共查询到18条相似文献,搜索用时 765 毫秒
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研究了内共振下简支边界屈曲黏弹性梁受迫振动稳态周期幅频响应.考虑Kelvin黏弹性本构关系,并通过对非平凡平衡位形做坐标变换,建立屈曲梁横向振动的非线性偏微分-积分模型.基于对控制方程的Galerkin截断,得到多维非线性常微分方程组.在前两阶模态内共振存在的条件下,运用多尺度法分析截断后的控制方程,利用可解性条件消除长期项,获得一阶主共振下的幅值与相角方程.通过数值算例以展示系统稳态幅频响应关系以及失稳区域,从而聚焦系统共振中存在的非线性现象,如跳跃现象、滞后现象,并讨论了双跳跃现象随轴向荷载的演化.通过直接数值方法处理截断方程,数值验证近似解析解,计算结果表明多尺度法具有较高精度. 相似文献
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轴向变速运动粘弹性弦线横向振动的复模态Galerkin方法 总被引:1,自引:0,他引:1
在考虑初始张力和轴向速度简谐涨落的情况下,利用含预应力三维变形体的运动方程,建立了轴向变速运动弦线横向振动的非线性控制方程,材料的粘弹性行为由Kelvin模型描述.利用匀速运动线性弦线的模态函数构造了变速运动非线性弦线复模态Galerkin方法的基底函数,并借助构造出来的基底函数研究了复模态Galerkin方法在轴向变速运动粘弹性弦线非线性振动分析中的应用.数值结果表明,复模态Galerkin方法相比实模态Galerkin方法对变系数陀螺系统有较高的收敛速度. 相似文献
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假设温度场与应变场相互耦合,研究了旋转扁薄球壳和锥壳的轴对称非线性热弹振动问题.基于von Krmn理论和热弹性理论,导出了本问题的全部控制方程及其简化形式.应用Galerkin技术进行时空变量分离后,得到了一个关于时间的非线性常微分方程组.根据方程的特点,分别用多尺度法和正则摄动法求得了壳体振动的频率与振幅间特征关系和振幅衰减规律的一次近似解析解,并讨论了壳体几何参数、热弹耦合参数以及边界条件等因素对其非线性热弹耦合振动特性的影响. 相似文献
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基于磁弹性广义变分原理和Hamilton原理,对处于外加磁场中的软铁磁体,建立了磁弹性动力学理论模型.分别通过关于铁磁杆磁标势和弹性位移的变分运算,获得了包含磁场和弹性变形的所有基本方程,并给出描述磁弹性耦合作用的磁体力和磁面力.采用摄动技术和Galerkin方法,将所建立的磁弹性理论模型用于外加磁场中铁磁直杆的振动分析.结果表明,由于磁弹性耦合效应,外加磁场将对铁磁杆的振动频率产生影响:当铁磁杆的振动位移沿着磁场方向时,其频率减小并出现磁弹性屈曲失稳;当铁磁杆的振动位移垂直于磁场方向时,其频率将会增大.理论模型能够很好地解释已有实验观测的振动频率改变现象. 相似文献
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基于修正的偶应力理论并考虑Lagrange应变张量所给出的几何非线性,运用Hamilton原理建立了微尺度悬臂管平面振动的积分-微分方程.通过Galerkin方法将原积分-微分方程离散成常微分方程组,研究了临界流速-质量比曲线的不同阶Galerkin近似解与精确解的符合程度以及它们对材料长度尺寸参数的依赖性.对不同的模态截断数,运用基于中心流形-范式理论的投影法计算了临界流速处系统的第一Lyapunov(李雅谱诺夫)系数和临界特征值关于流速的变化率,以此为基础分析了系统的分岔模式,探讨了模态截断数对系统动力学性质的影响.临界流速-质量比曲线的滞后部分及交点处的动力学性质表明,系统存在不同的分岔方向,用6个模态的Galerkin离散化方程作分岔图对此进行了验证,并通过理论分析及数值方法分别计算了颤振的固有频率. 相似文献
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首次建立了基于Timoshenko梁理论的微曲输流管道横向振动的动力学模型,并分析了流体流动影响下微曲管道横向自由振动的固有特征.采用广义Hamilton原理,导出了考虑流体影响的微曲管道横向振动的控制方程,通过Galerkin截断对控制方程离散化,再由广义本征值问题得到管道横向振动的固有频率,并研究了液体流速和弯曲幅度对管道横向固有振动特征的影响.发展了基于等效刚度和等效阻尼方法的考虑流体影响的微曲管道振动分析的有限元仿真计算方法,并通过有限元软件实现数值仿真,验证了Galerkin截断的分析结果以及所建立的Timoshenko微曲管道动力学模型的有效性.研究表明,流体的流速以及管道的弯曲幅度对管道横向振动固有频率均有显著影响. 相似文献
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Hamed Sadeghian Ghader Rezazadeh 《Communications in Nonlinear Science & Numerical Simulation》2009,14(6):2807-2816
This paper presents a comprehensive comparison study between the generalized differential quadrature (GDQ) and the well-known global Galerkin method for analysis of pull-in behavior of nonlinear micro-electro-mechanical coupled systems. The nonlinear governing integro-differential equation for double clamped MEMS devices which was derived using variational principle by the authors [Sadeghian H, Rezazadeh G, Osterberg PM. Application of the generalized differential quadrature method to the study of pull-in phenomena of MEMS switches. J Microelectromech Syst 2007;16(6):1334–40] is discretized by applying Galerkin and GDQ methods. The divergence instability or pull-in phenomenon is analyzed. Obtained results are compared with the results of the pervious works. The Galerkin method is implemented with effect of number of used shape functions. Different types of trail functions on calculated pull-in voltage are examined.Furthermore, compare to one term and two terms truncation Galerkin method, it is observed that the GDQ with small number of grid points (non-uniform) performs accurate results for nonlinear micro-electro-mechanical coupled behavior which requires a large number of grid points at high-order approximation. 相似文献
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非线性粘弹性梁的动力学行为 总被引:18,自引:3,他引:15
建立了描述受周期荷载作用的均匀粘弹性梁动力学行为的非线性偏微分-积分方程,梁的材料满足Leaderman非线性本构关系,对于两端简支的情形用Galerkin方法进行了2阶截断后,简化为常微分-积分方程,进一步简化为便于进行数值实验的常微分方程,最后用数值方法比较了1阶和2阶截断系统的动力学行为。 相似文献
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In the present study, a modified nonlocal elasticity theory is used for flutter and divergence analyses of the cantilever carbon nanotubes (CNTs) conveying fluid. The CNT is embedded in viscoelastic foundation and is subjected to an axial compressive load acting at the free end. An extreme high-order governing equation as well as higher-order boundary conditions is developed using Hamilton's principle for vibration and stability analysis of the CNT. The numerical solution for flutter and divergence velocities is computed using the extended Galerkin method. The validity of the present analysis is confirmed by comparing with molecular dynamics simulation (MDS) and numerical solutions available in the literature. In the numerical results, the effects of nonlocal parameter, surface effects, viscoelastic foundation and compressive axial load on the stability boundaries of the system are investigated. The results show that the stability boundaries of the CNT are strongly dependent on the small scale coefficient and surface effects. 相似文献
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Multi-step Timoshenko beams coupled with rigid bodies on springs can be regarded as a generalized model to investigate the dynamic characteristics of many structures and mechanical systems in engineering. This paper presents a novel transfer matrix method for the free and forced vibration analyses of the hybrid system. It is modeled as a chain system, where each beam and each rigid body with its supporting spring are dealt with one element, respectively. The transfer equation of each element is deduced based on separation of variables method. The system overall transfer equation is obtained by substituting an element transfer equation into another. Then, the free vibration characteristics are acquired by solving exact homogeneous linear equations. To compute the forced vibration response with modal superposition method, the body dynamic equations and augmented eigenvectors are established, and the orthogonality of augmented eigenvectors is mathematically proved. Without high-order global dynamic equation or approximate spatial discretization, the free and forced vibration analyses of the hybrid system are achieved efficiently and accurately in this study. As an analytical approach, the present method is easy, highly stylized, robust, powerful and general for the complex hybrid systems containing any number of Timoshenko beams and rigid bodies. Four numerical examples are implemented, and the results show that this method is computationally efficient with high precision. 相似文献
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圆形三向网架非线性动力稳定性分析 总被引:7,自引:2,他引:5
用拟板法将网架简化为平板,给出表层应变与中面位移的非线性关系.根据薄板的非线性动力学理论,建立了在直角坐标系中三向网架的非线性动力学方程,又将此方程转化为极坐标系轴对称非线性动力学方程.在周边固定条件下,引入异于等厚度板的无量纲量,对基本方程无量纲化.利用Galerkin法得到一个三次非线性振动方程,在无外激励情况下,讨论了稳定性与分岔问题.在外激励情况下,用Melnikov方法研究了圆形三向网架可能发生的混沌运动.通过数字仿真绘出了发生混沌的相平面图. 相似文献
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The nonlinear Galerkin methods are numerical schemes well adapted to the long-term integration of nonlinear evolution partial differential equations. In this paper, a class of high-order nonlinear Galerkin methods are provided. Moreover, convergence results with high-order spectral accuracy are derived for the schemes introduced. 相似文献
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Ryan M. Brown 《Journal of Applied Mathematics and Computing》2010,33(1-2):83-102
The rate of change for the concentrations of chemical substances in a set of reactions is modeled by a nonlinear dynamical system, which warrants the use of numerical integration methods for differential equations. Previous work advocates the use of a specialized high-order Taylor series method because of an observed reduction in computation time. Contrastingly, we show combinatorial and computational difficulties of the standard Taylor series method, which may dramatically increase computational time or reduce the quality of output. We provide two implementations, a naïve algorithm and an algorithm employing dynamic programming; we are able to overcome only some numerical obstacles and therefore conclude that the Taylor series approach is insufficient for large sets of reactions having many chemical substances. 相似文献
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An algebraic Newton-multigrid method is proposed in order to efficiently solve systems of nonlinear reaction-diffusion problems with stochastic coefficients. These problems model the conversion of starch into sugars in growing apples.
The stochastic system is first converted into a large coupled system of deterministic equations by applying a stochastic Galerkin finite element discretization. This method leads to high-order accurate stochastic solutions. A stable and high-order time discretization is obtained by applying a fully implicit Runge-Kutta method. After Newton linearization, a point-based algebraic multigrid solution method is applied. In order to decrease the computational cost, alternative multigrid preconditioners are presented. Numerical results demonstrate the convergence properties, robustness and efficiency of the proposed multigrid methods. 相似文献