无约束平面框架结构冲击响应分析(Ⅰ)——公式推导

运用广义Fourier级数方法推导了无约束平面框架结构受运动刚体冲击时的瞬态动力响应公式,利用这些公式得到冲击系统动力响应解析解．在公式推导过程中得出结构系统中弹性响应的动量之和为零的结论．从公式推导可以看出,模态分析法同样可以用来解决此类冲击问题．     

柔性头颅模型撞击弹性板的动态响应分析

将柔性接触撞击过程处理为一个振动系统响应,采用机械网络图和求机械阻抗的方法解决了这一动态响应问题。柔性接触撞击模型考虑了头部的实际结构,把头部简化成撞击部位的头皮和头骨的质量、头部其它部分的头骨和脑液的质量、头部的刚度、头皮和脑液的阻尼系数组成的振动模型,弹性板也同样简化成由质量、刚度和阻尼构成的振动模型。采用求激振点速度阻抗的方法,得到了系统的动态撞击力、头部所受到的撞击加速度值,以及板的弹性变形、系统的固有频率等动态响应。实验数据与计算数据符合较好,证明方法是计算撞击作用下系统动态响应的实用方法,从而为头部撞击保护设计提供参考。     

二维八次对称准晶的断裂动力学问题

基于准晶弹性流体动力学模型,采用有限差分法研究了含Griffith裂纹八次对称准晶在不同冲击载荷下的动态响应,得到了应力、位移和应力强度因子的数值结果,讨论了不同冲击载荷对动力学行为的影响.     

带刚性限位的双层隔振系统的离散随机模型

研究由多刚体组成的带刚性限位的双层隔振系统,对其冲击后受到周期性外激励和低强度噪声扰动共同作用下可能会产生的碰撞进行了分析．基于单向约束多体动力学理论,导出了此隔振系统的最大Poincaré映射,建立了其冲击后的零次近似随机离散模型和一次近似随机离散模型．通过对一MTU公司的柴油机隔振系统冲击作用后振动响应的调查指出,由于可能发生间歇性碰撞,该系统呈现复杂的非线性特性．零次近似模型和一次近似模型有较大的区别,低强度的噪声也会对系统产生较大的影响．得到的结果对如何正确设计带刚性限位的双层隔振系统提供了理论参考依据．     

旋翼/机身非线性气弹耦合配平及稳定性分析

根据Hamilton原理,采用中等变形梁理论,将桨叶离散为15自由度梁单元,用准定常气动模型建立旋翼/刚性机身耦合的有限元非线性方程,用时间有限元法进行气弹耦合配平计算,得到桨叶和机身运动的周期解．在此基础上,引入Peters动态入流模型分析耦合系统的稳定性．并研制相应的计算程序,可用于桨叶响应、桨叶和桨毂载荷、旋翼操纵等方面的分析计算．算例分析结果与相关文献吻合较好,且同时满足桨叶响应和配平方程的收敛性要求．     

弹性板受撞击的动力响应分析

文献[1]分析了弹性板受撞击的动力响应,应用该方法的条件是撞击物可视为刚体且接触局部变形与撞击力的关系已知。木文提出了碰撞过程中碰撞反力的模拟表达式,对撞击物不作任何假设,避开接触局部变形问题,只考虑碰撞过程中板的动力响应,利用冲量、动量关系和动力微分方程及数值方法求解,因此适用范围更广。文中给出了算例,与已有正确解答符合得很好。     

窄带随机噪声激励下线性碰撞系统的响应

研究了单自由度线性单边碰撞系统在窄带随机噪声激励下的次共振响应问题．用Zhuravlev变换将碰撞系统转化为连续的非碰撞系统,然后用随机平均法得到了关于慢变量的随机微分方程．在约束距离为0时,用矩方法给出了系统响应幅值二阶矩的解析表达式．在约束距离不为0时,近似地得到了系统响应幅值二阶矩的解析表达式．讨论了系统阻尼项、窄带随机噪声的带宽和中心频率以及碰撞恢复系数等参数对于系统响应的影响．理论计算和数值模拟表明,系统响应幅值将在激励频率接近于次共振频率时达到最大,而当激励频率逐渐偏离次共振频率时,系统响应迅速衰减．数值模拟表明提出的方法是有效的．     

计及需求响应不确定性的综合能源系统多目标优化调度管理

需求响应作为电力系统的重要调节手段,可显著提升系统灵活性和经济性。利用价格弹性构建了包含价格与激励措施的需求响应模型,并在此基础上考虑需求响应的不确定性,以综合能源系统经济性和环保性为优化目标,构建了综合能源系统多目标优化调度模型。利用E约束法将多目标优化模型转化为单目标优化模型,得到Pareto最优解集,运用模糊决策法从中选取最优方案。基于实际案例进行测算,结果表明价格型与激励型需求响应手段的结合能够实现削峰填谷,有效降低系统的运行成本和碳排放量。     

弹性振动的闭环系统

细长体的飞行器在飞行中考虑了既有刚性运动又有弹性振动的运动,由于刚性运动对弹性振动的影响,通过安装在飞行器上面的仪表所测得的角速度作为反馈信号输入到控制器,由控制器输出端输出信号到执行机构来实现反馈控制,把刚性运动飞行器、弹性振动飞行器同时考虑作受控对象,这里我们研究了由刚性飞行器、弹性飞行器和控制器三者形成的闭环系统的弹性振动问题,得到了求闭环系统的频率和振型的公式,设计控制器使得闭环系统渐近稳定的条件和能控性、能观测性的条件。     

轴向运动三参数黏弹性梁弱受迫振动的渐近分析

研究了轴向运动三参数黏弹性梁的弱受迫振动．建立了轴向运动三参数黏弹性梁受迫振动的控制方程．使用多尺度法渐近分析了运动梁的稳态响应,导出了解稳定性边界方程、稳态振幅的表达式以及稳态响应非零解的存在条件．依据Routh-Hurwitz定律决定了非线性稳态响应非零解的稳定性．     

Impact indentation of a rigid body into an elastic layer. Axisymmetric problem

An axisymmetric contact-impact problem is considered for an elastic layer subjected to normal indentation of a rigid body. An exact analytical solution is obtained in the case of a blunt shape of the indenter having a given velocity, and the stress pattern under multiple reflections is analyzed depending on the layer thickness. A numerical solution of the problem with arbitrary indenter shape is obtained on the basis of the simplified model of the theory of elasticity having a single displacement coincident with the impact direction. The explicit finite difference algorithm is designed on the basis of the mesh dispersion minimization technique. A parametric analysis is presented of the stress pattern developed with time with respect to variations of irregular shapes of the indenter and its masses.     

刚柔耦合系统动力学建模及分析

准确预测经历大范围刚体运动和弹性变形的柔性体的行为,是当前柔性多体系统动力学领域关注的主要课题.基于线性理论的传统方法由于无法计及动力刚化效应,导致在许多实际应用中得到错误的结果.本文从离心力势场的概念出发,应用Hamilton原理建立了具有动力刚化效应的刚柔耦合系统的运动方程,证明了该方程解的周期性,并采用了Frobenius方法给出了其精确解的一般形式.通过算例分析了刚体运动对弹性运动的模态和频率的影响.     

Bi-nonlinear vibration model of tubing string in oil & gas well and its experimental verification

Fluid-induced vibration (FIV) prediction is an important prerequisite work in wear and fatigue analysis of tubing string in oil & gas well. The finite element method, energy method and Hamiltonian principle are comprehensively used to establish a single nonlinear vibration model of pipe conveying fluid, taking into account the longitudinal/lateral coupled vibration. Based on the contact/impact theory of elastic/plastic body, the nonlinear contact-impact model of tubing-casing is established and introduced into the single nonlinear vibration model to form a bi-nonlinear vibration model of tubing string in oil & gas well. The bi-nonlinear model is numerically discretized by the finite element method, solved by Newmark− β method, and verified preliminarily by a classical contact/impact example in literature in which the influence of inflow is not taken into account temporarily. A similar experiment of tubing vibration is designed and completed to further test the validity of the bi-nonlinear vibration model by comparing the frequency-domain and time-domain responses of the experiment with those from the model. The analysis shows that the bi-nonlinear model has good calculation accuracy and the vibration response law is basically consistent with the experimental results, which can provide an effective theoretical analysis tool for FIV behavior of tubing string in oil & gas well.     

Waves induced by the longitudinal impact of a rod against a stepped rod in contact with a rigid barrier

The longitudinal elastic central impact of a rod system, consisting of a uniform rod having a pre-impact velocity against a stepped rod which is in a state of rest and interacts by means of unilateral constraints with a rigid barrier, is modelled.     

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.     

General relations for waves in one-dimensional elastic systems

Common features inherent in waves propagating in one-dimensional elastic systems are pointed out. Local laws of energy and wave momentum transfer when the Lagrangian of an elastic system depends on the generalized coordinates and their derivatives up to the second order inclusive are presented. It is shown that in a reference system moving with the phase velocity, the ratio of the energy flux density to the wave momentum flux density is equal to the phase velocity. It is established that for systems, the behaviour of which is described by linear equations or by nonlinear equations in the unknown function, the ratio of the mean values of the energy flux density to the wave momentum density is equal to the product of the phase and group velocities of the waves.