柔性悬臂梁与钢球碰撞机制模拟与响应分析

采用线性-弹簧阻尼模型模拟钢球与梁之间的碰撞机制,研究了钢球碰撞下柔性悬臂欧拉梁的衰减振动问题;通过分析推导并建立了整个系统的分段非线性动力学方程。数值结果表明:碰撞是一个瞬时的能量传递过程,碰撞前后梁与钢球的速度均会发生突变;柔性梁从碰撞中获得初始能量,在自身阻尼的作用下作衰减振动;改变系统的参数如钢球质量与速度、碰撞位置等均会对梁的衰减振动产生显著的影响。     

一种评价旋转态内嵌流体欧拉梁自适应减振效果的新方法

为了评价内嵌式粘性流体单元自适应减振方法(IVFUM)消减运动柔性结构残余振动的效果,进行了旋转态内嵌粘性流体欧拉梁自适应减振试验,对残余振动信号进行了处理。针对旋转态下的内嵌粘性流体欧拉梁残余振动信号具有刚体衰减转动的慢变信号与柔性结构残余振动快变信号相耦合的非平稳特征以及模态参数随时间变化的特点,提出了结合小波包、经验模式分解(EMD)、随机减量技术(RDT)、希尔伯特变换(HT)的综合信号处理方法。提取了内嵌粘性流体欧拉梁的一阶主振动响应信号,识别了梁的一阶模态参数(无阻尼固有频率和等效模态阻尼比)。与SDOF模型处理的数据结果进行比较,欧拉梁残余振动衰减的变化趋势基本一致,表明本文提出的方法在实际应用中是有效可行的。可以推断欧拉梁内嵌1/3左右空腔容积的水在2～5 Hz的旋转频率时,由于流动性较好,可以有效地消减运动柔性结构的残余振动。为半定量评价内嵌粘性流体方式对运动的工程柔性结构残余振动衰减效果提供了有效的依据。     

非线性非完整系统的碰撞方程

有关线性非完整系统的碰撞方程,已有文章[1]阐述清楚了。本文引入了δ_+-函数及δ~-函数,对非线性非完整系统进行了研究,並给出了该系统的碰撞方程。     

移动柔性梁作用下简支梁的动力响应

对移动结构作用下梁的响应问题进行了推广,采用柔性梁作为移动结构模型,在考虑结构柔性和悬挂连接的前提下对系统的耦合振动进行了分析.根据一般边界条件梁建立振动方程,通过量纲一参数以及模态叠加法处理系统动力学方程.以简支边界条件为例,得到了梁响应的数值结果,对系统主要参数即移动结构频率、移动速度及连接刚度对简支梁振动的影响进行了讨论.结果表明:考虑移动体的柔性频率对简支梁的振动会产生一定的影响.     

线性强化型弹塑性弯曲直梁挠曲线方程

针对材料在弹塑性阶段的应用不完全问题,本文用弹塑性分区最小势能原理,推导出线性强化模型下弯曲直梁的势能分区准则和欧拉方程.求解出集中载荷作用下悬臂梁和简支梁的挠曲线方程,将挠曲线方程代入MATLAB软件进行数值计算并将其结果与ANSYS对比分析.结果表明:数值解与有限元值均满足实际工程中允许的误差范围,给出的方法可为解...     

作大范围回转运动柔性梁斜碰撞动力学研究

为正确估计由于碰撞引起的多柔体系统动力学特性的变化,针对作大范围回转运动的柔性梁与一固定斜面发生斜碰撞的情况,在考虑刚柔耦合效应的多柔体系统动力学建模理论的基础上,利用假设模态法建立起重力场作用下的柔性梁一致线性化动力法向碰撞过程中系统的动力行为。基于Ｈｅｒｔｚ接触理论和非线性阻尼项建立法向碰撞接触模型,基于线性切向接触刚度建立柔性梁切向碰撞接触模型,提出的数值算法保证了计算结果的合理性,给出的仿     

DYNAMIC SUBSTRUCTURE METHOD FOR PROPAGATION OF ELASTIC-PLASTIC WAVE INDUCED BY IMPACT

通过建立弹塑性碰撞动态子结构模型,推导了模态坐标下的控制方程,提出了模拟柔性结构碰撞激发弹塑性波传播的动态子结构方法,并对其中的主模态的存在性和主模态截断的收敛性进行了证明.通过对柔性杆纵向碰撞和柔性梁横向碰撞两个算例的计算,并将计算结果与理论解和三维动力有限方法计算结果进行了对比,验证了该方法的数值收敛性和计算碰撞弹塑性波传播的有效性.     

非对称混杂边界轴向运动Timoshenko梁橫向振动分析

研究两端带有扭转弹簧且弹簧系数均可任意变化的非对称混杂边界下的轴向运动Timoshenko梁的横向振动.利用非对称混杂边界条件推导对应任意弹簧系数的系统超越方程以及特征函数.运用数值方法计算系统的固有频率及其相应的模态函数,并研究确定梁的刚度、轴向速度以及边界处扭转弹簧的刚度的影响.通过数值算例,比较7imoshenko梁、瑞利梁、剪切梁和欧拉梁的固有频率随轴向速度的变化,分析转动惯量和剪切变形的影响.     

分数导数型本构关系描述粘弹性梁的振动分析

本文研究粘弹性梁在周期激励作用下的受迫振动问题。梁的材料满足Kelvin-Volgt分数导数型本构关系。基于动力学方程、本构关系和应变－位移关系建立了小变形粘弹性梁的振动方程。采用分离变量法分析粘弹性梁的自由振动,导出模态坐标满足的常微分－积分方程和模态函数满足的常微分方程,对于两端简支的截面梁给出了固有频率和模态函数。对于简谐激励作用下粘弹性梁的受迫振动,利用模态叠加得到了稳态响应。最后给出数值算例说明本文方法的应用。     

全弹性平面运动机器人的高精度运动控制和振动抑制算法研究

为实现对基座、关节和臂均存在弹性的空间机器人运动高精度控制及多重振动抑制,建立了基座、关节和臂全弹性空间机器人动力学模型,并采用运动有限维PD重复学习控制及振动同步抑制方案进行研究.首先,利用线性弹簧、扭转弹簧和欧拉-伯努力梁理论,假设模态法和动量守恒定律,采用拉格朗日方程建立了弹性基座、柔性关节和柔性臂空间机器人动力学模型,之后,选取反映柔性臂振动的前两阶模态及基座和关节刚性运动变量为慢变子变量,选取基座和关节弹性振动变量为快变子变量,根据奇异摄动理论将系统降维分解成慢、快变子系统.最后设计了慢变子系统的运动有限维PD重复学习控制及快变子系统的线性最优双重减振控制构成的总控制器.数值仿真结果验证了算法的有效性.     

Parametric excitation of beams moving over supports

Studied in this work are the formulation of equations of motion and the response to parametric excitation of a uniform cantilever beam moving longitudinally over a single bilateral support. The equations of motion are generated by using assumed modes to discretize the beam, by regarding the support as a kinematic constraint, and by employing an alternate form of Kane's method that is particularly well suited to systems subject to constraints. Instability information is developed using the results of perturbation analysis for harmonic longitudinal motions of small amplitude and with Floquet theory for general periodic motions of any amplitude. Results demonstrate that definitive instability information can be obtained for a beam moving longitudinally over supports based on the frequencies of free transverse vibration of a beam that is longitudinally fixed.     

惯容器对隔振系统动态性能影响研究

本文设计了一种滚珠丝杠惯容器及ISD隔振系统,通过实验研究了惯性轮的转动惯量对惯容值的影响;同时,分析了滚珠丝杠惯容器的机械动力学特性,推导了ISD隔振系统的振动传递率计算公式,探讨了惯容器对ISD隔振系统动态特性的影响。在电机被动、主动和混合隔振工况下,开展了弹簧阻尼系统和ISD隔振系统的振动性能对比实验,验证了惯容器对振动系统固有频率和减振效果的影响规律。研究结果表明,惯容器可降低振动系统的固有频率,使共振频率向低频移动,共振振幅降低;在共振频率附近,惯容器可抑制共振振幅,惯容值越高,抑制效果越明显;ISD隔振系统在低频的减振效果优于传统的弹簧阻尼系统;随着频率比的增加,ISD隔振系统的传递率趋于稳定值,惯容器会引起高频隔振性能降低。     

Performances of dynamic vibration absorbers for beams subjected to moving loads

The goal of this work is a general assessment regarding the performances of linear and nonlinear dynamic vibration absorbers (DVAs) applied to the specific problem of moving loads or vehicles. The problem consists of a simply supported linear Euler–Bernoulli beam excited with a moving load/vehicle; a DVA is connected to the beam in order to reduce the vibrations. The moving vehicle is modeled by a single degree of freedom mass spring system. The partial differential equations governing the beam dynamics is reduced to a set of ordinary differential equations by means of the Bubnov–Galerkin method. A parametric analysis is carried out to find the optimal parameters of the DVA that minimize the maximum vibration amplitude of the beam. For the case of a moving vehicle, the energy absorbed by the DVA is evaluated. Comparisons among the performances of different types of linear and DVAs are carried out. The goal is to clarify if the use of nonlinearities in the DVAs can effectively improve their performances. The study shows that the most effective type of DVA for the test cases considered is the piecewise linear elastic restoring force.     

架空输电线防振锤阻尼特性实验研究

本文利用梁的振动理论对防振锤的阻尼特性进行研究。通过正弦激励下的共振驻留法,分别对不同型号以及同种型号不同锤头质量的防振锤进行振动实验,应用能量平衡原理得到了防振锤的阻尼特性曲线,分析了不同模态响应在阻尼耗能中的贡献。考虑不同类型阻尼对于减振性能的作用,在Lazan阻尼假设的基础上,利用经验公式推导了阻尼系数计算公式。结果表明,钢绞线变形大小直接影响防振锤的阻尼值大小;阻尼对减小共振频率附近的受迫振动幅值作用明显,验证了防振锤的减振性能;同时锤头质量的变化可以影响阻尼曲线的变化。以上结论可为防振锤的防振设计和应用提供参考。     

Non-linear parametric vibration and stability of axially moving visco-elastic Rayleigh beams

An axially moving visco-elastic Rayleigh beam with cubic non-linearity is considered, and the governing partial-differential equation of motion for large amplitude vibration is derived through geometrical, constitutive, and dynamical relations. By directly applying the method of multiple scales to the governing equations of motion, and considering the solvability condition, the linear and non-linear frequencies and mode shapes of the system are analytically formulated. In the presence of damping terms, it can be seen that the amplitude is exponentially time-dependent, and as a result, the non-linear natural frequencies of the system will be time-dependent. For the resonance case, through considering the solvability condition and Routh–Hurwitz criterion, the stability conditions are developed analytically. Eventually, the effects of system parameters on the vibrational behavior, stability and bifurcation points of the system are investigated through parametric studies.     

磁约束双层夹心悬臂梁的振动分析

采用在约束层端部上设置永磁体的新方法可使阻尼层获得比传统约束阻尼处理方法更高的剪应变，从而增强粘弹层的阻尼耗能，降低共振峰。本文应用Hamilton原理，推导了全覆盖双层约束阻尼悬臂梁的运动方程，对模型进行了实验验证；分析了不同物理和几何参数下该方法的减振效果。研究表明，磁约束能提高阻尼减振效果。随着阻尼层厚度的增加，无磁约束的共振峰降低较少，而有磁约束的共振峰急剧降低，减振效果明显。阻尼层剪切模量G的变化对磁约束减振效果的影响较大；当G小于一定值时，减振效果明显，但当G大于一定值时，减振效果急剧降低。在不同的约束层弹性模量和厚度下，磁约束仍起作用。此外，分析了具有较大控制力的主被动混合磁约束振动控制方法的可行性。     

Structural damping identification method using normal FRFs

All structures exhibit some form of damping, but despite a large literature on the damping, it still remains one of the least well-understood aspects of general vibration analysis. The synthesis of damping in structural systems and machines is extremely important if a model is to be used in predicting vibration levels, transient responses, transmissibility, decay times or other characteristics in design and analysis that are dominated by energy dissipation. In this paper, new structural damping identification method using normal frequency response functions (NFRFs) which are obtained experimentally is proposed and tested with the objective that the damped finite element model is able to predict the measured FRFs accurately. The proposed structural damping identification is a direct method. In the proposed method, normal FRFs are estimated from the complex FRFs, which are obtained experimentally of the structure. The estimated normal FRFs are subsequently used for identification of general structural damping. The effectiveness of the proposed structural damping identification method is demonstrated by two numerical simulated examples and one real experimental data. Firstly, a study is performed using a lumped mass system. The lumped mass system study is followed by case involving numerical simulation of fixed–fixed beam. The effect of coordinate incompleteness and robustness of method under presence of noise is investigated. The performance of the proposed structural damping identification method is investigated for cases of light, medium, heavily and non-proportional damped structures. The numerical studies are followed by a case involving actual measured data for the case of a cantilever beam structure. The results have shown that the proposed damping identification method can be used to derive an accurate general structural damping model of the system. This is illustrated by matching the damped identified FRFs with the experimentally obtained FRFs.     

Matlab编程实现求解基于振型叠加法的多自由度动力学系统的时域和频域响应

给出了求解多自由度动力学系统响应的M atlab程序,这些程序基于振型叠加法可用于求解由质量矩阵M和刚度矩阵K以及常见阻尼矩阵描述的线性离散系统的时域和频域解.对于无阻尼系统,用户可以选择数值解或符号解析解(以时间或频率表示),并利用复模态叠加法计算了阻尼系统的数值解.总结了模态叠加方法下动力学响应的求解,并在简短的M atlab程序中实现.以三自由度系统和悬臂梁模型为例说明了程序的应用.这些程序也可用于工程应用中,通过对商用有限元软件包产生的质量和刚度进行后处理,产生感兴趣的时域和频域响应.     

Suppression of multiple modal resonances of a cantilever beam by an impact damper

Impact dampers are usually used to suppress single mode resonance. The goal of this paper is to clarify the difference when the impact damper suppresses the resonances of different modes. A cantilever beam equipped with the impact damper is modeled. The elastic contact of the ball and the cantilever beam is described by using the Hertz contact model. The viscous damper between the ball and the cantilever beam is modeled to consume the vibrational energy of the cantilever beam. A piecewise ordinary differential-partial differential equation of the cantilever beam is established, including equations with and without the impact damper. The vibration responses of the cantilever beam with and without the impact damper are numerically calculated. The effects of the impact absorber parameters on the vibration reduction are examined. The results show that multiple resonance peaks of the cantilever beam can be effectively suppressed by the impact damper. Specifically, all resonance amplitudes can be reduced by a larger weight ball. Moreover, the impacting gap is very effective in suppressing the vibration of the cantilever beam. More importantly, there is an optimal impacting gap for each resonance mode of the cantilever beam, but the optimal gap for each mode is different.     

A note on vibrations of damped linear systems

In a damped linear system, for the free vibrations to be oscillatory with decaying amplitude, it is proven that the mass and damping matrices must be positive definite. Also, a certain matrix product involving the mass, damping and stiffness matrices must be commutative.