共查询到20条相似文献,搜索用时 31 毫秒
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Nonlinear dynamics of composite laminated cantilever rectangular plate subject to third-order piston aerodynamics 总被引:1,自引:0,他引:1
This paper presents the analysis of the nonlinear dynamics for a composite laminated cantilever rectangular plate subjected to the supersonic gas flows and the in-plane excitations. The aerodynamic pressure is modeled by using the third-order piston theory. Based on Reddy’s third-order plate theory and the von Kármán-type equation for the geometric nonlinearity, the nonlinear partial differential equations of motion for the composite laminated cantilever rectangular plate under combined aerodynamic pressure and in-plane excitation are derived by using Hamilton’s principle. The Galerkin’s approach is used to transform the nonlinear partial differential equations of motion for the composite laminated cantilever rectangular plate to a two-degree-of-freedom nonlinear system under combined external and parametric excitations. The method of multiple scales is employed to obtain the four-dimensional averaged equation of the non-automatic nonlinear system. The case of 1:2 internal resonance and primary parametric resonance is taken into account. A numerical method is utilized to study the bifurcations and chaotic dynamics of the composite laminated cantilever rectangular plate. The frequency–response curves, bifurcation diagram, phase portrait and frequency spectra are obtained to analyze the nonlinear dynamic behavior of the composite laminated cantilever rectangular plate, which includes the periodic and chaotic motions. 相似文献
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建立了一类三自由度含间隙碰撞振动系统的力学模型,求解了系统六维n?1周期运动的周期解及其Poincaré映射。通过理论分析和数值模拟相结合的方法,分析了该系统在强共振点附近,系统两参数控制的局部动力学行为。即在两参数平面上共振点的附近变化两控制参数,进行数值模拟并划分两参数平面的拓扑区域;分析了以“四方形”和“四叶形”异宿轨道为特征的存在于强共振点附近的Hopf分岔不变圈和次谐分岔4?4周期运动,并进一步分析了四阶次谐分岔向混沌的演化过程。 相似文献
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直线运动柔性梁非线性动力学--主参数共振与内共振联合激励 总被引:11,自引:4,他引:11
针对基础直线运动柔性梁,基于Kane方程建立了相应的非线性动力学方程。采用多尺度法并结合笛卡尔坐标变换,导出了系统受前两阶模态间3:1内共振及第二阶模态主参激共振时的非线性调制方程组.数值求解了该方程组的定常解及相应的稳定性问题。研究表明,系统的平凡、单模态、双模态稳态解共存,超临界及亚临界叉形分岔只发生在单模态状态下,相反,鞍结分岔及Hopf分岔只在双模态状态下产生,一些稳定的极限环随参数变化经一系列倍周期分岔后导致运动的突然跳跃。 相似文献
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A. Pielorz 《Acta Mechanica》2004,167(1-2):1-12
Summary. Finite oscillations of a thin beam are analyzed, taking into account large deflections and rotations with small strains. It is shown that, depending on the assumptions, problems for an elastic and viscoelastic beam lead to solving hyperbolic or parabolic nonlinear partial differential equations. As an example, a cantilever beam is considered. The solutions for nonlinear vibrations are obtained by means of the Galerkin method, and numerical results are presented graphically for four material models. 相似文献
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研究Winkler地基上材料非线性矩形薄板受参数激励的参数共振动问题。按照弹性力学理论建立Winkler地基上材料非线性矩形薄板受参数激励的动力学方程。利用Galerkin方法将其转化为非线性振动方程。应用非线性振动的多尺度法求得系统满足主参数共振条件的一次近似解,并进行数值计算,分析定常解的稳定性。给出主参数共振系统参数平面的分岔集和幅频响应方程的分岔图。分析激励、调谐值、阻尼系数、非线性参数、几何参数对共振响应曲线的影响。 相似文献
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Based on the modified couple stress theory, the coupled longitudinal-transverse nonlinear behaviour of an imperfect microbeam is investigated numerically. The equations governing the longitudinal and transverse motions are obtained using Hamilton’s principle for the system with an initial geometric imperfection. The Galerkin scheme is employed to discretize the two partial differential equations of motion, yielding a set of second-order nonlinear ordinary differential equations with coupled terms. This set is cast into new set of first-order nonlinear ordinary differential equations and solved by means of the pseudo-arclength continuation technique. The nonlinear resonant response of the system along with bifurcations are presented via frequency–response curves. Moreover, the effect of different system parameter on the frequency–response curves is highlighted. 相似文献
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Kiyoshi Kotani Ikuhiro Yamaguchi Lui Yoshida Yasuhiko Jimbo G. Bard Ermentrout 《Journal of the Royal Society Interface》2014,11(95)
Gamma oscillations of the local field potential are organized by collective dynamics of numerous neurons and have many functional roles in cognition and/or attention. To mathematically and physiologically analyse relationships between individual inhibitory neurons and macroscopic oscillations, we derive a modification of the theta model, which possesses voltage-dependent dynamics with appropriate synaptic interactions. Bifurcation analysis of the corresponding Fokker–Planck equation (FPE) enables us to consider how synaptic interactions organize collective oscillations. We also develop the adjoint method (infinitesimal phase resetting curve) for simultaneous equations consisting of ordinary differential equations representing synaptic dynamics and a partial differential equation for determining the probability distribution of the membrane potential. This method provides a macroscopic phase response function (PRF), which gives insights into how it is modulated by external perturbation or internal changes of parameters. We investigate the effects of synaptic time constants and shunting inhibition on these gamma oscillations. The sensitivity of rising and decaying time constants is analysed in the oscillatory parameter regions; we find that these sensitivities are not largely dependent on rate of synaptic coupling but, rather, on current and noise intensity. Analyses of shunting inhibition reveal that it can affect both promotion and elimination of gamma oscillations. When the macroscopic oscillation is far from the bifurcation, shunting promotes the gamma oscillations and the PRF becomes flatter as the reversal potential of the synapse increases, indicating the insensitivity of gamma oscillations to perturbations. By contrast, when the macroscopic oscillation is near the bifurcation, shunting eliminates gamma oscillations and a stable firing state appears. More interestingly, under appropriate balance of parameters, two branches of bifurcation are found in our analysis of the FPE. In this case, shunting inhibition can effect both promotion and elimination of the gamma oscillation depending only on the reversal potential. 相似文献
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A study of the dynamics of a continuously stirred tank reactor with feedback control of the temperature 总被引:1,自引:0,他引:1
Feedback control of the temperature in the continuously stirred tank reactor (CSTR) will be studied in this paper. The control is achieved by continuously changing the input flow rate in response to the temperature. In particular the effect the control has on the temperature-dependent oscillations will be investigated. The steady-state solutions and emergence of periodic solutions through the Hopf bifurcation will be analyzed both theoretically and numerically. The region into which all trajectories are ultimately drawn will be defined in the phase plane^ as well as the areas in parameter space to which oscillations will be confined. Finally several nonlinear controlling functions are presented which ensure the system does not exhibit oscillations. 相似文献
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K. V. Avramov 《Acta Mechanica》2012,223(2):279-292
The system of three partial differential equations with respect to displacements (Donnell equations) is used to analyze nonlinear
vibrations of a cylindrical shell. The Galerkin method is applied to every partial differential equation to obtain a finite-degree-of-freedom
model of the shell. The system of ordinary differential equations with respect to the general coordinates of the radial shell
displacements is derived. The nonlinear modes of free vibrations are calculated using the harmonic balance method. The stability
analysis of periodic motions is performed. 相似文献
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该文研究了受周期激励轴向运动大挠度板横向振动的稳定性及分岔现象。在von Kàrmàn非线性大挠度板理论基础上,利用达朗贝尔原理建立系统的动力学模型。通过Galerkin截断,将时间变量和空间变量、位移函数和应力函数耦合在一起的偏微分方程离散,得到系统运动常微分方程。利用数值方法分析板随轴向运动速度、外激励力幅值、长宽比和轴向拉力变化时的运动分岔行为。利用最大Lyapunov指数和Poincaré映射图识别系统的动力学行为。结果发现,当板的某些参数变化时,系统出现分岔现象。不同参数时,系统呈现周期运动、倍周期运动、概周期运动,甚至混沌运动。 相似文献
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研究轴向变速运动大挠度薄板横向振动的稳定性及分岔现象。在von Kàrmàn非线性大挠度板理论基础上, 利用达朗贝尔原理建立系统的动力学模型。通过Galerkin截断, 将时间变量和空间变量、位移函数和应力函数耦合在一起的偏微分方程离散, 得到系统运动常微分方程。利用数值方法分析板随平均速度、速度脉动幅值和外激励力变化时的运动分岔行为。利用最大Lyapunov指数和Poincaré映射图识别系统的动力学行为。结果发现, 当板的某些参数变化时, 系统出现分岔现象。不同参数时, 系统呈现周期运动、倍周期运动、概周期运动, 甚至混沌运动。 相似文献
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弹性支承下弧齿锥齿轮系统的振动分析属于高维非线性动力学问题,其参数平面中的域界结构研究对实施振动抑制与控制具有重要意义。以某新型航空发动机的中心轴弧齿锥齿轮传动系统为研究对象,建立了7自由度非线性动力学模型。采用Adomian分解算法求解振动方程的分级响应。基于胞映射和庞加莱截面的思想,在支承刚度与啮合频率、支承阻尼与啮合频率以及支承刚度与支承阻尼所构成的参数平面中,分析了弧齿锥齿轮非线性系统的不同周期振动之间以及周期振动和混沌振动之间的域界。借助平面域界图,研究了参数平面内系统振动分岔类型与分岔结构。研究结果为弧齿锥齿轮系统的支承参数设计与振动主动控制提供了依据,并可根据系统参数所处的范围对弹性支承下弧齿锥齿轮系统的振动形态进行预测。 相似文献
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研究了一类周期系数力学系统因周期运动失稳而产生Hopf-Flip分岔的问题.首先根据拉格朗日方程给出了该力学系统的运动微分方程,并确定其周期运动的具有周期系数的扰动运动微分方程,再根据周期系数系统的稳定性理论建立了其给定周期运动的Poincaré映射,进一步根据该系统的特征矩阵的特征值穿越单位圆情况分析判断该Poincaré映射不动点失稳后将发生Hopf-Flip分岔,并用数值计算加以验证.结果表明,非共振条件下,系统的周期运动可通过Hopf-Flip分岔,进而演变成次谐运动,而三阶强共振条件下系统周期运动失稳后形成不稳定的次谐运动. 相似文献
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In this work, well-known methods of solving nonlinear partial differential equations have been used to study steady plane magneto-gas-dynamic orthogonal, aligned, and transverse flow problems when the velocity magnitude is constant on each individual streamline. In the study of the orthogonal case, Monge's method for solving second-order nonlinear partial differential equations is used. The hodograph and Charpits' methods are applied in the other two cases of aligned and transverse flows to investigate the geometries and solutions for the flow problems. 相似文献
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热环境中功能梯度圆板的非线性动力响应分析 总被引:1,自引:0,他引:1
研究了热环境中功能梯度圆板在横向简谐激励作用下的非线性动力响应和动应力问题。针对陶瓷-金属功能梯度圆板, 考虑几何非线性、材料物理性质参数随温度变化及材料组分沿厚度方向按幂律分布的情况, 应用虚功原理给出了热载荷与横向简谐载荷共同作用下的非线性振动偏微分方程。在固支无滑动的边界条件下, 利用伽辽金法得到了达芬型非线性强迫振动方程。通过数值算例, 给出了关于体积分数指数的分岔图, 相图、Poincare映射等响应图以及动应力变化规律图, 讨论了材料体积分数指数和温度场对功能梯度圆板非线性动力响应的影响。结果表明: 热环境中功能梯度圆板随体积分数指数的变化可使系统出现周期响应、倍周期响应和混沌响应。功能梯度圆板中心处动应力在系统发生分岔或出现混沌响应时出现大幅变化, 而且在混沌响应时具有不可预测性。 相似文献
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输液管道颤振失稳的时滞控制 总被引:1,自引:0,他引:1
采用时滞主动控制方法对输液管道的颤振失稳进行控制,以提高输液管道系统的临界流速.首先构造时滞控制策略并建立时滞控制的偏微分方程;然后利用伽辽金法离散时滞偏微分方程将其转化为时滞微分方程组,从理论上分析时滞微分方程的稳定性,并通过Matlab Biftool软件包对时滞控制系统的特征根分布情况进行模拟,与稳定性理论分析结果相当吻合;最后通过有限差分法对时滞偏微分方程进行数值模拟,与稳定性理论分析结果基本吻合.结果表明:通过时滞主动控制输液管道的颤振,控制策略简单,而且效果较好. 相似文献