有任意脱层复合材料梁的非线性动力稳定性

基于弹性理论建立了有脱层复合材料梁的基本方程式，研究了有任意脱层的考虑横向剪切变形的复合材料梁的非线性动力稳定性，对脱层梁进行分区处理，方便地描述了脱层长度，脱层位置，利用振型函数作为位移函数的形函数，采用增量谐波平衡法对基本方程式进行求解，考虑了不同脱层位置和不同脱层长度对脱层梁的非线性动力稳定性的影响，得出了各种情况下的动力不稳定性区域。     

风力机叶片挥舞/摆振的动力失速非线性气弹稳定性研究

研究动力失速风力机叶片的非线性气弹系统的稳定性。叶片结构采用具有挥舞/摆振耦合的典型截面模型,动力失速非线性气动载荷的计算采用基于半经验的ONERA非定常、非线性气动模型。为了减少由于线性化气弹稳定性分析模型带来的误差,直接采用时间域数值积分法,对叶片挥舞/摆振耦合非线性气弹方程组进行数值积分,研究叶片动力失速诱发颤振的稳定性,分析了缩减速度、预尖锥角的影响,并且针对目前文献很少报道的结构阻尼参数的影响问题进行了研究。     

隐式中点法对于非线性阻尼结构的稳定性

用能量守恒的方法证明了隐式中点法对于非线性指数阻尼的结构动力方程为数值稳定。工程中常用的双线性本构模型作为这种指数模型的特殊情况,同样满足数值稳定性条件。为了验证证明过程的可靠性,对一个单自由度体系和两个多自由度结构进行动力非线性计算分析,对比不同时间增量步的计算结果。从而给出了针对这种非线性动力方程计算的稳定的数值积分方法,为动力计算数值稳定性提供理论基础。     

结构-滑移基础-土非线性相互作用体系主共振与分叉

本文基于修改后的非线性Davidenkov动力模型，采用非线性有限元得到基础与土之间的滑移刚度，从而建立了结构－滑移基础－地基土相互作用体系。用平均法研究体系的主共振，得到主共振定常解和幅频响应函数，讨论了定常解的稳定性。根据奇异性理论求得开折参数平面下的转迁集和分叉图，从分叉图出发讨论了体系的动力行为，得到了一些有益的结论。     

爆炸冲击载荷作用下夹层开顶扁球壳的非线性动力稳定性分析

该文对爆炸冲击作用下夹层开顶扁球壳的非线性轴对称动力稳定性问题进行研究.基于Reissner假设和Hamilton原理,得到了夹层开顶扁球壳在冲击载荷作用下的非线性动力控制方程;采用Galerkin方法对非线性动力控制方程进行求解,得到以刚性中心位移表达的非线性动力响应方程,并应用Runge-Kutta方法进行数值求解...     

非线性结构动力方程求解的显式差分格式的特性分析

本文针对软化非线性结构体系动力方程,分析了作者推导出的求解方程的显式差分格式的收敛性及稳定性,分别给出了结构体系处于非线性正刚度及屈服后的负刚度反应阶段时显式差分格式的稳定条件。稳定性分析结果表明,只要结构体系处于初始反应的粘-弹性阶段时显式差分格式满足稳定性条件,则可以保证软化非线性结构体系反应求解的整个过程中格式的计算稳定性。     

具有结构阻尼的复合材料薄壁梁的动力失速非线性颤振特性

研究具有结构阻尼的复合材料薄壁梁动力失速非线性颤振特性。采用受ONERA非线性气动力作用的复合材料薄壁梁的气弹模型分析非线性气弹稳定性;采用复合材料薄壁梁的模态阻尼分析模型进行结构阻尼预测,复合材料结构阻尼对复合材料薄壁梁气弹系统稳定性影响通过引入比例阻尼矩阵的方式予以考虑。采用Galerkin法对具有结构阻尼的气弹方程进行离散化,同时利用片条理论对非线性广义气动力进行计算。借助特征值方法及时域积分法分析复合材料薄壁梁非线性颤振边界及气弹响应的稳定性。通过数值分析,揭示复合材料结构阻尼、纤维铺层角对复合材料薄壁梁非线性颤振边界影响。结果表明,结构阻尼用于抑制复合材料薄壁梁的动力失速非线性颤振,增强气弹稳定性,具有十分明显作用效果。     

一类混合隔振系统非线性动力特性分析

研究磁悬浮—气囊主被动混合隔振系统的非线性动力特性,包括对系统的稳定性分析和位移响应的计算及其模拟仿真。通过对磁悬浮—气囊主被动混合隔振装置的简化,建立与之相适应的非线性动力微分方程;利用谐波平衡法对非线性微分方程进行求解,研究系统方程的幅频响应曲线在不同参数下的变化规律;由Lyapunov稳定性定理对系统进行稳定性判断;通过Simulink软件对整个系统进行模拟仿真得出位移的功率谱曲线,分析结果表明混合隔振系统在低频激励下的稳定性更好,隔振效果明显。     

非线性动力吸振器的动力学分析

运用非线性振动的模态方法对非线性动力吸振器进行了动力学分析,研究了该类吸振器的反共振工作点、工作点的稳定性以及阻尼对反共振工作点的影响.     

含分层损伤复合材料层合板非线性动力稳定性

采用Reddy 的板高阶剪切变形简化理论研究了含分层损伤复合材料层合板的非线性动力稳定性问题。建立了分层模型, 推导了考虑几何非线性和阻尼效应的Methieu 方程, 给出了该方程的解析解表达式; 研究了参数振动解的稳定性; 然后通过典型数例讨论了分层损伤对层合板固有频率、屈曲临界力以及动力稳定区域的影响; 研究了保守与非保守体系的外载荷的激励频率对层合板第一参数振动的振幅的影响, 以及线性、非线性阻尼对非保守体系的最大牵引深度的影响。由典型算例讨论可知, 随着复合材料层合板分层损伤的扩大, 其动力稳定性能逐渐减弱, 特别是损伤接近层合板的中面时, 分层损伤对其动力稳定性能的影响最大。      

非线性弹性地基上矩形薄板的动力学研究

本文研究了非线性弹性地基上矩形薄板的非线性振动特性和振动稳定性。在考虑了地基板阻尼和非线性效应的基础上,建立了小挠度矩形板横向均布简谐激励作用下的非线性动力学方程;用谐波平衡法研究了其非线性振动特性;导出了频率响应方程,研究了频率响应特性;讨论了非线性因素的影响,得出了忽略地基板非线性因素的条件;分析了地基板的非线性振动的稳定性,得出了稳定区和不稳定区的分界线方程。     

Analysis of nonlinear dynamic stability for carbon nanotube-reinforced composite plates resting on elastic foundations

This article studies nonlinear dynamic stability of carbon nanotube-reinforced composite (CNTRC) plates resting on an elastic foundation. The single-walled carbon nanotubes (SWCNTs) are aligned and distributed in the form of uniformly distributed (UD) and functionally graded (FG) reinforcements. The governing equations are established based on classic plate theory, which is converted to a Mathieu-type equation by using a two-step perturbation technique, and then solved by adopting an incremental harmonic balanced (IHB) method. In numerical results, the effects of nonlinear geometric factor, distribution and fraction volume of CNTs, and foundation stiffness on principle dynamic unstable regions are discussed.     

Winkler地基上材料非线性矩形薄板主参数共振研究

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。     

具有初始应力加劲板的非线性动力学特性

针对工程结构中常用的加劲板,研究了其在初始应力作用下的非线性振动特性。将母板与加劲肋分开考虑,其中母板按薄板理论考虑,加劲肋按Euler-Bernoulli梁理论考虑,根据母板与加劲肋的应力与应变关系建立系统的应变能表达式,同时结合系统的动能表达式,并利用Lagrange方程建立系统的非线性动力微分方程。运用椭圆函数求得加劲板单模态的非线性频率,采用同伦分析方法求解加劲板的3∶1内共振。通过参数分析,重点讨论初始应力变化对系统非线性动力特性的影响,并得出初始应力的存在对加劲板非线性动力特性的影响规律。     

Nonlinear vibration of smart circular functionally graded plates coupled with piezoelectric layers

Nonlinear vibration analysis of thin circular pre-stressed functionally graded (FG) plate integrated with two uniformly distributed piezoelectric actuator layers with an initial nonlinear large deformation are presented in this paper. Nonlinear governing equations of motion are derived based on classical plate theory (CPT) with von-Karman type geometrical large nonlinear deformations. A nonlinear static problem is solved first to determine the initial stress state and pre-vibration deformations of the plate that is subjected to in-plane forces and applied actuator voltage. By adding an incremental dynamic state to the pre-vibration state, the differential equations that govern the nonlinear vibration behavior of pre-stressed piezoelectrically actuated circular FG plate are derived. An exact series expansion method is used to model the nonlinear electro-mechanical vibration behavior of the structure. Control of the FG plate’s nonlinear deflections and natural frequencies using high control voltages are studied and their nonlinear effects are evaluated. In a parametric study the emphasis is placed on investigating the effect of varying the applied actuator voltage as well as gradient index of FG plate on the dynamic characteristics of the structure.     

Nonlinear dynamic response of laminated plates resting on nonlinear elastic foundations by the discrete singular convolution-differential quadrature coupled approaches

In this paper, nonlinear dynamic response of rectangular laminated composite plate resting on nonlinear Pasternak type elastic foundations is investigated. First-order shear deformation theory (FSDT) is used for modeling of moderately thick plates. The plate formulation is based on the von Karman nonlinear equation. The resulting nonlinear governing equations for transient analysis of laminated plates on elastic foundation are integrated using the discrete singular convolution-differential quadrature coupled approaches. The nonlinear governing equations of motion of plate are discretized in space and time domains using the discrete singular convolution and the differential quadrature methods, respectively. The validity of the present method is demonstrated by comparing the present results with those available in the open literature. The effects of the foundation parameters, boundary conditions and geometric parameters of plates on nonlinear dynamic response of laminated thick plates are investigated.     

轴向变速运动大挠度薄板的非线性动力学行为

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。     

Nonlinear vibration and dynamic response of shear deformable laminated plates in hygrothermal environments

This paper deals with hygrothermal effects on the nonlinear vibration and dynamic response of shear deformable laminated plates. The temperature field considered is assumed to be a uniform distribution over the plate surface and through the plate thickness. The material properties of the composite are affected by the variation of temperature and moisture, and based on a micro-mechanical model. The formulations are based on higher-order shear deformation plate theory and general von Kármán-type equation of motion, which includes hygrothermal effects. The equations of motion are solved by an improved perturbation technique to determine nonlinear frequencies and dynamic responses of shear deformable antisymmetric angle-ply and unsymmetric cross-ply laminated plates. The numerical illustrations concern the nonlinear vibration and dynamic response of the shear deformable laminated plates under different sets of hygrothermal environmental conditions. Effects of temperature rise, the degree of moisture concentration, and fiber volume fraction on natural frequencies, nonlinear to linear frequency ratios and dynamic responses are studied.     

梯形板的非线性动力分析

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。     

Study of mechanical behavior of circular FGM micro-plates under nonlinear electrostatic and mechanical shock loadings

This paper deals with the study of mechanical behavior of a circular functionally graded material (FGM) micro-plate subjected to a nonlinear electrostatic pressure and mechanical shock. It is assumed that the FGM micro-plate is made of metal and ceramic and that material properties are changed continuously along the plate thickness according to a typical function. The nonlinear equation of static deflection and dynamic motion is solved using a step-by-step linearization method and Galerkin-based reduced order model, respectively. In order to find the response of the FGM micro-plate to the electrostatic load and analyze stability of fixed points, static deflection, time history and phase portrait for different applied voltages and initial conditions are illustrated and the effects of different percentages of metal and ceramic constituent on the response of the system are investigated. In addition, effects of mechanical shocks characteristics (amplitudes and durations) on the stability of FGM micro-plate are studied.