium configuration on the nonlinear vibrations through the analysis of two planar structures. Both structures present a two-to-one internal resonance and a primary response of the second mode. The equations of motion are reduced to two degrees of freedom and contain all geometrical and inertial nonlinear terms. These equations are derived by modal superposition with additional subsidiary conditions. In the two cases analyzed, the deformed equilibrium configuration virtually coincides with the undeformed configuration. Also, 2% is the maximum difference presented by the first two lower frequencies. The modes are practically coincident for the deformed and undeformed configurations. Nevertheless, the analysis of the frequency response curves clearly shows that the effect of the deformed equilibrium configuration produces a significant translation along the detuning factor axis. Such effect is even more important in the amplitude response curves. The phenomena represented by these curves may be distinct for the same excitation amplitude. 相似文献