Mathematical Model of Dynamics of Micropolar Orthotropic Elastic Thin Bars with Free Fields of Displacements and Rotations

In the present paper, initial-boundary value problem of plane stress state of micropolar theory of elasticity is considered for orthotropic material in the domain of thin rectangle. General hypotheses are formulated, which are the qualitative results of the asymptotic method of integration of the stated initial-boundary value problem. On the basis of the accepted hypotheses general applied one-dimensional models of dynamics of bending deformation of micropolar orthotropic elastic thin bars with free fields of displacements and rotations are constructed with and without consideration of shear deformations. With the help of the constructed models different dynamic problems of micropolar bars can be studied. Here concrete problems of free and forced vibrations of hinged supported micropolar orthotropic elastic thin bar are studied. Numerical analysis is done and specific features of dynamic characteristics of micropolar material are revealed. Particularly, it is shown that there is a frequency of vibrations of the micropolar bar that does not depend on bar sizes.

Wind-induced vibration control of bridges using liquid column damper

The potential application of tuned liquid column damper (TLCD) for suppressing wind-induced vibration of long span bridges is explored in this paper.By installing the TLCD in the bridge deck,a mathematical model for the bridge-TLCD system is established.The governing equations of the system are developed by considering all three displacement components of the deck in vertical,lateral,and torsional vibrations,in which the interactions between the bridge deck,the TLCD,the aeroelastic forces,and the aerodynamic forces are fully reflected.Both buffeting and flutter analyses are carried out.The buffeting analysis is performed through random vibration approach,and a critical flutter condition is identified from flutter analysis.A numerical example is presented to demonstrate the control effectiveness of the damper and it is shown that the TLCD can be an effective device for suppressing wind-induced vibration of long span bridges,either for reducing the buffeting response or increasing the critical flutter wind velocity of the bridge.

APPLICATION OF THE MODIFIED ITERATION METHOD TO NONLINEAR VIBRATION OF CORRUGATED CIRCULAR PLATES

In this paper, the modified iteration method is successfully extended to investigate the nonlinear free vibration of corrugated circular plates with full corrugations. The analytical relation for the amplitude-frequency response of corrugated circular plates is obtained and discussions on the influences of geometrical parameters on vibration behaviours of corrugated circular plates are made. The present results are practically important in the design of elastic elements in precision instruments.

DYNAMIC RESPONSE OF SHAPE MEMORY ALLOY SYSTEM AND ITS VIBRATION CONTROL

A hysteric model is represented to describe the dependence of restoring force on deformation of pseudoelastic SMA.The dynamic response of the system is investigated by means of mathematical models.The result shows that this kind of vibration absorbing system can suppress vibration with large amplitude effectively.Furthermore,the vibration absorbing system can work in optimum state by adjusting temperature and using piezoelectric sensors and actuators.

LARGE AMPLITUDE VIBRATION OF THIN ANNULAR PLATES

A pure analytic solution of the axisymmetric large amplitude free vibration of thin annualar plates is presented in this paper: By using the modified iteration method, we derive an analytic relation for the amplitudes vs. frequencies of vibrations. The present paper shows the great potentiality of this method to tackle the large amplitude vibration problems of plates.

NONLINEAR VIBRATION AND THERMAL-BUCKLING OF A HEATED ANNULAR PLATE WITH A RIGID MASS

On the basis of Hamilton's principle and dynamic version of von Karman's equations, the nonlinear vibration and thermal-buckling of a uniformly heated isotropic annular plate with a completely clamped outer edge and a fixed rigid mass along the inner edge are studied. By parametric perturbation and numerical differentiation, the nonlinear response of the plate-mass system and the critical temperature in the mid-plane at which the plate is in buckled state are obtained. Some meaningful characteristic curves and data tables are given.

位置扰动影响下的拖拉机底盘横向振动模型研究

为了探明行走速度、地面坡度和地面摩擦因数对拖拉机底盘横向稳定性的影响,建立了拖拉机动力学模型。考虑两种拖拉机失稳类型,即翻车和打滑引起的拖拉机底盘不稳定,为每种情况确定了稳定性指数。选取MITSUBISHI MT-2501D拖拉机进行试验与分析,结果表明:行走速度和地面坡度对所有稳定性指标都有显著的负相关影响(P<0.05),拖拉机的稳定性受拖拉机打滑的影响比翻车的影响更大。因此,为了提高该拖拉机底盘的整体稳定性,应该优先考虑提高由拖拉机打滑动力学得出的拖拉机稳定性指数。研究结果可为提高拖拉机田间运行稳定性提供新的研究思路及技术参考。

双轮支柱式起落架刹车振动分析与减振优化

以某型双轮支柱式起落架为研究对象,对飞机刹车诱导低频振动问题进行了研究,首先建立了完备的飞机着陆刹车滑跑整机六自由度数学模型,并在Simulnk中完成模型的搭建,用以分析了刹车控制律的部分参数对抖振的影响。其次,以轮轴中心航向加速度的RMS值作为振动量化指标,与结合系数效率一同设置为优化目标,基于NSGA-Ⅱ算法对液压刹车控制系统参数进行多目标优化设计,得到了优化变量的Parato最优前沿面和TOPSIS方法折衷最优解。最后,根据得到的优化设计方案对比分析优化前后的轮轴中心振动响应,并设置多组仿真工况检验了优化方案对不同着陆环境的适应性。结果显示优化后的起落架轮轴中心加速度Rms值最大降幅能达到14.53%,结合系数效率最大增幅为3.65%,表明所提出的起落架减振优化设计方法具有良好的实现性。

垂直井内上击器解卡过程中钻柱振动数学模型的建立与求解及动态解卡力分析

对于油气井内解卡过程中的钻柱振动情况及动态解卡力,目前还没有有效的分析方法。该研究建立了垂直井内上击器解卡过程中考虑钻井流体阻尼的钻柱振动数学模型,并进行了求解,分析了几个主要因素对动态解卡力的影响。首先,介绍了上击器解卡过程中钻柱振动的三个阶段:(1)拉伸储能阶段,对钻柱进行静力学分析;(2)泄压阶段,结合拉伸储能阶段的计算结果,通过特征函数展开法与拉普拉斯变换求解了泄压阶段的钻柱振动数学模型;(3)撞击阶段,引入了将钻柱-钻柱轴向撞击的强非线性问题转化为多段钻柱振动的线性问题的求解思路,通过紧差分方法对撞击阶段的钻柱振动数学模型进行求解,获得了钻柱中的弹性波传播规律以及动态解卡力。其次,建立了与三个阶段相应的数学模型并求解。然后,采用该模型计算了无阻尼情况下的荷载场与动态解卡力,经低通滤波处理后的计算结果与相应条件下的解析解以及ABAQUS软件所得结果均有较好的吻合,验证了该工况下解法的准确性。最后,分析了震击启动拉力、上击器位置、钻井流体黏度、以及芯轴有效距离对动态解卡力的影响。所得结论对使用震击解卡的作业过程具有一定的指导意义。

MATHEMATICAL ANALYSIS OF TRANSVERSE VIBRATION OF CONICAL SPIRAL TUBE BUNDLE WITH EXTERNAL FLUID FLOW

The conical spiral tube bundle is a new type of heat transfer elements used to enhance heat transfer through flow-induced vibration. The effect of the external fluid flow on the transverse vibration of the conical spiral tube bundle is investigated with a mathematical method proposed in this article. Firstly, the natural vibration of the tube bundle is obtained by the hammering excitation method and the mode shapes of the transverse vibration are discussed. Then the effect of the external fluid flow on the transverse vibration of tube bundle is analyzed by a combination of experimental data, empirical correlations and FEM. The results show that in the frequency range from 0 Hz to 50 Hz, there exist six transverse vibrations. The external fluid flow has a significant effect on the frequency of the tube＇s transverse vibration, which are decreased by about 18% to 24% when the external fluid flow speed is 0.3 m/s.

Comparison of rheological analytic model with numerical simulation in powder injection molding filling process

Mathematical model of filling disk-shaped mold cavity in steady state was studied.And the mathematical model under vibration field was developed from the model in steady state.According to the model of filling disk-shaped mold cavity in steady state,the filling time,the distribution of velocity field and the pressure field were obtained.The analysis results from rheological analytic model were compared with the numerical simulation results using Moldflow software in the powder injection molding filling process.Through the comparison,it is found that it is unreasonable to neglect the influence of temperature when calculated the pressure changing with the time at the cavity gate,while it can be neglected in other situations such as calculating the distribution of the velocity fields.This provides a theoretical reference for the establishment of correct model both in steady state and under vibration force field in the future.

Investigation into the effect of friction decay factor on the modelling and attenuation of stick-slip vibrations of oilwell drilling systems

The self-excited stick-slip oscillations of oilwell drillstrings are attributed to the nonlinear interaction between the drill-bit and the rock formation.Development of more accurate models will lead to improved predictions allowing more potential for successful suppression of the drillstring vibrations,thus reducing damage to the drilling system,prevention of expensive failures and increased output from the oilwell.In this paper,the effect of the transition from static friction to Coulomb friction on modelling of stick-slip phenomenon of oil well drill string is investigated through an analysis of the so called‘decay factor’.Based on a distributed-lumped parameter model(DLPM)of the drilling system,the governing equations of motion for the system are obtained.By using different values of decay factor(low,high and medium),the stick-slip vibrations of the drill string are validated against published data from full-scale drill strings.The results from the simulation show that lowering the decay factor increases the critical speed and thus reduces the propensity for stick slip motion.However,a reduction in the decay factor also has the effect of inducing worse stick-slip motion once the critical speed has been reached.The results indicate the wider impact of both correct modelling of the decay factor,but also the importance of correct characterisation of the mud viscosity and drill/well contact for more accurate selection of drilling parameters in the field.

磁流变半主动座椅悬架建模及振动特性分析

磁流变阻尼器力学模型及控制电流逆模型对半主动控制系统的控制精度具有重要影响.采用正弦及余弦型魔术公式,基于骨架曲线与滞回分离的建模方法,建立改进的磁流变阻尼器动态阻尼力模型;采用基于Sobol序列的差分-禁忌混合优化算法对阻尼力模型进行参数识别,构建包含激励特性及控制电流参数的通用数学模型;在试验测试及正向模型基础上,利用自适应神经模糊系统建立阻尼器控制电流逆模型.研究结果表明:本文建立的正逆模型均能够有效表征磁流变阻尼器的非线性行为及滞回特性;改进魔术公式模型在不同激励特性及电流工况下的平均百分比误差在3.4%附近变化;逆向动力学模型计算的控制电流误差均方根值为0.086 9~0.1171 A;经过控制电流逆模型与阻尼器正向模型串联模型计算的预测阻尼力误差均方根值为阻尼器最大阻尼力的5.6%;通过试验测试与仿真结果对比,验证了本文提出的阻尼器数学模型具有较好的精度和适用性,能够改善座椅悬架系统振动传递特性.

Cooling of Granules in Vibrating, Suspended Bed: Engineering Simulation

Here we suggest an algorithm for calculation of the process parameters and design of a vertical cooler with inclined, gas-permeable blades and with a vibrating, suspended layer of granules on them (Vibrating Fluidized Bed—VFB). The algorithm is based on the use of the equations of heat and material balance, taking into account the influx of moisture into the layer with cold air and dust—as a carryover. Mode entrainment of dust particles and moisture from the VFB is described by using empirical formulas and Π-theorem. To calculate the cooling time of granules a model of the dynamics of a variable mass VFB was built, which linked the geometrical and physical process parameters to a single dependency. An example showed that mass flow of granules of 248 kg/h and a volume flow of air of 646 m3/h with temperature of 30℃ to cool the zeolite granules from 110℃ to 42℃ for 49 s required a vertical apparatus of rectangular shape with four chambers and with volume of 0.2 m3. A comparative analysis of technological parameters of the projected cooler with the parameters of typical industrial apparatuses showed that for all indicators: the cooling time of granules, the flow rate of gas (air) and the heat flow, a 4-chambered, vertical apparatus of rectangular shape with VFB was the most effective.

基于滑模控制的多自由度采摘机械臂振动抑制方法

针对机器人末端柔性负载的残余振动问题,提出了一种多自由度采摘机械臂振动的滑模控制方法。考虑到组成结构、运动原理、动力方式等因素,构建了多自由度采摘机械臂数学模型。获取采摘机械臂的振动信号,并对其进行特征分析,计算机械臂振动控制量,生成采摘机械臂全局滑模面,设计了具有自动调节系数的滑膜控制器。对比实验显示,优化后的滑膜控制器由于工作时机械臂的运动参数会根据采摘任务产生动态变化,机械臂振动幅值明显减小,振动频率下降,而且能够消除轮廓误差,振动抑制效果明显,能够适合采摘需要。

行星轮齿轮箱太阳轮齿根裂纹传递特性分析

采用集中参数模型,考虑啮合振动的内部激励,分别对齿轮箱内啮合和外啮合两种方式下的振动信号特征进行了分析。引入改进高斯窗的时变路径函数和考虑齿轮箱材料的时不变路径函数,改进行星轮齿轮箱箱体表面振动信号模型,分析太阳轮齿根在正常和裂纹情况下,不同传递路径对箱体表面振动信号调制现象的定量影响规律。仿真和实验对比分析表明:太阳轮齿根裂纹主要影响啮合频率倍频的边频带成分;该模型能够准确分析齿轮箱正常工况和太阳轮齿根裂纹情况下振动信号的频率、幅值和边频信息,可用于太阳轮齿根裂纹故障诊断。

真空断路器触头弹跳规律分析及参数优化

在综合考虑非线性绝缘拉杆力和触头碰撞接触力的基础上,建立了ZN63A-12真空断路器触头系统在合闸过程中的振动数学模型,利用MATLAB对其求解得到了触头的碰撞接触弹跳规律与影响参数,并引入遗传算法对断路器触头系统进行优化。结果表明:触头合闸过程有两次明显的弹跳,并得出了弹跳规律,幅度与周期由触头质量、系统阻尼与弹簧刚度所决定。算法优化后,合闸所需时间与弹跳总时间分别缩短为37.90 ms和0.901 ms,最大振幅减小到0.061 mm,触头弹跳时间和最大振幅分别降低了61.4%和82.8%。同时,使用断路器动特性测试仪进行实验,将计算结果与测量结果进行对比,两者高度一致,验证了振动数学模型及理论计算的准确性。

机车轴箱轴承冲击故障非平稳振动机理分析

滚动轴承是机车车辆走行部的关键部件,其故障概率较大,振动机理复杂,具有非平稳性,故障诊断困难。为解决该问题,从研究机车轴箱滚动轴承故障发生的机理入手,对冲击故障振动信号加以研究。在实际工况下,着重考虑了载荷和工作转速这两个非线性非平稳性因素,并在此基础上建立了机车滚动轴承冲击故障的数学模型。通过所建立的数学模型,对其进行MATLAB仿真信号分析,同时以某大学轴承故障数据集中的外圈故障为例,开展进一步的MATLAB仿真分析,在一定程度上验证了机理分析和所建立数学模型的正确性。

石油钻机钻井中钻杆粘滑振动的建模和控制方法

石油钻机钻井作业过程中,由于强烈扭矩振动和井下摩阻所引起的钻杆粘滑振动现象不仅对作业效率有影响,还会带来钻杆钻头损伤问题,由此提出一种钻杆粘滑振动的建模及控制方法。将钻杆划分为较小扭矩部分,对整个系统进行动态建模,通过扭矩模型和粘滑振动模型关联分析,为了减少控制过程的粘滑振动,提出转速控制、钻头重量控制和钻杆底部阻尼控制三部分,当钻杆长度划分为受力部分时,利用数学模型使得每种控制策略均对部分分析适用,而钻头重量控制与钻杆底部阻尼控制则采用两种控制方案。实验表明,该方法对底层钻井参数的控制要比表面参数控制更有效,可提高钻井作业效率、降低作业成本。

输电导线融冰体系脱冰振动数学模型及振动试验

针对输电导线直流融冰短接操控系统融冰作业时,覆冰脱落引起悬臂组合机构产生位移和应力变化,进而导致结构失稳、动触头脱出及绝缘破坏等事故,开展脱冰振动特性分析及试验研究。首先,利用拉格朗日方程并结合假设模态法,考虑不同脱冰工况、参数属性及振动方向、结构内部耦合关系等因素,建立了融冰体系悬臂组合机构脱冰振动数学模型,并利用Matlab软件采用改进欧拉法对数学模型进行求解;其次,建立融冰体系有限元模型开展仿真分析,数学模型求解结果与同工况条件下有限元仿真分析结果比对,发现悬臂组合机构位移及应力最大相对误差分别为5.89%和4.62%;验证了建立数学模型时所作假设的合理性及数学模型的准确性;最后,在融冰体系上安装振动在线监测装置,开展融冰体系脱冰振动试验测试,进一步验证了数学模型的准确性。