具损伤压电智能层合板的非线性主动控制和损伤监测

基于Hamilton原理、高阶剪切变形板理论、von Krmn型几何非线性应变-位移关系以及应变能等效原理,考虑压电层的质量和刚度及复合材料层内的损伤效应,建立了具损伤压电智能层合板的非线性运动方程．采用耦合正、逆压电效应的负速度反馈控制原理,形成闭环控制回路,实现了对压电智能层合板的主动控制和损伤监测．数值计算中,以四边简支面内不可动的层合矩形板为例,讨论了压电层位置对振动控制的影响,以及损伤程度和损伤位置对传感层输出电压的影响,提出一种损伤监测的方法．     

具界面损伤压电智能层合板的非线性自由振动分析

基于广义6自由度板理论、应变等效原理和Hamilton变分原理,通过引入三维弹性平衡方程和静电平衡方程的通解来构造满足界面间力电耦合关系和各类连续条件的位移、电势分布形函数,建立了具铺设层内和层间界面处损伤效应的压电智能层合板的非线性运动控制方程组,并运用Galerkin 方法进行求解.数值算例中,分别讨论了,不同损伤程度、压电层厚度、厚跨比及长宽比对四边简支非理想界面压电智能层合板线性自由振动频率和非线性幅频响应曲线的影响.     

基于剪切效应纤维梁单元的结构非线性有限元数值模拟

基于Euler-Bernoulli梁理论的经典纤维模型忽略了剪切变形给截面带来的影响,为了得到更加精确的梁单元模型,该文基于考虑剪切效应的纤维梁单元,根据Timoshenko梁理论,推导了该纤维梁单元的刚度矩阵,并结合弹塑性增量理论,同时考虑了几何非线性和材料非线性的双重影响,建立了压弯剪复杂应力状态下结构非线性有限元...     

基于拟线性化方法的非线性系统闭环反馈控制保辛算法

提出了一种求解非线性系统闭环反馈控制问题的保辛算法．首先,通过拟线性化方法将非线性系统最优控制问题转化为线性非齐次Hamilton系统两端边值问题的迭代格式求解．然后,通过作用量变分原理与生成函数构造了保辛的数值算法,且该算法保持了原Hamilton系统的辛几何性质．最后,通过时间步的递进完成状态与控制变量的更新,进而达到闭环控制的目的．数值算例表明:保辛算法具有较高的计算精度和较快的收敛速度．此外,将闭环反馈控制与开环控制分别应用于驱动小车上的倒立摆控制系统中,结果表明:在存在初始偏差的情况下,开环控制会导致稳定控制任务的失败,而闭环反馈控制能够在一段时间后消除初始偏差的影响,并使系统达到稳定状态．     

周期结构区域中压电问题的双尺度有限元方法

近年来纤维压电复合材料的力电性能预测已发展为一个重要的研究领域．对力电耦合周期结构的复合材料问题,通过引入匹配的边界层得到了电势与位移解的新型双尺度有限元计算方法,建立了电势与位移的双尺度耦合关系,分析了双尺度有限元解的误差.数值算例验证了方法的有效性．     

考虑表面效应的压电纳米梁的振动研究

一维压电纳米材料在微纳米机电系统(MEMS/NEMS)中应用广泛,对其力学性能的有效表征至关重要.基于Gurtin-Murdoch表面理论,建立了一种表征一维纳米材料表面效应的新模型.基于Timoshenko梁理论,建立了考虑表面效应的压电纳米梁控制方程,推导了几种不同边界条件下压电纳米梁的频率方程和振型方程的精确解.提出了一种在有限元软件中实现表面效应模拟的计算方法,在ABAQUS中实现了考虑表面效应的压电纳米梁的数值模拟.理论结果和有限元模拟结果吻合较好,验证了理论模型的正确性和有效性.表面效应对纳米梁振动的频率影响显著,而在某种程度上对振型有一定的影响.     

Hamilton等参元与智能叠层板的半解析法

根据压电材料修正后的Hellinger-Reissner(H-R)变分原理,建立了各向异性压电材料4节点Hamilton等参元的一般形式．为智能叠层板自由振动问题和带有压电块的叠层悬臂梁的瞬态响应等问题提出了一种新的半解析法．数学模型的基本步骤:将压电层和主体层看成独立的三维体,在平面内离散各层,分别建立各层的方程;根据主体层和压电层在连接界面上广义应力和广义位移的连续条件,联立主体层和压电层的方程得到全结构的控制方程．等参元不限制智能板侧面的几何边界形状、板的厚度和层数,有广泛的应用领域．     

静水压力下压电弹性圆柱振动的主动控制

对静水压力下压电弹性层合壳的振动控制进行了研究。首先利用Hamiltion原理推导出压电弹性层合壳的非线性动力基本方程，进一步得到了静水压力作用下封闭压电弹性层合壳的动力方程。对两端简支条件下的压电弹性圆柱壳的振动问题进行了求解，并基于速度反馈控制法得到了带压电感测层／激励层的层合圆柱壳的主动控制模型，相应的数值结果表明在载荷的情况下，压电层上施加合适大小，方向的电压可以改变圆柱壳的静变形。对于系统的动力响应问题，速度反馈的增益越大，越能抑制系统在共振区的振动，验证了该控制模型抑制结构振动的有效性。     

刚-柔耦合系统离心力效应模型及姿态机动稳定性

研究非线性离心力对刚-柔耦合系统的大范围姿态运动的影响．首先从离心力势场的概念出发,推导了刚-柔耦合系统的非线性模型;然后通过近似计算分析了非线性离心力对系统姿态运动的动态效应;最后,在只有系统姿态与姿态速率测量值的条件下,基于能量范数选择Liapunov函数,证明了采用PD反馈控制律能够确保大角度姿态机动过程的稳定性．     

非线性随机效应模型的置信域

本文对非线性随机效应模型,建立了微分几何框架,推广了Bates＆Wates关于非线性模型几何结构．在吡基础上,我们导出了关于固定效应参数和子集参数的置信域的曲率表示,这些结果是BatesandWates(1980),Hamilton(1986)与Wei(1994)等的推广．     

The Vibrational Behavior of Coupled Bladed Disks with Variable Rotational Speed

Low pressure steam turbine blades are subjected to high static and dynamic loads during operation. These loads strongly depend on the turbine's rotational speed, leading to entirely new load conditions. To avoid high dynamic stresses due to the forced vibrations, a coupling of the blades, such as shrouds or snubber coupling, is applied to reinforce the structure. In this work the influence of the rotational speed on the vibration behavior of shrouded blades is investigated. Two fundamental phenomena are considered: the stress stiffening and the spin softening effect. Both effects are caused by centrifugal forces and affect the structural mechanical properties, i.e. the stiffness matrix K , of the rotating system. Since the rotational speed Ω appears quadratically, it is possible to derive the stiffness matrix as a second order matrix polynomial in Ω² [3]. In the case of shrouded blades, contact forces between neighboring blades must be taken into account. The contact status and the pressure distribution in particular is strongly influenced by the rotational speed, respectively, centrifugal forces, caused by the untwisting and radial deformation of the blades. For the calculation, a three dimensional structural mechanical model including a spatial contact model is considered. The solution of the nonlinear equations of motion is based on the well known Multiharmonic Balance Method [2]. Here, the nonlinear forces are computed in the time domain and transferred in the frequency domain by the use of the Fast Fourier Transformation (FFT), also known as the Alternating Frequency Time method (AFT) [1]. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonlinear dynamics and dynamic instability of smart structural cross-ply laminated cantilever plates with MFC layer using zigzag theory

In this paper, a novel dynamic model for smart structural systems cross-ply laminated cantilever plate with smart material Macro fiber composites (MFC) layer is presented by using zigzag function theory. The nonlinear dynamic response and dynamic instability of the smart structural systems are studied for the first time. The plate is subjected to the uniformed static and in-plane harmonic excitation conjunction with electrically loaded under different electric boundary conditions. The partial layer-wise theory which the first shear deformation theory is expanded by introducing the zigzag function in the in-plane displacement components is adopted. The carbon fiber reinforced composite material T800/M21and macro fiber composites (MFC-d31) M8528-P3 are implemented. By Lagrangian equation and Chebyshev polynomial, the equations of motion are derived for the laminated plate. The validation and convergence are studied by comparing results with literatures. The dynamic instability regions and the critical buckling load characteristics can be obtained for different layer sequences, geometric dimensions and also the electromechanical effects are considered. Nonlinear dynamic responses of the laminated plate are studied by using numerical calculation. It can be seen that in certain state the plate will loses stability and the periodic, multiple period as well as chaotic motions of the plate are found.     

Implementation of a cohesive zone model for crack closure analysis of rotors

The presence of a crack in a rotor introduces a local flexibility which affects its dynamic response. Moreover, the crack may open and close during the vibration period. The crack status is a function of time and also depends on the rotational speed and the vibration amplitude of the rotor. This nonlinear case is still a challenging research topic especially in the field of closing crack in the rotating shaft. A cohesive zone model is developed in order to analyze the stiffness of a crack in a rotating shaft. The proposed expression will be compared to three different crack models, namely, a breathing crack model, a switching crack model and an open crack model. Moreover, a cohesive law to predict and to analyse the stress at the crack tip is presented. The numerical model is implemented using a finite element formulation. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dynamic modeling and analysis of rotating FG beams for capturing steady bending deformation

A dynamic analysis of rotating functionally gradient (FG) beams is presented for capturing the steady bending deformation by using a novel floating frame reference (FFR) formulation. Usually, the cross section of bending beams should rotate round the point at the neutral axis while centrifugal inertial forces are supposed to act on centroid axis. Due to material inhomogeneity of FG beams, centroid and neutral axes may be in different positions, which leads to the eccentricity of centrifugal forces. Thus, centrifugal forces can be divided into three componets: transverse component, axial component and force moment acting on the points of the neutral axis, in which transverse component and force moment can make the beam produce the steady bending deformation. However, this speculation has not been presented and discussed in existing literatures. To this end, a novel FFR formulation of rotating FG beams is especially developed considering centroid and neutral axes. The FFR and its nodal coordinates are used to determine the displacement field, in which kinetic and elastic energies can be accurately formulated according to centroid and neutral axes, respectively. By using the Lagrange's equations of the second kind, the nonlinear dynamic equations are derived for transient dynamics problems of rotating FG beams. Simplifying the nonlinear dynamic equations obtains the equilibrium equations about inertial and elastic forces. The equilibrium equations can be solved to capture the steady bending deformation. Based on the steady bending state, the nonlinear dynamic equations are linearized to obtain eigen-frequency equations. Transient responses obtained from the nonlinear dynamic equations and frequencies obtained from the eigen-frequency equations are compared with available results in existing literatures. Finally, effects of material gradient index and angular speed on the steady bending deformation and vibration characteristics are investigated in detail.     

基于非约束模态的中心刚体-Timoshenko梁动力学建模与分析北大核心CSCD

梁的横向变形会导致梁纵向缩短,建模过程中考虑梁横纵变形二次耦合项则存在动力刚化现象,这说明梁的纵向变形会对模型的广义刚度造成影响.对于做旋转运动的梁结构,旋转运动时还会受到离心力的作用而产生轴向拉力,轴向拉力同样也会引起梁的轴向变形,这种影响对粗短梁更加明显.以大范围运动中心刚体-Timoshenko梁模型为研究对象:首先,运用Timoshenko梁理论以及Hamilton原理建立含离心力的动力学模型;其次,引入非约束模态概念,采用Frobenius方法求解非约束模态振型函数以及固有频率;最后,通过数值仿真探究不同恒定转速时非约束模态与约束模态广义刚度的差异和非约束模态条件下离心力对模型的影响.     

Rigid–flexible coupling dynamic analysis on a mass attached to a rotating flexible rod

A rigid–flexible coupling dynamic analysis is presented where a mass is attached to a massless flexible rod which rotates about an axis. The rod is limited to small deformation so that the mass is constrained to move in the plane of rotation. A strongly nonlinear model of the system is established based on the couplings between the elastic deflections of the mass and rigid rotation, in which the mass deflection and rigid rotation are both treated as unknown variables. The additional inertia forces on the mass and coupling mechanism are elucidated in the system model. In the case of varied but prescribed rigid rotation, a set of time-varying differential equations governing mass motion is obtained. The trajectories of mass motion are examined for the spin-up and spin-down rotation. Under constant rigid rotation, a set of ordinary differential equations is further attained, and the issues with dynamic frequencies and critical angular velocity of the system are analyzed. The effects of the centrifugal, Coriolis and tangential inertia forces on the dynamic responses are discussed.     

Chaotic vibration analysis of rotating,flexible, continuous shaft-disk system with a rub-impact between the disk and the stator

The chaotic vibration analysis of a rotating flexible continuous shaft-disk system with rub-impact is studied. The system is modeled as a continuous shaft with a rigid disk in its mid-section with Coriolis and centrifugal effects included. The governing partial differential equations of motion are extracted based on the Euler–Bernoulli beam theory. The assumed modes method is used to discretize partial differential equations and the resulting equations are solved via numerical methods. Time series, phase plane portrait, power spectra, Poincaré map, bifurcation diagrams, and Lyapunov exponents are used to analyze the vibration behavior of the system. Initially, the case is investigated in which no Coriolis or centrifugal effects are considered. Then, another case is studied in which these effects are considered. The results confirm the claim that the rub-impact occurs at lower speed ratios due to the Coriolis and centrifugal forcing effects, and that the dynamic behaviors of the system for the two cases are much different as a result of the rub-impact in the second case. Periodic, quasi-periodic, sub-harmonic, and chaotic states can be observed while the appearance or disappearance of the chaos is different. The centrifugal forcing effect plays a greater role than that of the Coriolis force on the incidence of the rub-impact. These results can be useful in identifying the undesirable behaviors in these types of rotating systems.     

Numerical analysis of dynamic behavior of stream turbine blade group

This paper considers the stream turbine blade group as a rotationally periodic structure and the complex constraint method has been induced. The effect of the centrifugal force to dynamic vibration frequency has been considered by introducing a nonlinear large deformation equation. A method has been given to introduce the special constraint between the fin heaves of every blade during dynamic analysis.