热弹耦合运动斜板振动特性研究

分析无量纲运动速度、边长比、斜角,无量纲热弹耦合因子等参数对热弹耦合运动斜薄板振动特性的影响。以运动热弹耦合运动斜薄板为研究对象,基于弹性薄板小挠度弯曲理论,建立运动微分方程,采用微分求积法进行离散建立热弹耦合运动斜板的特征方程。得到了热弹耦合运动斜板前3阶模态的无量纲复频率与运动速度之间的关系曲线。结果表明,相同条件下,第1阶模态发散失稳的临界速度随着斜板角度的增加而减小,第1阶模态的发散失稳临界速度随着无量纲热弹耦合因子的增大而增大。     

轴向运动热弹耦合楔形梁的振动特性

以工程中的基本构件楔形梁作为研究对象,分析梁在温度场和弹性场耦合条件下的振动特性。采用D'Alembert原理建立两端固支热弹耦合运动梁的运动微分方程,依据微分求积法得到其特征方程,并对两端固支耦合热弹运动梁的复频率进行了数值计算。得到不同的梁高比下,两端固支轴向运动热弹耦合梁的复频率和速度与频率的变化关系。楔形梁的第一阶模态发散失稳的临界速度随着梁高比的减小而减小,单一模态颤振的临界速度也呈现同样的变化趋势。     

摩擦离合器摩擦片的热弹耦合振动分析

基于弹性薄板小挠度理论和考虑变形影响的热传导方程,建立了摩擦离合器摩擦片的热弹耦合圆环板模型和相应的运动微分方程,采用微分求积法离散运动微分方程和边界条件,得到了离合器摩擦片在横向温度变化影响下前3阶无量纲固有频率与无量纲角速度和热弹耦合系数之间的关系曲线。研究(计算)结果表明,摩擦片的前3阶无量纲固有频率随着无量纲角速度和无量纲热弹耦合系数的增大而增大,不同的边界条件对摩擦片横向振动固有频率的增大幅度有一定的影响。该结论为摩擦离合器的设计与性能分析提供了一定的理论基础。     

斜支承导向的TPU薄膜振动特性研究

TPU薄膜在生产过程中有斜支承导向辊对薄膜起导向传输和支承作用,此外还需要有加热烘干系统进行即时干燥,这些过程都不可避免的引起TPU薄膜的横向振动,从而影响薄膜的制备精度和质量。根据D’Alembert原理,建立具有运动速度的TPU薄膜的动力学模型及热传导方程,解耦后得到含有热弹耦合系数的运动TPU薄膜振动方程;考虑薄膜导向辊斜支承作用,建立无量纲化的斜支承下TPU薄膜的振动方程;采用微分求积法对耦合方程进行离散,研究运动TPU薄膜复频率变化对无量纲速度、斜支承角度、热弹耦合系数、张力比的影响,定量分析各参数对运动TPU薄膜振动稳定性的影响,从而提高汽车TPU薄膜的涂布精度和制备质量。     

变密度印刷纸带的非线性自由振动特性分析

关于变密度纸带振动的研究多数局限于小挠度线性问题的讨论,对于变密度印刷纸带大挠度非线性振动问题的研究很少。然而,在实际中,由于印刷图文的分布不同纸带的密度是变化的。研究变密度运动印刷纸带的非线性振动特性。基于von Karman薄板理论推导出轴向运动纸带大挠度振动方程,应用Bubnov-Galerkin方法对振动偏微分方程组进行离散,利用椭圆积分法对微分方程进行求解,得出纸带非线性振动的频率表达式。分析了不同初始条件下,密度系数,无量纲运动速度和长宽比对运动纸带大挠度振动复频率的影响。该研究为提高印刷设备的工作稳定性提供理论依据。     

轴向运动功能梯度梁的横向振动

新型非均匀复合材料,功能梯度材料具有防止脱层和减缓热应力等优良性能,将其应用于功能梯度梁的结构有着非常重要的工程应用价值。基于Euler-Bernoulli梁理论和Hamilton原理,建立轴向运动功能梯度梁横向自由振动的运动微分方程,其中假设功能梯度梁的材料特性沿梁厚度方向按各组分材料体积分数的幂函数连续变化;再对运动微分方程和边界条件进行量纲一处理,采用微分求积法对其进行离散化,导出系统的广义复特征方程,然后计算分析轴向运动功能梯度简支梁横向振动复频率的实部和虚部随量纲一轴向运动速度、梯度指标等参数的变化情况,并讨论量纲一轴向运动速度和梯度指标对功能梯度梁的横向振动特性以及失稳形式的影响。     

轴向运动黏弹性梁受力参激振动稳定性的多尺度分析

研究了轴向匀速运动黏弹性梁的运动稳定性。考察轴向拉力在初始拉力的基础上做微小简谐变化的参激振动。建立了受轴向拉力参数激励时轴向运动梁的控制微分方程,黏弹性本构关系引入了物质时间导数。轴向运动梁两端的边界受由带有扭转弹簧的套筒铰支约束的混杂边界条件。应用多尺度法直接求解轴向运动梁参激振动的控制方程,并导出了当扰动拉力的频率接近未扰系统任意两个固有频率之和及任一固有频率2倍时所发生的组合共振和主共振的稳定边界方程。数值例子给出了黏弹阻尼对轴向运动黏弹性梁参激振动发生组合共振和主共振的影响,结果显示:不论组合共振还是主共振发生时,失稳区域均会随轴向运动黏弹性梁的黏弹阻尼增大而减小。     

Timoshenko模型轴向运动梁的横向振动特性分析

通过对梁微单元体的受力分析,导出Timoshenko模型的轴向运动梁横向振动的运动方程, 并利用复模态分析方法及半解析半数值方法, 研究两端铰支条件下轴向运动梁横向振动的振动模态及固有频率.文中还讨论运动梁前两阶固有频率随轴向运动速度变化的情况.最后利用数值算例对Timoshenko梁、Euler梁、Rayleigh梁及剪切梁的固有频率进行比较, 分析转动惯量及剪切变形的影响.     

振动磨机环扇形激振板的横向振动与稳定性分析

振动磨机的磨粉效果与激振系统动力学响应有较大关系,其激振系统的横向振动和稳定性研究具有重要的理论意义.根据弹性薄板小挠度理论和哈密顿原理,建立振动磨机环扇形激振板的运动微分方程.采用微分求积法离散方程和边界条件,计算得到环扇形板前三(四)阶无量纲复频率随无量纲角速度的变化情况,分析半径比和扇形角对环扇形板横向振动的影响.结果 显示在不同的旋转角速度情况下,环扇形板会发生发散失稳和颤振耦合失稳现象.该结论为振动磨机的设计与研究提供了一定的理论基础.     

点支承对受随从力梁稳定性的影响

利用在梁的不同位置增加一定刚度的点支承,来提高随从力作用下梁的稳定性.建立随从力作用下点弹性支承梁的运动微分方程,利用微分求积法得到复特征方程.通过求解复特征方程,得出点支承梁复频率与随从力的变化关系,以及支承刚度对梁失稳形式的影响.计算结果表明,支承位置靠近自由端时,随着支承刚度的增加,梁的失稳形式由颤振转化为屈曲;支承位置靠近固定端时,随着支承刚度的增加,梁的失稳形式保持颤振;当刚性支承距离固定端大约处,随从力失稳临界值最大,梁的稳定性最高.     

轴向运动带的横向与纵向非线性振动

研究轴向运动带的横向和纵向自由振动问题。利用Hamilton原理,建立轴向运动带横向和纵向自由振动的耦合动力学模型。基于Galerkin方法对轴向运动带系统模型的状态变量作离散,得到带有非线性项的常微分方程组。通过数值仿真,给出轴向运动带的横向振动与纵向振动比较,轴向运动速度对带的横向振动和纵向振动的影响,以及初张力对带的横向振动和纵向振动的影响。     

Natural frequencies,modes and critical speeds of axially moving Timoshenko beams with different boundary conditions

In this paper, natural frequencies, modes and critical speeds of axially moving beams on different supports are analyzed based on Timoshenko model. The governing differential equation of motion is derived from Newton's second law. The expressions for various boundary conditions are established based on the balance of forces. The complex mode approach is performed. The transverse vibration modes and the natural frequencies are investigated for the beams on different supports. The effects of some parameters, such as axially moving speed, the moment of inertia, and the shear deformation, are examined, respectively, as other parameters are fixed. Some numerical examples are presented to demonstrate the comparisons of natural frequencies for four beam models, namely, Timoshenko model, Rayleigh model, Shear model and Euler–Bernoulli model. Finally, the critical speeds for different boundary conditions are determined and numerically investigated.     

轴向运动简支-固支梁的横向振动和稳定性

研究一端简支一端固支轴向运动梁的横向振动和稳定性。提出在给定边界条件下确定一匀速运动梁固有频率和模态函数的方法。当轴向运动速度在其常平均值附近作简谐波动时,应用多尺度法给出轴向变速运动梁参数共振时的不稳定条件。用数值仿真说明相关参数对固有频率和不稳定边界的影响。     

轴向运动Timoshenko梁固有频率的求解方法研究

研究两端铰支边界条件下Timoshenko模型轴向运动梁的横向振动问题,分别利用复模态分析方法和Galerkin方法求解系统的固有频率;讨论轴向运动梁前两阶固有频率随轴向运动速度的变化情况;最后给出数值算例,分析复模态分析方法、二阶Galerkin截断和四阶Galerkin截断方法对固有频率结果精确度的影响.     

轴向运动矩形板的谐波共振与稳定性分析

针对轴向运动矩形薄板的非线性振动问题,在给出薄板运动的动能和应变能的基础上,应用哈密顿变分原理,推得几何非线性下轴向运动薄板的非线性振动方程。通过位移函数和应力函数的设定,并应用伽辽金积分法,得到四边简支边界约束条件下受横向激励载荷作用轴向运动薄板的达芬型振动方程。利用多尺度法对系统的非线性谐波共振问题进行求解,得到稳态运动下关于共振幅值的幅频响应方程。依据李雅普诺夫运动稳定性理论对定常解的稳定性进行分析,得到解的稳定性判别式。通过数值算例,得到不同横向载荷和轴向速度下共振幅值的变化规律曲线图以及对应的相图,讨论分岔点变化以及倍周期运动规律,分析横向激励载荷和轴向运动速度对系统非线性动力学行为的影响。     

Dynamic analysis of an axially moving beam subject to inner pressure using finite element method

A dynamic model of an axially moving flexible beam subject to an inner pressure is present. The coupling principle between a flexible beam and inner pressure is analyzed first, and the potential energy of the inner pressure due to the beam bending is derived using the principle of virtual work. A 1D hollow beam element contain inner pressure is established. The finite element method and Lagrange’s equation are used to derive the motion equations of the axially moving system. The dynamic responses are analyzed by Newmark-β time integration method. Based on the computed dynamic responses, the effects of inner pressure on beam dynamics are discussed. Some interesting phenomenon is observed.     

Dynamic Behaviors of Axially Moving Viscoelastic Plate with Varying Thicknessn

Structural components of varying thickness draw increasing attention these days due to economy and light-weight considerations. In view of the absence of research in vibration analysis of viscoelastic plate with varying thickness, this study devotes to investigate the dynamic behaviors of axially moving viscoelastic plate with varying thickness. Based on the thin plate theory and the two-dimensional viscoelastic differential constitutive relation, the differential equation of motion of the axially moving viscoelastic rectangular plate is derived, the plate constituted by Kelvin-Voigt model has linearly varying thickness in the y-direction. The dimensionless complex frequencies of axially moving viscoelastic plate with four edges simply supported are calculated by the differential quadrature method, curves of real parts and imaginary parts of the first three-order dimensionless complex frequencies versus dimensionless moving speed are obtained, the effects of the aspect ratio, thickness ratio, the dimensionless moving speed and delay time on the dynamic behaviors of the axially moving viscoelastic rectangular plate with varying thickness are analyzed. When other parameters keep constant, with the decrease of thickness ratio, the real parts of the first three-order natural frequencies decrease, and the critical divergence speeds of various modes decrease too, moreover, whether the delay time is large or small, the frequencies are all complex numbers.     

Output feedback boundary control of an axially moving system with input saturation constraint

This paper is concerned with boundary control for an axially moving belt system with high acceleration/deceleration subject to the input saturation constraint. The dynamics of belt system is expressed by a nonhomogeneous hyperbolic partial differential equation coupled with an ordinary differential equation. First, state feedback boundary control is designed for the case that the boundary states of the belt system can be measured. Subsequently, output feedback boundary control is developed when some of the system states can not be accurately obtained. The well-posedness and the uniformly bounded stability of the closed-loop system are achieved through rigorous mathematical analysis. In addition, high-gain observers are utilized to estimate those unmeasurable states, the auxiliary system is introduced to eliminate the constraint effects of the input saturation, and the disturbance observer is adopted to cope with unknown boundary disturbance. Finally, the control performance of the belt system is illustrated by carrying out numerical simulations.     

NONLINEAR DYNAMIC BEHAVIOR OF VISCOELATIC TPANSMISSION BELT

The nonlinear dynamic responses of viscoelastic axially transmssion belts are investigatedand the Kelvin viscoelastic differential constitutive model is employed to characterize the materialproperty of belts. The generalized equation of motion is obtained for a viscoelatic axially transmissionbelts with geometric nonlinearity first, and then is reduced to be a set of second-order nonlinear ordi-nary differential equations by applying Galerkin's method. Finally the effects of viscosity parameterand elastic parameter and the moving velocity of the belts on the transient responses are investigatedby the research of digital simulation.