非线性粘弹性桩耦合运动中的混沌分析

研究轴向周期载荷作用下非线性粘弹性桩纵横向耦合运动中的混沌运动。桩体材料满足Leaderman非线性粘弹性本构关系和近似的非线性几何关系，考虑桩体发生纵横向运动的耦合，得到的方程为耦合的非线性偏微分一积分方程；利用Galerkin方法将方程简化并进行数值计算，揭示非线性粘弹性桩的混沌运动和分岔等动力学行为。     

作大范围运动矩形薄板的建模理论和有限元离散方法

研究了作大范围运动薄板的耦合动力学建模理论和离散化方法。对作大范围运动的薄板建立了耦合动力学模型，计及了在结构动力学中对薄板动力学特性影响很小的二次耦合变形量。用有限元方法对秉性薄板进行离散，基于Jourdain速度变分原理导出了作大范围运动薄板的动力学方程。计算了作旋转运动的薄板的变形，将仿真结果与不计二次耦合变形量的传统方法进行比较表明，随着转速的提高，仿真结果出现明显的差异。此外，将本文有限元与假设模态法的计算结果进行比较，揭示了高速旋转时假设模态法的局限性，表明取无大范围运动的高阶模态可以提高假设模态法的计算精度。     

计及变形耦合项的平面柔性梁动力学建模及频率分析

考虑了变形产生的几何非线性效应对作大范围运动的平面柔性梁的影响，在其纵向、横向的变形位移中均考虑了变形的二次耦合变量，从非线性应变-变形位移的原理出发，说明增加耦合变量后。使得剪应变近似为零，由此得出的变形模式更符合工程实际和简化需要。考虑两个方向的变形耦合后，采用有限元离散，通过Lagrange方程导出系统的动力学方程。最后对一作旋转运动的平面柔性梁进行仿真计算，并对其固有频率进行分析研究。将本文模型所得的结论。与一次耦合动力学模型、零次近似模型进行比较，说明了三种模型的差异。得到了作旋转运动的平面柔性梁的一些新特点。     

基于双向流固耦合的机载导弹分离动力学研究

导弹与载机之间的安全与稳定分离过程对导弹飞行稳定性和载机安全具有非常重要作用。为了研究大长径比机载导弹弹射分离过程中与载机之间的相互干扰以及导弹在分离过程中相对于载机的运动轨迹,该文分别使用刚体六自由度（6DOF）方法和计算流体力学/计算结构动力学（CFD/CSD）双向流固耦合方法对典型空空导弹发射分离过程进行了数值模拟,刚体6DOF方法基于对流体力学控制方程与外弹道6DOF运动方程的耦合求解,而CFD/CSD双向流固耦合方法基于对流体力学控制方程与结构运动方程的耦合求解。两种方法得到了导弹分离时的整个气动流场及其变化特性,揭示了不同时刻导弹气动系数随时间的变化曲线和导弹弹道参数,比较与分析了两种计算结果的异同,并对导弹结构弹性变形对其分离运动的影响进行了讨论。     

轴向运动粘弹性夹层梁热力耦合振动频率分析

研究了温度场与位移场相互耦合时,轴向运动粘弹性夹层梁的横向振动特性。基于Euler-Bernouli梁理论和Kelvin粘弹性材料本构关系,建立了轴向运动粘弹性夹层梁横向振动控制方程;考虑材料变形与传热的相互影响,得到相应的热力耦合状态下轴向运动粘性夹层梁的耦合控制方程。采用Galerkin截断得到相应的热力耦合动力系统。用数值方法分析了相关热参数对梁振动频率的影响。     

柔性梁的刚-柔耦合动力学特性研究

该文研究在大范围运动是自由的情况下柔性梁的刚－柔耦合动力学特征，从连续介质力学理论出发，在纵向变形位移中计及了耦合变形量，用Jourdain速度变分原理导出了柔性梁的刚－柔耦合动力学方程，用频谱分析方法对带中心刚体的悬臂梁进行动力学分析表明，柔性梁的系统一阶固有频率低于把梁视作刚体的系统固有频率wr，频率的差异随着wr，增大而增加，在初始条件一定的情况下，系统的二阶固有频率随着wr增大而增高，揭示了大范围运动和变形运动的相互耦合的特征。     

大范围运动刚体-柔性梁刚柔耦合动力学分析

对自由大范围运动情况下刚体-柔性梁系统的刚柔耦合动力学特性进行了研究.考虑系统作平面大范围运动及柔性梁的纵向和横向变形,在纵向变形位移中计及横向弯曲引起的轴向缩短,即耦合变形项.采用假设模态法对柔性梁进行离散,运用拉格朗日方程推导出系统刚柔耦合动力学方程.分大范围运动为转动、平动,平面运动进行了动力学仿真,重点探讨了大范围平动下的刚体-柔性梁系统的刚柔耦合动力学特性.首先研究了系统在外界激励作用下的耦合动力学,其次分析了已知大范围平动对柔性梁小变形运动的影响.结果表明:零次近似模型不能反映大范围平动和柔性梁小变形运动之间的耦合作用;在不同的大范围平动加速度下,柔性梁中既可存在动力刚化效应,也可存在动力柔化效应.     

薄壁弹体压药强度的理论计算与试验研究

弹体的强度是弹丸在压药及发射过程中安全的重要保证，本文通过建立有限元模型分析计算了薄壁弹体压药过程中的应力场，同时采用应变片测量方法测取了薄壁弹体的压药时各点时的应力值，从而能较准确地较核弹体的压药过程中的结构强度和弹体变形。     

导弹耦合作用研究

本文提出了轴对称导弹弹体在复杂条件作用下的动力学模型的建立方法,并对导弹弹体的振动特性及柔性变形对弹道的影响进行了研究。首先,依据传统的导弹飞行力学理论,分别建立了控制力、气动力耦合作用下的刚性导弹和柔性导弹弹体动力学模型;然后,在铁木辛柯梁弯曲理论的基础上,推导出控制力、气动力和弹性振动耦合作用下的柔性弹体变形方程;最后根据上述模型,分析了柔性变形对弹道参数的影响.     

作大范围运动的空间桁架结构动力分析

作高速大范围运动的弹性体，由于运动和变形的耦合将产生动力刚化现象，传统的动力学理论难以计及这种影响。本文在有限元方法中首次引入了单元耦合形函数（阵），以此将单元弹性位移表示为单元结点位移的二阶小量形式。利用几何非线性的应变－位移关系式，在小变形假设条件下确定了单元耦合形函数。在此基础上，根据Ｋａｎｅ方程，运用模态坐标压缩，并通过适当的线性化处理，得到了一致线性化的动力学方程。编制了计及动力刚化的空间桁架结构有限元分析程序。仿真算例的计算结果验证了理论和算法的正确性     

Impact stability of a bar

The paper discusses the stability of an ideally straight elastic bar, which is subjected to a longitudinal and central impact by a rigid body. In such conditions the longitudinal-flexural vibrations signal the instability of the bar. Differential equations of the coupled vibrations of the bar during the impact have been developed and the corresponding initial-boundary problem has been formulated. That is the problem of eigen-values, defining the critical parameters of the impact.It has been found that besides the velocity of the impact, the slenderness of the bar and the mass ratio, the critical parameters depend also on the geometrical features of the impacting body and on the cross-section of the bar.     

Vibration analysis of two orthogonal slender single-walled carbon nanotubes with a new insight into continuum-based modeling of van der Waals forces

Transverse vibrations of doubly orthogonal slender single-walled carbon nanotubes (SWCNTs) at the vicinity of each other are of interest. The van der Waals (vdW) forces play an important role in dynamic interactions between two adjacent nanotubes. Using Lennard-Jones potential function, such a phenomenon is appropriately modeled by a newly introduced vdW force density function. By employing Hamilton’s principle, the equations of motion are obtained based on the nonlocal Rayleigh beam theory. In fact, these are integro-partial differential equations and seeking an exact or even analytical solution to them is a very difficult job. Therefore, an efficient numerical solution is proposed. The effects of the intertube distance, slenderness ratio, small-scale parameter, aspect ratio, and elastic properties of the surrounding medium on the free vibration of the nanosystem are addressed. The obtained results could be regarded as a pivotal step for better realizing of dynamic behaviors of more complex systems consist of multiple orthogonal networks of nanotubes.     

基础竖向多频参数激励下圆弧拱平面内动力失稳研究

地震波、冲击波、环境振动激励会通过地基基础传递到拱上,致使拱发生动力失稳失去承载能力。为深入研究拱在基础竖向激励下的动力稳定性,该文基于能量法,建立了基础竖向激励下圆弧拱平面内动力稳定能量方程,利用哈密顿原理得到了拱面内径向和切向振动的耦合控制方程,求解了圆弧拱平面内失稳前的动轴力与动弯矩解析解。引入拱轴线不可压缩假设,解决了圆弧拱平面内动力控制方程的解耦问题。利用伽辽金法建立了基础竖向多频激励下圆弧拱平面内二阶常微分动力稳定方程,运用多尺度法推导了基础竖向多频激励下圆弧拱平面内动力失稳的临界激励频率解析公式,得到了圆弧拱同时发生一阶反对称参数共振和二阶正对称共振失稳的动力不稳定域,并利用有限元数值分析验证了理论解析解的正确性。进一步分析了拱矢跨比、长细比和圆心角对动力不稳定域的影响。     

饱和土中大直径嵌岩桩纵向振动特性研究

根据B iot饱和土理论和R ay le igh-Love杆理论,计及土层及桩的径向运动影响,导出了考虑横向惯性效应的端承桩与饱和土的纵向耦合振动频域的解析解和时域半解析解,对比了考虑与不考虑横向惯性效应时,大直径嵌岩桩纵向振动引起的土层复阻抗的异同以及桩顶导纳和时域反射的特征。研究表明:长径比越小,横向惯性效应越明显,而泊松比和激振频率对饱和土层阻抗及桩顶响应也有重要影响。通过工程实例对比表明,当桩的长径比较小时,用考虑横向惯性效应的计算方法可以得到更好的拟合效果。     

Dynamic behaviour of edge-cracked shear deformable functionally graded beams on an elastic foundation under a moving load

This paper studies the dynamic response of functionally graded beams with an open edge crack resting on an elastic foundation subjected to a transverse load moving at a constant speed. It is assumed that the material properties follow an exponential variation through the thickness direction. Theoretical formulations are based on Timoshenko beam theory to account for the transverse shear deformation. The cracked beam is modeled as an assembly of two sub-beams connected through a linear rotational spring. The governing equations of motion are derived by using Hamilton’s principle and transformed into a set of dynamic equations through Galerkin’s procedure. The natural frequencies and dynamic response with different end supports are obtained. Numerical results are presented to investigate the influences of crack location, crack depth, material property gradient, slenderness ratio, foundation stiffness parameters, velocity of the moving load and boundary conditions on both free vibration and dynamic response of cracked functionally graded beams.     

Dynamic analysis of an inclined Timoshenko beam traveled by successive moving masses/forces with inclusion of geometric nonlinearities

In the first part of this paper, the nonlinear coupled governing partial differential equations of vibrations by including the bending rotation of cross section, longitudinal and transverse displacements of an inclined pinned?Cpinned Timoshenko beam made of linear, homogenous and isotropic material with a constant cross section and finite length subjected to a traveling mass/force with constant velocity are derived. To do this, the energy method (Hamilton??s principle) based on the large deflection theory in conjuncture with the von-Karman strain-displacement relations is used. These equations are solved using the Galerkin??s approach via numerical integration methods to obtain dynamic responses of the beam under act of a moving mass/force. In the second part, the nonlinear coupled vibrations of the beam traveled by an arbitrary number of successive moving masses/forces are investigated. To do a thorough study on the subject at hand, a parametric sensitivity analysis by taking into account the effects of the magnitude of the traveling mass or equivalent concentrated force, the velocity of the traveling mass/force, beam??s inclination angle, length of the beam, height of the beam and spacing between successive moving masses/forces are carried out. Furthermore, the dynamic magnification factor and normalized time histories of the mid-point of the beam are obtained for various load velocity ratios, and the results are illustrated and compared to the results obtained from traditional linear solution. The influence of the large deflections caused by a stretching effect due to the beam??s immovable end supports is captured. It is seen that the existence of quadratic?Ccubic nonlinear terms in the coupled governing PDEs of motion renders stiffening (hardening) behavior of the dynamic responses of the beam under the action of a moving mass/force.     

平流层飞艇气动阻力的参数分析

为了研究环境参数及外形布局对平流层飞艇气动阻力的影响,在验证CFD数值模拟方法的基础上,从气动阻力包括压差阻力与摩擦阻力的角度探讨了风速、动力粘度系数、空气密度、Re数、长细比及尾翼对飞艇气动阻力的影响规律及机理。结果表明:气动阻力系数随风速与空气密度的增加而减小,随动力粘度系数的增加而增加;气动阻力系数随Re数减小的趋势,取决于摩擦阻力系数随Re数的减小趋势;随长细比的增加,摩擦阻力系数呈现增加趋势,但气动阻力系数呈现先减小后增加的趋势;尾翼对气动阻力系数的影响主要体现在压差阻力系数的改变。     

Energy expressions and free vibration analysis of a rotating double tapered Timoshenko beam featuring bending–torsion coupling

In this study, free vibration analysis of a rotating, double tapered Timoshenko beam featuring coupling between flapwise bending and torsional vibrations is performed. At the beginning of the study, kinetic and potential energy expressions of a rotating Timoshenko beam having single cross-sectional symmetry are derived in a detailed way by using several explanatory tables and figures. In the following section, Hamilton’s principle is applied to the derived energy expressions to obtain the governing differential equations of motion. The parameters for the hub radius, rotational speed, rotary inertia, shear deformation, slenderness ratio, bending–torsion coupling and taper ratio are incorporated into the equations of motion. In the solution part, an efficient mathematical technique, called the differential transform method (DTM), is used to solve the governing differential equations of motion. Using the computer package, Mathematica, the mode shapes are plotted, the effects of the incorporated parameters on the natural frequencies are investigated. The calculated results are tabulated in several tables and plotted in several graphics.     

波浪场中水中悬浮隧道动力响应的研究

针对水中悬浮隧道在波浪力作用下动力响应的问题,通过Hamilton原理推导得到了悬浮隧道管段和锚索的运动控制方程,同时考虑了锚索横向和轴向变形之间的耦合作用,建立了悬浮隧道的动力响应模型,在时间域内采用逐步积分法迭代求解其运动控制方程。波浪力采用Airy线性波理论和Morison方程计算。计算结果表明:当锚索长细比较大时,锚索的自振模态会被激发,其横向和轴向变形之间的耦合作用不可忽略。随着入射波高或悬浮隧道重浮比的增加,悬浮隧道的横荡位移以及横摇角增大,但结构的垂荡位移以及锚索中的应力受波浪的影响较小。     

Optimal tracking control of flow velocity in a one-dimensional magnetohydrodynamic flow

This article considers a dynamic optimization problem arising in a one-dimensional magnetohydrodynamic flow, which can be modelled by coupled partial differential equations, where the external control input (external induction of magnetic field) takes a multiplicative effect on the system states (momentum and magnetic components). The aim is to drive the flow velocity to within close proximity of a desired target of flow velocity at the pre-indicated terminal time. First, the Galerkin method is utilized to reduce the original dynamic optimization problem to a lower finite-dimensional dynamic optimization problem governed by a set of ordinary differential equations. Then the control parameterization method is employed to parameterize the finite-dimensional optimization problem and thus obtain an approximate optimal parameter selection problem, which can be solved using gradient-based optimization techniques, such as sequential quadratic programming. The exact gradients of the cost functional with respect to the decision parameters, which are the key advantages of this approach, are computed using the analytical equations. Finally, numerical examples are illustrated to verify the effectiveness of the proposed method. The novel scheme of this article is to develop an effective computational optimal control method for realizing the optimal tracking control of flow velocity in a one-dimensional magnetohydrodynamic flow.