薄壁圆柱壳在流体脉动激励下的振动特性分析

摘要：为深入研究薄壁圆柱壳在流体脉动激励下的运动特性,应用Donnell简化壳理论,考虑阻尼、结构非线性和附加质量的影响,建立了薄壁圆柱壳在流体脉动激励下的非线性振动方程。基于Galerkin方法将偏微分方程转化为方便求解的常微分方程,利用多尺度法求解了系统主共振的一次近似解,得到了系统稳态响应的转迁集与分岔图,并通过奇异性分析,得到了系统工作稳定性和可靠性的结构参数区域。对薄壁圆柱壳在流体作用下的振动特性进行了数值模拟和实验研究,考察了阻尼系数、脉动频率、液体深度等对系统动力学特性的影响。研究表明,考虑阻尼、结构非线性和附加质量的非线性振动方程更能体现薄壁圆柱壳在流体脉动激励下完整的动力学特性,同时系统中存在多种分岔行为。     

双曲正切型非线性包装系统跌落冲击响应分析

目的分析得到双曲正切型无阻尼非线性包装系统跌落冲击的近似解析解,解决典型工况下双曲正切型非线性包装系统跌落冲击响应求解问题。方法采用PEM分析系统的跌落冲击响应,得到冲击响应的一阶近似解;通过包装动力学的能量法,得到无阻尼系统的精确最大位移值;对近似解进行修正。结果在足够的精度范围内,修正后的最大位移响应值、最大加速度响应值以及系统响应周期非常接近于龙格-库塔数值解。结论为双曲正切型非线性包装系统跌落冲击响应分析提供了一种新的近似分析方法。     

拉索-阻尼器-弹簧系统的阻尼特性分析

该文研究得到了拉索-阻尼器-弹簧系统的复特征频率方程。在阻尼器和弹簧安装点距拉索锚固点长度与拉索长度之比远远小于1的假设条件下,得到了拉索-阻尼器-弹簧系统模态阻尼比的近似解析解,该近似解析解与数值计算得到的精确解对比吻合良好。当弹簧和阻尼器处于同一侧时将会减小拉索所能获得的最大模态阻尼值,而当阻尼器与弹簧在拉索两端时弹簧对阻尼的影响几乎可以忽略。当阻尼器仍处于拉索锚固点附近而弹簧位置向中间移动时由阻尼器引起的频率变化量仍是小量的条件下,得到了结合数值频率解的拉索-阻尼器-弹簧系统模态阻尼比近似解析式。此时拉索所能获得最大模态阻尼比、对应的最优阻尼系数、无量纲频率与弹簧位置、刚度之间存在明确的变化关系。该文研究成果对于拉索端部同时附加橡胶减振器和阻尼器、附加阻尼器的索网结构减振设计具有重要的参考价值。     

阻尼对正切型包装系统易损件冲击谱影响

研究考虑易损件的正切型包装系统在半正弦脉冲激励下的冲击特性.建立考虑阻尼的二自由度非线性产品包装系统模型,得到冲击动力学方程并数值求解.讨论了易损件与主体连接部阻尼和缓冲垫阻尼对易损件冲击谱的影响规律.结果表明,在低频率比处连接部阻尼和材料阻尼的影响均很显著,而在高频率比处,连接部阻尼几乎没有影响.研究结论为产品包装设计提供科学依据.     

跳车冲击过程中的桥梁动态位移响应分析

以1/4简构车辆和含阻尼简支梁桥为对象,建立可描述跳车冲击过程的车桥耦合振动分析模型。采用Newmark-β积分法获得车桥耦合系统振动响应的数值解。在不同高度、不同跳车位置以及不同车速等工况下,重点讨论跳车冲击过程中桥梁竖向动态位移响应的表现特征。数值分析表明:在文中考虑的跳车冲击工况下,桥梁竖向动态位移存在显著差异;不同跳车高度对动态位移峰值影响很小;不同跳车位置时的竖向动态位移表现各有不同,靠近跨中处,在桥梁前半跨发生跳车冲击对桥梁竖向动态位移值的影响明显大于后半跨,远离跨中处,桥梁前半跨动态位移值与后半跨相近,且最大竖向动态位移表现出滞后特征;不同车速对桥梁竖向位移值影响不同。     

考虑流体效应的船-桥碰撞数值模拟法研究

有别于传统的不考虑流体对被撞桥墩影响的船-桥碰撞问题,该文在动水压力计算的基础上,建立了考虑流体效应的船-桥碰撞的附加质量计算模型,并与流构耦合计算模型以及不考虑流体影响的计算模型在能量转换、碰撞力、船艏撞深、桥墩位移、应力、截面内力以及计算效率等方面的结果进行了比较分析。结果表明:流体对船艏碰撞力影响较小,但能降低船舶的损毁程度;流构耦合计算模型中的墩顶水平位移响应要略小于附加质量模型和不考虑流体影响时的计算结果;不同计算模型所得桥墩有效应力基本相同且具有相同的分布规律;船-桥碰撞附加质量模型在计及流体与结构相互作用的同时,具有较高的精度和计算效率。     

三次非线性包装系统关键部件冲击响应影响因素分析

研究考虑易损件的三次非线性包装系统在半正弦脉冲激励下的冲击特性。建立二自由度非线性产品包装系统模型,得到冲击动力学方程并数值求解。讨论了频率比、质量比、缓冲垫阻尼、连接部阻尼、脉冲激励幅值和系统参数对系统冲击响应的影响规律,结果表明,各参数对系统冲击响应加速度峰值、最大变形量影响显著,研究结论为产品包装设计提供科学依据。     

非线性包装系统跌落冲击响应分析的 HFAF法

目的针对单自由度无阻尼Duffing方程,应用何氏频率-振幅关系(HFAF)得到简单的近似解析解。方法以三次非线性包装系统为研究对象,应用何氏频率-振幅(HFAF)关系分析系统跌落冲击响应,得到跌落冲击响应的近似解;为提高解的精度,与包装动力学分析的能量法结合,通过能量法求解最大位移及加速度,对近似解进行修正。结果修正后的近似解其位移和加速度峰值与数值分析的结果相比较,相对误差小于0.1%,近似解解析表达简单,物理意义明确。结论研究结果可为非线性包装系统跌落冲击响应分析提供一种新的快速近似分析方法。     

正切非线性包装系统跌落冲击的MSLP解EI北大核心CSCD

针对有阻尼正切型非线性包装系统在发生跌落冲击时的响应问题,基于摄动法(multi-scale Lindstedt-Poincare,MSLP)讨论了系统跌落冲击响应的一、二次近似解。并与龙哥库塔法(R-K)的数值结果及相关文献进行了对比,对比结果显示:对于正切型强非线性包装系统,MSLP计算的最大位移和加速度响应的一阶近似解与R-K数值结果对比的相对误差分别为1.35%和3.28%,二次近似阶的相对误差分别为0.62%和1.84%,在不进行能量修正的情况下,比同伦摄动法、牛顿谐波平衡法的精度更高。考虑阻尼系统能量修正的复杂性,所求有阻尼正切型非线性系统跌落冲击一次近似解析具有较好的精度和简洁的形式,为此类问题的求解及工程应用提供了参考。     

采用向量式有限元的斜拉索振动控制仿真

采用向量式有限元(Vector Form Intrinsic Finite Element(VFIFE)),建立斜拉索模型,通过给空间点增加附加作用力来模拟阻尼器对斜拉索的作用。模拟了拉索激振和振动衰减的过程,利用Hilbert变换处理拉索的衰减时程,得到拉索的附加阻尼比,分析了阻尼器的线性粘滞阻尼系数、阻尼器内刚度、阻尼器运动部分质量、阻尼器支撑刚度,及斜拉索垂度对附加阻尼比的影响;并将结果与附加阻尼比通用计算公式计算结果进行对比。结果表明,采用VFIFE建立斜拉索-阻尼器系统能准确地模拟阻尼器对斜拉索的振动控制作用;模拟得到的结果与通用计算公式给出的结论相符;系统存在最优阻尼系数和最优阻尼比;阻尼器内刚度的增大和支撑刚度的减小将降低系统阻尼比;阻尼器运动部分质量的增大将增大系统阻尼比;拉索垂度对第1阶模态阻尼比的降低影响较大,对于高阶模态的影响很小。     

Prediction of cushion curves of polymer foams using a nonlinear distributed parameter model

Polymer foams are commonly used in the protective packaging of fragile products. Cushion curves are commonly used within the packaging industry to characterize a foam's impact performance. These curves are two-dimensional representations of the deceleration of an impacting mass versus static stress. Cushion curves are currently generated from exhaustive experimental test data. This study represents the first time that the physics of the mass-cushion impact have been analysed by modelling the foam as nonlinear, continuous rod. Using a single mode of vibration and excluding the effects of damping, the maximum displacement during the impact can be obtained from a polynomial describing the maximum elastic energy in the foam. The displacements can be used to recover the amplitude of the deceleration shock pulse. Numerical and analytical analysis of the model with damping is considered in its ability to predict the shock pulse shape, duration, and amplitude at various static stresses, foam thickness, and drop heights as compared with experimental data. Furthermore, both the analytical and numerical results agree and are primarily within the expected lab-to-lab variability of 18% documented in ASTM D1596 - Standard Test Method for Dynamic Shock Cushioning Characteristics of Packaging Material.     

Towards incorporating impact losses into random vibration analyses: a model problem

A benchmark model random vibration problem is considered for an SDOF system with a one-sided inelastic barrier at its equilibrium position under Gaussian white-noise excitation. An analytical solution is obtained for an expected response energy by cycle-to-cycle application of the method of moments with successive conditional and unconditional averaging. The solution, valid both for small and ‘not very small' impact losses, leads to a formula for the equivalent viscous damping factor, which may be used to account for impact losses. Monte-Carlo simulation results show that this formula provides generally better accuracy than one obtained by stochastic averaging. They also illustrate applicability of the formula for certain more complicated random vibration problems.     

Added mass effect on flapping foil

Unsteady effects caused by accelerating bodies in water play a very important role in biological propulsion. However, such propulsion mechanisms are challenging for simulation as both body geometry and locomotion patterns are quite complex and a natural first step is to model the motion of a standard man-made airfoil. The work presents simulations of harmonic oscillations of a NACA 0012 foil in water and the hydrodynamic forces generated were obtained by a Boundary Element Method (panel method) code. The focus is placed on one of the most important unsteady effects, the added mass effect, which has not been sufficiently addressed in the literature. The corresponding unsteady forces were obtained through appropriately devised two-dimensional added mass tensor. The computational results were compared to existing analytical ones and a maximum error of 10⁻⁶ was obtained for the added mass coefficients of the circle of unit diameter. The development of a dedicated numerical approach for the calculation of the added mass tensor is necessitated by the lack of analytical solution for a variety of wing shapes such as NACA foils. The simulations showed that for the range of investigated parameters the inertia thrust and lift generated by the flapping foil increase sharply when the added mass contribution is considered. For example, if the Strouhal number is set to 0.3 and the ratio between the wing and fluid densities to 0.3, the time average of the inertia thrust increases by 23 times and the maximum of the inertia lift is ca. 37 times larger when the added mass effect is considered. Generally, a densities' ratio of order 1 results in an increase of the time-average inertia thrust of order 10. It was confirmed that, as the densities' ratio becomes larger, the contribution of the added mass to the generated inertia forces decreased. As the Strouhal number increases, the added mass effect was found to be more dominant due to the imposed motion kinematics, i.e. the pitch amplitude. The obtained results show clearly that for the specific case of flapping flight in dense fluids the unsteady effects caused by the object acceleration are of prime importance for two reasons: (i) accurate estimate of the generated thrust and (ii) realistic assessment of the resulting structural loads.     

基于直杆共轴碰撞理论的桥梁地震反应邻梁碰撞分析模型

桥梁结构在强烈地震动作用下,伸缩缝两边的主梁会因运动的相对位移大于伸缩缝间距而发生碰撞,造成桥梁结构损坏,甚至引发落梁。研究目的是建立较合理的邻梁碰撞问题分析模型。通过引入表征邻梁碰撞相互作用的碰撞弹簧,基于直杆共轴碰撞理论建立了邻梁碰撞问题的分析模型,采用解析与数值结合的方法研究了碰撞弹簧刚度比a、邻梁长度比12/ll和阻尼比x等参数对碰撞力、碰撞持续时间和耗能的影响。利用美国加州强震观测计划(CSMIP)获得的邻梁碰撞强震记录,估计了碰撞弹簧刚度约为0.5倍的较短主梁轴向刚度。     

Modelling and analysis of coupled nonlinear oscillations of a floating body in two degrees of freedom

Summary We describe a mathematical model to investigate the effect of coupled nonlinear oscillations of a floating body in time domain under the influence of sinusoidal waves. To account for hydrodynamic forces, a mathematical formulation for added mass moments of inertia, damping and restoring moments is presented for roll and yaw. Using perturbation technique, we obtain order wise solutions in the normalized domain wherein the assumption on small distortion holds. On applying Laplace transform, a zeroth-order solution is obtained in closed form whereas for higher order solutions we resort to the Runge-Kutta method with adaptive step size algorithm. For analyzing the model result we perform numerical experiments for a vessel of mass 19190 tons under the action of a beam wave of frequency 0.74 rad/sec and 1.0 m wave height. The validity of the numerical scheme is checked by comparing with the analytical solution for uncoupled zeroth-order roll and then we proceed to examine the effect of coupled behavior of roll and yaw for higher-order approximations. The inter-dependence between wave frequency (ω), system frequency (β) and damping factor (ζ) is obtained to reveal system stability. Model results indicate an artificial increase in amplitude for uncoupled roll, and also emphasize the contribution of viscous damping in roll in contrast to added mass in yaw.     

分数阶Duffing振子的亚谐共振

研究了含分数阶微分项的Duffing振子的亚谐共振,利用平均法得到了系统的一阶近似解。提出了亚谐共振时等效线性阻尼和等效线性刚度的概念,分析了分数阶微分项的系数和阶次对系统动力学特性的影响。建立了亚谐共振定常解的幅频曲线的解析表达式,并得到了亚谐共振周期响应的存在条件和稳定性判断准则。最后进行了数值解和解析解的比较,证明了解析结果的准确性,并通过数值仿真研究了分数阶微分项的参数对亚谐共振解的存在条件、稳定性条件和系统幅频曲线的影响。     

输电线路防舞阻尼器系统参数分析及设计研究EI北大核心CSCD

针对目前覆冰导线舞动频发现状,提出了一种通过在导线靠近输电塔位置处设置阻尼器来减振耗能从而实现输电线路舞动抑制的方法。基于Hamilton原理运用多阶伽辽金函数推导得到了导线-阻尼器系统的广义运动方程,并以某750 kV单档八分裂输电线路为例进行运动方程特征值分析,得到了导线-阻尼器系统的动力特性,探索了导线的垂度参数、阻尼器安装位置、阻尼系数及刚度系数等对系统等效阻尼比的影响,阻尼器安装位置越靠近跨中,系统的最大阻尼比提升效果越明显,两侧对称安装阻尼器可以有效地减小最优阻尼系数。采用数值算例和有限元数值仿真技术比较了粘滞阻尼器与负刚度阻尼器(NSD)对导线系统的减振效果,并针对NSD提出了参数的优化设计方法。研究表明:相比传统阻尼器,NSD可以在较低阻尼系数下有效地提高系统各阶的最大阻尼比,且能够明显降低导线系统的自振频率;系统所能达到的一阶最大阻尼比对NSD安装位置的变化不敏感;通过有限元仿真证实了,基于NSD的输电导线阻尼器设置方案相较于传统阻尼器方案具有更好的防舞性能。     

水流作用下双圆柱墩混凝土梁桥的动力响应实测与数值模拟

西藏达林大桥为一座7跨桥面连续的混凝土梁桥,下部结构采用双圆柱桥墩。2018年7月,在水流作用下达林大桥桥墩及桥面出现了显著的顺桥向振动。该文报道了水流作用下大桥的动力响应实测与数值模拟研究。实测表明:桥梁顺桥向振动表现为桥梁一阶纵向模态为主的拍振,横桥向为随机微振动;顺桥向最大加速度约为0.08 m/s2,梁端最大位移约为1.56 mm。基于一阶纵向振动模态参数,将双圆柱墩梁桥简化为单自由振动体系,在2 m/s~10 m/s流速范围内(折减流速U_r=1.69~8.45、雷诺数Re=2.6×106~1.3×107)进行了二维流固耦合数值模拟,得到了桥墩双圆柱升阻力系数以及不同结构阻尼比时的涡振响应。并对桥墩振型与水流流速剖面等三维效应进行修正,得到了墩顶位移随流速变化的关系。结果表明:上游柱尾流对下游柱的脉动涡激升力有显著增强作用,在3 m/s~6 m/s流速范围内双圆柱桥墩出现了涡激振动。在考虑三维修正后,ζ=0.01工况下墩顶位移数值模拟结果与实测值较为吻合。随着阻尼比ζ的增加,涡振最大振幅变小,锁定区间基本不变。     

An Arbitrary Lagrangian-Eulerian finite element method

This paper describes an Arbitrary Lagrangian- Eulerian (ALE) finite element method for the simulation of fluid domains with moving structures. The fluid is viscous, incompressible and unsteady and the fluid motion is solved by a fractional step discretization of the Navier-Stokes equations. The emphasis is on convection dominated flows, and a three-step method is used for the convection term. The moving structure causes the mesh of the fluid domain to move, and a new algorithm is proposed to solve the important and crucial problem of the calculation of the mesh velocities. Numerical calculations of the added mass and added damping of a vibrating two-dimensional circular cylinder in the frequency Reynolds number range Re _w =20−2000 are performed to evaluate the proposed ALE finite element method. The numerically calculated added mass and added damping are compared to both analytical and numerical results. To further demonstrate the generality of the method, a numerical simulation of flow past an oscillating schematic sports car is presented.     

Design rules for composite sandwich wakeboards

Wakeboarding is a water sport born in the mid 1980s that derives from surfing and water skiing. The objective of this work is to understand the failure mechanism and evaluate the maximum hydroelastic loads during the slamming phenomena of the board used in this sport, in order to provide reliable design rules to follow during the design process. Wakeboards are usually built as a composite sandwich structure, with plastic foam core and CFRP (carbon fibre reinforced plastics) or GFRP (glass fibre reinforced plastics) faces. Several specimens were extracted from a real board and tested in three point bending to investigate the major failure mechanisms. These data are later used in a parametric full-scale SPH numerical model investigation of the water-entry event. The numerical results show that, due to the fluid–structure interaction, there is a maximum deformation that the board cannot overreach even for very high impact energies. This limits the maximum impact stresses reached during the water entry of wakeboards. From these numerical results, mathematical relations between design variables are drawn by using analytical formulas based on classical sandwich theory. As result of this research, practical guidelines (formulas, tables and graphs) on the effects of total mass, initial impact velocity, board curvature and core and face strength and thickness are outlined to give reliable design rules.