基于时间有限元方法的旋转柔性叶片动力学响应分析

将时间有限元方法引入到柔性多体系统的数值计算中,研究了旋转柔性叶片系统的刚-柔耦合响应问题.首先,基于非线性梁理论,建立了旋转柔性叶片系统的中心刚体-柔性梁模型,构造柔性叶片系统考虑一次近似耦合的Lagrange函数;其次,采用假设模态方法对空间坐标进行离散,建立系统的时间有限元格式;最后,通过数值实验,分析了柔性叶片的动力学响应.该方法直接构造了系统的离散积分格式,并自动保证了该格式是保辛的,因而具有较高的数值精度和稳定性.数值结果表明:时间有限元可以有效地求解旋转柔性叶片系统内低频大范围运动与高频弹性振动之间的刚-柔耦合问题.     

基于四元数表示的多体动力学系统及其保辛积分算法

将四元数引入多体动力学系统,用以描述刚体转动分量,继而据此将问题转入约束动力学领域,建立相关的Lagrange体系.然后引入作用量并进行有限元近似,并保证格点上严格满足约束条件,则根据分析结构力学基本理论,可导出逐步积分的递推格式,并且积分保辛.该法具有未知数少、计算量小等优点,数值结果令人满意.     

应用多刚体离散化方法对梁的动力屈曲和后屈曲分析

基于梁的多刚体离散化模型（有限段模型）,建立了梁的链式多刚体-铰链-弹簧系统模型,利用坐标变换方法建立了相应的非线性多自由度系统的参数振动方程,并利用约束参数法对所得到的多度系统的Mathieu-Hill方程进行了梁的动力屈曲分析,得到系统的参数共振域．因为所用的离散化模型与动力方程对梁的变形并无限制,所以可以用所得到的数学模型在其失稳域对梁的动力后屈曲进行数值仿真分析．通过实例的数值仿真,证明了这种梁的参数振动模型与分析方法的正确性．     

具有结构内阻尼磁性刚体航天器姿态动力学稳定性分析

在地球引力场和磁场中,在考虑了航天器结构内阻尼及气体阻力的影响条件下,研究磁性刚体航天器在绕地球圆轨道运行时可能出现的混沌问题.根据动量矩定理建立动力学模型,应用Melnikov方法证明了动力系统在一定条件下会发生混沌行为,并且给出了解析判据.最后利用数值仿真分析了系统的动力学行为,理论结果与数值仿真结果相一致.     

基于欧拉角的分导飞行器多模型自适应姿态控制

基于欧拉角的变换得到了刚体飞行器的一种多模型自适应控制律,它能解决转动惯量不确定并随时发生突变的分导飞行器的姿态控制问题.该控制策略可以有效地检测出转动惯量发生突变,并及时切换到最合适的控制器.通过理论分析证明了该控制策略的闭环全局渐近稳定.数值仿真表明该方案的有效性.     

带弹性附件充液矩形贮箱俯仰运动动态响应

首先建立了俯仰运动矩形贮箱刚-液-弹耦合系统在外力矩作用下的耦合动力学模型,给出满足边界条件的速度势函数和液面波高的级数表达式,采用伽辽金法离散,将动力学模型转化为常微分方程组,得到刚-液-弹耦合系统的固有频率,给出简单的近似表达式,分析了转动中心距静液面不同位置时刚-液-弹耦合系统各阶固有频率的变化规律,系统转动中心距静液面较近时,耦合后液体反对称模态和刚体的固有频率对比耦合前减小,较远时则增大,最后进行数值验证,比较分析了液体和弹性体对刚体姿态的影响．     

基于人机耦合的下肢外骨骼动力学分析及仿真

建立了一种包含人机交互力的人体-外骨骼模型，对人体和外骨骼分别采用7连杆的刚体模型进行建模，建立其D-H坐标系，得到人机模型在运动过程中的变化矢量.采用Newton-Euler方程建立动力学方程式，将人机之间的交互力简化为弹力，根据运动中人体和外骨骼质心之间的距离变化得到其相对位移，从而求得运动过程中交互力的大小.最终在ADAMS(automatic dynamic analysis of mechanical system)仿真软件中对动力学模型进行仿真，并将动力学方程得到的关节力矩代入到仿真中，验证了该人体-外骨骼模型的正确性.     

多刚体系统的外碰撞动力学方程

本文讨论了两个多刚体系统之间相互碰撞的动力学问题,给出了碰撞冲量和广义速度增量已经解耦的,且适合于计算机程式求解的外碰撞动力学模型,该模型具有实用价值。     

多体气动弹性系统超声速颤振分析

对一类多体气动弹性系统超声速颤振问题进行研究.分别采用多体动力学理论、活塞理论建立了弹性结构系统的动力学模型与超声速非定常气动力模型,得到了由微分代数方程表示的多体系统气动弹性动力学方程.通过数值求解微分代数方程的特征值问题,研究了多体系统在平衡位置小扰动运动的稳定性,完成了多体气动弹性系统超声速颤振分析.应用该方法研究了板状翼面及含操纵面翼面的超声速颤振问题,并得到了操纵面处于不同位置时翼面的颤振速度.结果表明,所发展的多体气动弹性系统超声速颤振分析方法,适用于由多个部件组成的工程结构颤振分析.     

细长杆的Cosserat动力学模型和变分原理

利用Cosserat理论建立了细长杆的三维非线性动力学模型,借助伪刚体法和变分原理得到了Cosserat杆的包括各种形变的三维空间运动方程.     

自由下落猫的非完整运动规划最优控制研究

研究猫在自由下落时姿态运动规划问题．自由落体的猫在空中转体运动由于角速度不可积,姿态运动方程呈现为非完整形式．当系统角动量为0时,导出由两个对称刚体组成的自由下落猫的非完整姿态运动方程．利用该非完整方程系统的控制问题可转化为无漂移系统的非完整运动规划问题．基于Ritz近似理论,给出自由落体猫姿态运动规划的Gauss-Newton算法．最后对自由落体猫作了数值仿真实验,仿真结果验证了该算法的有效性．     

水轮发电机定子系统磁固耦合双重共振

以双壳系统模型为水轮发电机定子系统的物理模型,建立了三相对称稳态运行状态下定子系统的磁固耦合振动方程.分析了定子系统磁固耦合的双重共振,指出其响应具有跳跃现象,在某些参数域上有多解共存现象.     

Modeling via the internal energy balance and analysis of adhesive contact with friction in thermoviscoelasticity

In this paper we introduce and investigate a model for adhesive contact with friction between a thermoviscoelastic body and a rigid support.A PDE system, consisting of the evolution equations for the temperatures in the bulk domain and on the contact surface, of the momentum balance, and of the equation for the internal variable describing the state of the adhesion, is derived on the basis of a surface damage theory by M. Frémond.The existence of global-in-time solutions to the associated initial–boundary value problem is proved by passing to the limit in a carefully tailored time-discretization scheme.     

On computer implementation of the Hertz elastic contact model and its simplifications

The paper is concerned with an elastic contact model of rigid bodies which is developed in the framework of the Hertz model. For this new model, we suggest more effective algorithms with reduced computational time. We also present an algorithm for representation of the geometry of the contacting surfaces in the local contact coordinate system. This coordinate system tracks permanently the surfaces of the bodies, which are able to contact. An approach to computation of the normal elastic force is presented. It is based on the reduction to a single transcendental scalar equation that includes the complete elliptic integrals of the first and second kinds. The computational time in the Hertz-model simulation was considerably reduced due to the use of the differential technique for computation of the complete elliptic integrals and due to the replacement of the implicit transcendental equation by a differential one. Using the classic solution of the Hertz contact problem, we then present an invariant form for the force function, which depends on the geometric properties of the intersection of the undeformed volumes occupied with the rigid bodies (so-called volumetric model). The reduced expression for the force function obtained is shown to be different from that accepted in the classic contact theory hypotheses. Our expression has been tested in several examples dealing with bodies that contact elastically including Hertz’s classical model. In the context of the Hertz contact problem, an approximate model for computation the resulting wrench of the dry friction tangent forces is set up. The wrench consists of the total friction force and the drilling friction torque. The approach under consideration naturally extends the contact model constructed earlier. The dry friction forces and torque are integrated over the contact elliptic spot. Generally an analytic computation of the integrals mentioned is bulk and cumbersome leading to decades of terms that include rational functions depending on complete elliptic integrals. To be able to implement a fast computer model of elastically contacting bodies, one should first set up an approximate model in the way initially proposed by Contensou. To verify the model developed, we have used results obtained by several authors. First we test our method on the Tippe-Top dynamic model. Simulations show that the top’s evolution can be verified with a high quality compared with the use of the theory of set-valued functions. In addition, the ball bearing dynamic model has been also used for a detailed verification of different approaches to the computation of tangent forces. Then the friction model of the regularized Coulomb type and the approximate Contensou one, each embedded into the whole bearing dynamic model, were thoroughly tested and compared. It turned out that the simplified Contensou approach provides a computer model that runs even faster compared with the case of the point contact. In addition, the volumetric model demonstrated a reliable behavior and an acceptable accuracy.     

Three-species food web model with impulsive control strategy and chaos

A three-species ecological model with impulsive control strategy is developed using the theory and methods of ecology and ordinary differential equation. Conditions for extinction of the system are given based on the theory of impulsive equation and small amplitude perturbation. Using comparison involving multiple Lyapunov functions, the system is shown to be permanent. Further, the influence of the impulsive perturbation on the inherent oscillation are studied numerically and is found to depict rich dynamics, such as the period-doubling bifurcation, the period-halving bifurcation, a chaotic band, a narrow or wide periodic window, and chaotic crises. In addition, the largest Lyapunov exponent is computed. This computation demonstrates the chaotic dynamic behavior of the model. The qualitative nature of concerned strange attractors is also investigated through their computed Fourier spectra. The foregoing results have the potential to be useful for the study of the dynamic complexity of ecosystems.     

Transfer matrix method for the free and forced vibration analyses of multi-step Timoshenko beams coupled with rigid bodies on springs

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.     

基于云模型的定性运算理论与方法

将定性值像定量值一样参与运算和推导,是定性理论走向真正实际应用必须解决的极为关键的研究问题.相关研究提出的方法在此方面均有一定的局限性.本文提出了一种基于云模型的定性运算理论与方法.首先在云模型基本运算的基础上提出了基于云模型的定性关系演算方法,其次提出了基于云模型的一元一次定性方程的求解方法.理论和方法能比较科学合理地计算出定性值,且具有定性与定量相互融合的特点.为定性演算和推导在系统分析和仿真等领域中进一步应用提供了重要的借鉴方法.     

Cyclotomic p-adic multi-zeta values in depth two

In this paper we compute the values of the p-adic multiple polylogarithms of depth two at roots of unity. Our method is to solve the fundamental differential equation satisfied by the crystalline frobenius morphism using rigid analytic methods. The main result could be thought of as a computation in the p-adic theory of higher cyclotomy. We expect the result to be useful in proving non-vanishing results since it gives quite explicit formulas.     

Nonlinear dynamics of a simplified engine-propeller system

This paper presents a procedure for studying dynamical behaviors of a simplified engine-propeller dynamical system consisting of a number of bodies of plane motions. The equation of motion of the complex system is obtained using the Lagrange equation and solved numerically using the 4th order Runge–Kutta method. Various simulations were performed to investigate the transient and steady state behaviors of the multiple body system while taking into consideration the engine pressure pulsations, nonlinear inertia of moving bodies, and nonlinear aerodynamic load. Sub-harmonics and super harmonics in the steady state responses for different power and propeller pitch settings are obtained using the fast Fourier transform. Numerical simulations indicate that the 1.5 order is the dominant order of harmonics in the steady state oscillatory motion of the crankshaft. The findings and procedure presented in the paper are useful to the aerospace industry in certifying reciprocating engines and propellers. The crankshaft oscillatory velocities obtained from the simplified rigid body model are in good agreement with the experimental data for a SAITO-450 engine and a SOLO propeller at a 6″ pitch setting.