被动隔振的非线性动力学研究

研究了由基础振动激励的被动隔振体的非线性振动特性和振动稳定性。考虑隔振系统的非线性刚度和隔振材料的非线性阻尼,建立了被动隔振体的非线性动力学方程;用谐波平衡法研究了其非线性振动特性,导出了频率响应方程;讨论了非线性因素的影响;分析了隔振体振动的稳定性,得出了稳定区和不稳定区的分界线方程。     

非线性双层混合隔振系统控制研究

对非线性混合隔振系统的动力学特性进行了定性分析,并以滑膜变结构算法为基础设计了混合隔振系统的控制模型,通过相关算例验证了该控制模型在非线性刚度条件下的有效性,仿真结果表明:非线性混合隔振控制效果明显优于被动隔振和线性隔振系统,非线性刚度的引入可有效降低基础所受冲击载荷。文中所研究的控制方法对实际工程中非线性混合隔振系统的设计具有重要的指导意义。     

柔性基础非线性隔振系统动力学特性分析

建立了隔振对象-非线性隔振支承-柔性基础组成的耦合系统的一般性动力学模型,研究了应用振动功率流对非线性隔振系统进行效果分析的计算方法,给出了动力学方程初值问题表达式;并且基于Runge-Kutta法以某小型无人机的发动机隔振系统为算例,对几种非线性隔振器的隔振效果进行了数值仿真和分析。研究表明并联刚度隔振器和分段线性隔振器可有效减少隔振系统功率流的传递。     

被动隔振体的hopf分岔分析

本文建立了被动隔振体的非线性动力学方程。根据非线性振动理论,设立系统在弱非线性情况下的一次谐波解,通过平均法先求得系统的一次谐波的振幅随时间的变化方程,然后通过分析一次谐波的振幅发生hopf分岔的条件得到了被动隔振体系统发生hopf分岔的条件。     

聚氨酯泡沫塑料振动性能的试验研究

本文对一种增强泡沫塑料隔振材料进行振动性能试验研究.首先,设计了泡沫塑料隔振材料振动特性试验及试验装置;其次,对泡沫塑料隔振材料进行振动试验并获取试验数据;然后,对试验数据进行处理、分析和研究.试验研究表明,泡沫塑料隔振材料的振动特性不仅与振幅有关,还与振动频率有关;恢复力同时受频率和振幅的影响,并和变形历史有关,具有非线性滞后特性;在振动情况下表现出动刚度非线性和阻尼非线性的特性,变化十分复杂.试验研究为泡沫塑料隔振材料数学建模、参数辨识和动力学设计及动力优化准备了试验数据,提供了重要依据和奠定了良好基础.     

带限位器浮筏系统冲击响应的伪力法研究

引入一种新的方法——伪力法来计算带限位器非线性浮筏隔振系统的冲击响应。通过一种非线性分解,将非线性弹性力分解成一个线性力和一剩余非线性伪力,并实例计算分析了限位器刚度和间隙等因素对冲击响应的影响,为设计抗冲击浮筏隔振系统提供了有价值的依据。     

双层精密隔振平台的最优控制研究

将主动隔振技术应用到双层精密隔振系统中,设计双层主动隔振系统,建立其动力学方程和状态方程。根据精密制造和精密仪器的隔振需求,提出控制目标,建立系统的线性二次型调节器(linear quadratic regulator,LQR)最优控制模型,利用Matlab/Simulink软件进行仿真分析,在不同激励下研究主被动系统隔振对象的加速度响应大小。仿真结果表明:双层主动隔振系统的隔振效果远远优于被动隔振系统。     

碟形弹簧负刚度在低频精密隔振中的应用研究

负刚度机构可用于系统的低频隔振,本文设计了一种新型的利用碟形弹簧负刚度的低频被动垂直隔振系统。碟形弹簧具有非线性变形特性,并且在一定条件下,碟形弹簧具有负刚度的特性。将碟形弹簧在负刚度区间与正刚度弹簧并联,通过合理选择参数,使得隔振系统的刚度在平衡点附近趋向于零,隔振系统的固有频率可以达到极低,从而使其隔振频带加宽,可实现低频隔振的目的。通过计算机仿真计算,证明并联机构具有良好的低频隔振效果。     

低频非线性隔振器的动力学分析

针对低频隔振效果较好的一种具有负刚度机理的无源隔振系统,给出了隔振系统的基本结构模型,对其进行了力学分析,建立了强非线性动力学微分方程.分别利用谐波平衡法和切比雪夫逼近法对该方程进行非线性近似求解和线性近似求解,并进行数字模拟仿真,通过对比得出了非线性较线性分析具有较高的精度,且在0.5Hz时可以纠正线性求解的错误,对低频隔振器的设计有着一定的指导意义.     

时滞阻尼液固混合介质隔振系统的动力学研究

针对单一线性阻尼被动隔振无法兼顾共振区与隔振有效区的隔振性能问题,提出了时滞立方非线性主动阻尼控制策略。以具备分段线性刚度液固混合介质受控隔振系统为研究对象,运用多尺度摄动法对受控系统进行主共振分析,建立了等效刚度和等效阻尼的概念,并考察时滞对受控系统幅频特性与传递率特性的影响。研究结果表明:由于主动时滞的引入,立方非线性速度反馈增益既可调控阻尼,还可以调整隔振系统的等效刚度;与单一线性阻尼相比,立方速度反馈在不改变隔振有效区隔振效果的同时,显著降低了共振区的传递率;对于因鞍结分岔在主共振造成的幅值跳跃,通过选择合适的反馈时滞可以有效抑制跳跃的出现;通过稳定性分析发现,受控系统并非是全时滞稳定,因此最后给出控制器中反馈增益和时滞的参数区间设计方法。     

基于包络法的正交面齿轮齿廓尖化研究

提出了一种新型的3P-6SS并联机构,计算了其运动学反解。制作了这种并联机构的实物样机,并搭建了该并联机构的控制系统。基于数字信号处理器（DSP）编写了控制程序,并使用3P-6SS并联机构的实物样机进行了实验。在无抬笔、落笔控制的情况下,该并联机构写出了有联笔的字母“BUPT”;在有抬笔、落笔控制时,该机构写出了无连笔的数字“2008”。实验结果表明了反解算法的正确性和控制系统的有效性。     

Nonlinear free and forced vibration of simply supported shear deformable laminated plates with piezoelectric actuators

This paper deals with the nonlinear vibration and dynamic response of simply supported shear deformable cross-ply laminated plates with piezoelectric actuators subjected to mechanical, electrical and thermal loads. The material properties are assumed to be independent of the temperature and electric field. Theoretical formulations are based on the higher order shear deformation plate theory and general von Kármán-type equation, which includes thermo-piezoelectric effects. Due to the bending and stretching coupling effects, a nonlinear static problem is first solved to determine the pre-vibration deformation caused by temperature field and control voltage. By adding an incremental dynamic state to the pre-vibration state, the equations of motion are solved by an improved perturbation technique to determine nonlinear frequencies and dynamic responses of hybrid laminated plates. The numerical illustrations concern nonlinear vibration characteristics of unsymmetric cross-ply laminated plates. The results presented show the effects of temperature rise, applied voltage and stacking sequence on the nonlinear vibration and dynamic response of the plates.     

带间隙的双线滞回系统的非线性振动

分析了惯性振动圆锥破碎机的非线性动力响应问题。考虑到物料的滞回作用,将系统简化为具有间隙的双线性滞回单自由度力学模型。利用渐近法计算出系统的等效阻尼和等效刚度系数。进而利用Poincare截面、分叉图以及李氏指数等非线性动力学分析方法,研究了该模型的非线性动力响应。通过对模型的动力学分析,研究了含有滞回恢复力这种耗能比较大的非线性振动系统的周期、倍周期以及混沌振动及其出现特点。计算结果表明,在特定的参数范围内系统出现无序的混沌运动。     

轴向载荷作用下细长柔性旋转梁横向振动响应分析

将水平井柔性钻柱简化为轴向载荷作用下的细长柔性梁,建立了考虑几何大变形的非线性动力学方程,并且利用多重尺度法得到了柔性梁横向振动的平均方程。因钻柱转速和轴向力是影响钻柱振动的两个主要参数,故用改变转速的方法来对平均方程进行非线性动力学响应分析,给出了一阶、二阶模态下钻柱随转速变化的分叉图和不同转速下的相图。分析结果表明,系统响应经历了从周期到混沌再到二倍周期的变化过程,振动幅值有跳变现象出现,在共振条件下,柔性旋转梁振动幅值是有限值,并非无穷大,当轴向力发生变化时,可以通过控制转速变化达到定性、定量地控制柔性钻柱横向振动的目的。     

Nonlinear vibrational response of a single edge cracked beam

The nonlinear vibrational response of a breathing cracked beam was investigated. The study was done by using a new crack stiffness model to examine some of the nonlinear behaviors of a cantilever beam with a breathing crack. The quadratic polynomial stiffness equation of the cracked beam was derived based on the hypothesis that the breathing process of a crack depends on the vibration magnitude. The Galerkin method combined with the stiffness equation was used to simplify the cracked beam into a Single-degree-of-freedom (SDOF) lumped system with nonlinear terms. The multi scale method was adopted to analyze the nonlinear amplitude frequency response of the beam. The applicability of the stiffness model was discussed and parameter sensitivity studies on the dynamic response were carried out by the SDOF model for a cantilever beam. Results indicate that the new stiffness model provides an efficient tool to study the vibrational nonlinearities introuduced by the breathing crack. Therefore, it might be used to develop a nonlinear identification method of a crack in a beam.     

高速冷轧机辊系非线性动力学模型及控制参数优化

综合运用轧制过程动态轧制力模型、轧机系统分段非线性弹性力模型和分段非线性摩擦力模型,建立了考虑非线性因素耦合的高速冷轧机辊系动力学模型,采用平均法求解幅频响应方程,研究了轧机系统主要参数对轧机垂直振动的影响。分析结果表明：动态轧制力一次项刚度越小,轧机系统固有频率越大;动态轧制力三次项刚度不为零时,轧机系统出现明显跳跃现象;非线性弹性力起主导作用时,易发生跳跃现象;非线性摩擦力越大,轧机系统振动幅值越小,分段特性减弱;外扰力幅值越大,振动幅值越大,振动越剧烈;线性阻尼越大,振动幅值越小且减小幅度越缓慢。     

Using nonlinear springs to reduce the whirling of a rotating shaft

Vibrations in rotating machinery cause many problems such as fatigue of the rotating components, excessive noise, or transmission of vibration to the supporting structure. A major source of this vibration is out-of-balance forces and this paper proposes that the rotor response is reduced by suspending the machine on nonlinear springs. In the field of vibration isolation, nonlinear mounts have been proposed which have the same static stiffness as an equivalent linear support, i.e. load bearing capability, but at the same time offer a low dynamic stiffness, i.e. a lower natural frequency. Thus the isolator is effective over an increased frequency range. These mounts are known in the literature as high-static-low-dynamic-stiffness (HSLDS) mechanisms. In this paper, the rotor is suspended on a hardening HSLDS spring to considerably reduce the critical speeds to values far away from the operating speed. The advantages of the nonlinear supports are demonstrated using a simple two degree of freedom rotating machine model consisting of a rigid disk, and shafts, bearings and supports that are flexible but have negligible mass. Following a linear analysis to highlight the benefits of a low dynamic stiffness, an approximate analytical solution of the nonlinear equation of motion is presented. A comparison between the linear and nonlinear response shows the effectiveness of the nonlinear supports. Finally, the problems that occur if the nonlinearity is too strong are highlighted.     

On the Dynamics of Lubricated Cylindrical Roller Bearings,Part II: Linear and Nonlinear Vibration Analysis

This article is the second part of two companion papers. In the first article, curve-fitted relations of stiffness and damping coefficients of a single roller-to-race contact of lubricated roller bearings were developed. In the present work, these relations are applied to a rotor–bearing system. Two cases are studied to investigate the influence of lubricated cylindrical roller bearings on the vibration characteristics of the rotor system. In the first case, lubricated contacts are simulated as a linear spring–damper model. The overall stiffness and damping matrices are calculated by using the dynamic coefficients of individual load sharing rollers. These matrices are used in the finite element analysis of flexible rotor. In the second case, the nonlinear structural vibration of a lubricated cylindrical roller bearing is studied. Equations of motion of bearing elements are derived using the Lagrange equation. A nonlinear load–deflection contact model developed through the derived curve-fitted relations of dynamic coefficients is used in the equations of motion. Equations of motion are solved by a fourth-order Runge-Kutta integration method. The response of bearing elements under free vibration and due to rotating unbalance is studied for damped and undamped cases. Furthermore, results obtained using elastohydrodynamic finite and infinite contact theories are compared.     

Nonlinear finite element analysis of a laminated cylindrical shell with transverse matrix cracks

A clamped laminated cylindrical shell is presented to investigate nonlinear structural behavior involving geometrically nonlinear deformation. In the investigation, transverse matrix cracks are considered in the stiffness of the laminated cylindrical shell. Stiffness degradation is examined for several laminated angles and transverse crack density. Micro-mechanics theory on the composite material was used to derive the degraded stiffness of the laminated cylindrical shell due to the crack density. Iterative numerical scheme was developed to calculate the degraded composite stiffness which is a complicated relation with the crack density. A nonlinear finite element program was developed using 3-D degenerated shell element and the fist order shear deformation theory to consider the large deformation of the clamped laminated cylindrical shell. The updated Lagrangian method is used for nonlinear finite element analysis. Nonlinear structural responses of the laminated cylindrical shell were examined for various stacking sequences and crack density under transversely loaded pressure. Also, the effect of crack opening/closed was considered in the examination. Through this study, it is realized that the transverse matrix crack causes moderate stiffness reduction and affects the responses of the composite shell.     

含内阻的拉杆组合转子双稳态振动特性

为揭示含内阻组合转子复杂的双稳态振动特性,基于拉格朗日方程推导了含轮盘接触、非线性油膜力及内阻的组合转子非线性运动控制方程.采用升速和降速相结合的方法研究了组合转子跨2阶临界转速的非线性动力学行为及内阻机理.研究结果表明:组合转子双稳态振动特征显著,内阻导致出现双稳态现象的转速区间明显向低转速方向移动,在分析组合转子振...