关于复阻尼理论的两个基本问题

本文讨论有关复阻尼理论的两个重要的基本问题:复阻尼的实质问题和复阻尼结构动力响应的时域解法问题.为探究这两个问题,先建立了频率相关粘性阻尼理论,然后再给出复阻尼振子强迫振动响应的正确和适用的解答.     

ANLYTICAL SOLUTION OF THERMOELASTIC DAMPING IN RECTANGULAR MINDLIN MICRO PLATES 1)

首次给出了四边简支的 Mindlin 矩形微板热弹性阻尼的解析解. 基于考虑一阶剪切变形的 Mindlin 板理论和单向耦合热传导理论建立了微板热弹性耦合自由振动控制微分方程. 忽略温度梯度在面内的变化,在上下表面绝热边界条件下求得了用变形几何量表示的温度场的解析解. 进一步将包含热弯曲内力的结构振动方程转化为只包含挠度振幅的四阶偏微分方程. 利用特征值问题之间在数学上的相似性,在四边简支条件下给出了用无阻尼 Kirchhoff 微板的固有频率表示的 Mindlin 矩形微板的复频率解析解,从而利用复频率法求得了反映热弹性阻尼水平的逆品质因子. 最后,通过数值结果定量地分析了剪切变形、材料以及几何参数对热弹性阻尼的影响 规律. 结果表明,Mindlin 板理论预测的热弹性阻尼小于 Kirchhoff 板理论预测的热弹性阻尼. 两种理论预测的热弹性阻尼之间的差值在临界厚度附近十分显著. 另外,随着微板的边/厚比增大,Mindlin 微板的热弹性阻尼最大值单调增大,而 Kirchhoff 微板的热弹性阻尼最大值却保持不变.     

基于频率相关黏性阻尼模型的复模态叠加法

黏性阻尼模型存在每周期耗散能量与外激励频率相关的缺陷, 复阻尼模型时域计算结果存在发散现象. 为克服上述两种阻尼模型的不足, 在复阻尼模型基础上, 依据时频域转化原则推导了频率相关黏性阻尼模型. 频率相关黏性阻尼模型不仅具有每周期耗散能量与外激励频率无关的优点, 还保证了结构位移时程的稳定收敛. 混合结构由具有不同阻尼特性的材料组成, 其阻尼矩阵为非比例矩阵, 无法直接采用实模态叠加法. 根据频率相关黏性阻尼模型与复阻尼模型的转换关系, 提出了适用于混合结构的基于频率相关黏性阻尼模型的复模态叠加法. 算例分析结果表明, 与基于黏性阻尼模型的复模态叠加法相比, 基于频率相关黏性阻尼模型的复模态叠加法不仅计算结果唯一, 且不增加矩阵维度, 具有较高的计算效率. 小阻尼情况下, 两种方法的计算结果近似相等, 且与复阻尼模型的频域计算结果一致. 当阻尼比较大时, 两种方法的计算结果差异增大, 但频率相关黏性阻尼模型的复模态叠加法与复阻尼模型的频域计算结果仍保持一致.      

基于卷积非粘滞阻尼模型的超高层结构风效应分析

有限元方法中相对于对结构质量与刚度特性的描述,结构阻尼的描述仍具有较大的模糊性。随着新型建筑材料与复杂结构体系的发展,以及对计算机模拟要求的提高,阻尼作用的机理与相应阻尼模型的研究成为值得关注的问题。基于一种阻尼力与质点速度历程相关的卷积非粘滞阻尼模型,采用微分求积求解算法,对一个大型复杂超高层建筑结构的风振响应进行了分析,并与常用的比例粘滞阻尼模型进行了对比。对卷积非粘滞阻尼力模型系统的响应特征进行了分析,特别是该模型的松弛效应对结构响应的影响。另外,作为将这种新阻尼模型应用于实际工程的一次探索,本文采用微分求积算法,建立了一套可将该阻尼模型及其求解算法嵌入通用有限元软件的求解系统,可用于复杂结构的动力响应分析。     

On a Rayleigh Wave Equation with Boundary Damping

In this paper an initial-boundary value problem for a weakly nonlinear string (or wave) equation with non-classical boundary conditions is considered. One end of the string is assumed to be fixed and the other end of the string is attached to a dashpot system, where the damping generated by thedashpot is assumed to be small. This problem can be regarded as a simple model describing oscillations of flexible structures such as overhead transmission lines in a windfield. An asymptotic theory for a class ofinitial-boundary value problems for nonlinear wave equations is presented. Itwill be shown that the problems considered are well-posed for all time t. A multiple time-scales perturbation method incombination with the method of characteristics will be used to construct asymptotic approximations of the solution. It will also be shown that all solutions tend to zero for a sufficiently large value of the damping parameter. For smaller values of the damping parameter it will be shown how the string-system eventually will oscillate. Some numerical results are alsopresented in this paper.     

State-vector equation with damping and vibration analysis of laminates

Based on the modified mixed Hellinger-Reissner(H-R)variational principle for elastic bodies with damping,the state-vector equation with parameters is directionally derived from the principle.A new solution for the harmonic vibration of simply supported rectangular laminates with damping is proposed by using the precise integration method and Muller method.The general solutions for the free vibration of underdamping,critical damp and overdamping of composite laminates are given simply in terms of the linear damping vibration theory.The effect of viscous damping force on the vibration of com- posite laminates is investigated through numerical examples.The state-vector equation theory and its application areas are extended.     

求解非比例阻尼体系复模态的实模态摄动法

根据工程结构的实际情况,建立了非比例阻尼结构体系复模态特性的近似求解方 法------实模态摄动法. 这一方法以复Ritz向量展开原理为基础, 把非比例阻尼结构体系复模态特性的分析过程分解为两个基本步骤,首先以结构体系的实模 态向量构建复Ritz向量的求解子空间,然后通过非线性复代数方程组的求解代替扩阶后的复 特征值方程的求解,从而简化了计算过程.通过两个算例表明: 这一方法不仅计算简便，而且具有较高的计算精度和执行效率, 对于复杂的非比例阻尼系统是很适用的，具有一定的工程应用价值.     

一种计算非比例阻尼结构地震响应的新方法

在非比例阻尼结构地震响应分析中, 直接积分法和强迫解耦法均具有鲜明的优缺点, 考虑到计算精度和计算效率的均衡, 提出了一种可用于非比例阻尼结构地震响应计算的新方法---多自由度模态方程方法. 同时, 通过推导指出了直接积分法和强迫解耦法是所提出方法的两种特殊形式, 从而构建了非比例阻尼结构地震响应计算方法的完整理论体系. 最后采用数值算例验证了多自由度模态方程方法在非比例阻尼结构地震响应计算中的有效性, 并说明其可以通过合理划分结构分区来调节计算精度和计算效率.      

Characterization of the Damping Behavior of a Nanoindentation Instrument for Carrying Out Dynamic Experiments

A new displacement modulation based dynamic indentation method is demonstrated and shown to be effective for viscoelastic characterization of a glassy polymer. The analysis of dynamic experiments requires a complete understanding of the measuring system’s dynamic characteristics especially the damping. Accordingly, an improved method, based on the use of a wire spring, is developed for determining the damping characteristics. In general, damping in an indentation instrument is contributed by two elements: the eddy current damping from the electromagnetic loading coil and the squeeze film damping from the capacitive displacement transducer. Therefore, a method to determine the relative contribution from the different damping elements present in the system is demonstrated and the results are compared with the calibration obtained from the wire spring method. Finally, dynamic indentation tests are carried out on a glassy polymer to obtain the complex modulus; the values of which are compared with those obtained from bulk dynamic mechanical analysis (DMA) tests. Storage modulus values are found to be in good agreement with bulk data but some divergence in the case of loss modulus is observed. The calibration procedure of the measuring instrument is critically examined in view of these observations. Overall, displacement modulation based dynamic indentation is shown to be a promising method for viscoelastic characterization at the micron length scales. An erratum to this article can be found at     

附加自由阻尼结构系统的有限元分析和拓扑优化设计方法研究

给出了一种适用于车身等复杂附加阻尼结构系统的有限元建模和动态特性分析方法,包括附加自由阻尼薄壁结构和附加阻尼材料粘弹性特性的有限元建模方法以及附加阻尼结构动态特性的有限元分析方法。在此基础上,又以强迫振动响应最小为优化设计目标,给出了一个附加阻尼结构的拓扑优化设计方法,包括优化设计问题的列式和适用的求解算法。通过对一个简单薄壁构件和一个车身地板上的附加阻尼结构的拓扑优化设计,验证了提出的有限元分析和拓扑优化设计方法的有效性。     

结构阻尼模型及系统时域动响应

振动界对经典的非频变结构阻尼模型一直有种种争议,本文检查了它的前提并指出将该模型推广到系统时域动响应分析时导致的悖论.为了提供结构阻尼系统的时域动响应实用分析方法,文中分别提出了基于响应优势谱成份的粘性阻尼近似模型和基于粘弹性理论的三参数频变结构阻尼模型;它们既可逼近结构阻尼缓频变的特性,又可保证系统的时域动响应具有因果性.     

Mindlin 矩形微板的热弹性阻尼解析解

首次给出了四边简支的 Mindlin 矩形微板热弹性阻尼的解析解. 基于考虑一阶剪切变形的 Mindlin 板理论和单向耦合热传导理论建立了微板热弹性耦合自由振动控制微分方程. 忽略温度梯度在面内的变化,在上下表面绝热边界条件下求得了用变形几何量表示的温度场的解析解. 进一步将包含热弯曲内力的结构振动方程转化为只包含挠度振幅的四阶偏微分方程. 利用特征值问题之间在数学上的相似性,在四边简支条件下给出了用无阻尼 Kirchhoff 微板的固有频率表示的 Mindlin 矩形微板的复频率解析解,从而利用复频率法求得了反映热弹性阻尼水平的逆品质因子. 最后,通过数值结果定量地分析了剪切变形、材料以及几何参数对热弹性阻尼的影响 规律. 结果表明,Mindlin 板理论预测的热弹性阻尼小于 Kirchhoff 板理论预测的热弹性阻尼. 两种理论预测的热弹性阻尼之间的差值在临界厚度附近十分显著. 另外,随着微板的边/厚比增大,Mindlin 微板的热弹性阻尼最大值单调增大,而 Kirchhoff 微板的热弹性阻尼最大值却保持不变.      

Immersed boundary method for unsteady kinetic model equations

Predicting unsteady flows and aerodynamic forces for large displacement motion of microstructures requires transient solution of Boltzmann equation with moving boundaries. For the inclusion of moving complex boundaries for these problems, three immersed boundary method flux formulations (interpolation, relaxation, and interrelaxation) are presented. These formulations are implemented in a 2‐D finite volume method solver for ellipsoidal‐statistical (ES)‐Bhatnagar‐Gross‐Krook (BGK) equations using unstructured meshes. For the verification, a transient analytical solution for free molecular 1‐D flow is derived, and results are compared with the immersed boundary (IB)‐ES‐BGK methods. In 2‐D, methods are verified with the conformal, non‐moving finite volume method, and it is shown that the interrelaxation flux formulation gives an error less than the interpolation and relaxation methods for a given mesh size. Furthermore, formulations applied to a thermally induced flow for a heated beam near a cold substrate show that interrelaxation formulation gives more accurate solution in terms of heat flux. As a 2‐D unsteady application, IB/ES‐BGK methods are used to determine flow properties and damping forces for impulsive motion of microbeam due to high inertial forces. IB/ES‐BGK methods are compared with Navier–Stokes solution at low Knudsen numbers, and it is shown that velocity slip in the transitional rarefied regime reduces the unsteady damping force. Copyright © 2015 John Wiley & Sons, Ltd.     

混联Ⅰ型惯容系统基于李鸿晶谱的地震响应分析

针对设有混联Ⅰ型惯容系统的耗能结构基于李鸿晶谱的响应分析较为繁琐的问题,提出求解地震响应的简明封闭解法,并研究了惯容系统基本参数对减震性能的影响。首先,建立惯容系统和结构之间的微分型本构关系,并运用复模态法和虚拟激励法获得结构系列响应的统一解。其次,将结构系列响应的功率谱密度函数精确转化为复特征值及结构自振频率平方和表示的二次分解式,进而获得响应0阶～2阶谱矩的简明封闭解。最后,通过数值算例验证了所提方法的正确性及计算的高效性,对惯容系统参数的研究表明,当惯容系数和阻尼系数越大,结构减震效果越好,而刚度系数对结构的减震效果取决于惯容系统名义圆频率与结构自振圆频率的比值,当两者比值为0.9时减震效果最好。     

Damping Characterization and Viscoelastic Behavior of Laminated Polymer Matrix Composites Using a Modified Classical Lamination Theory

The damping property of materials can be defined as the ratio of dissipated energy over the total strain energy during the loading–unloading process, called the specific damping capacity (SDC). In this study, in order to characterize the damping properties of materials, a test plan in designed to extract the SDC of a single layer composite from hysteresis data. The theory of linear viscoelasticity incorporates a varying Young’s Modulus by using a complex stiffness modulus. Considering different lay-ups, the modified classical lamination plate theory is modified to represent both stiffness and SDC of laminates. The results are compared with experimental results for symmetric laminated specimen. This evaluation shows a very good agreement between theoretical and experimental results in the range of low frequency loading from 0.2 to 4 Hz. The complex compliance matrix changes the governing equation in to a complex form which contains both stiffness and damping properties.     

基于FPK方程的减摆器的非线性阻尼测试方法

受高斯白噪声外激的一阶非线性动力学方程能通过求解对应的FPK方程得到精确稳态解．本文基于这一结果导出减摆器非线性阻尼力与系统速度输出的概率结构的关系,将动力学系统中非线性阻尼力参数的测试问题转化测量系统的概率结构,并通过仿真进行了验证．     

液体边界层对平板结构振动阻尼效应分析

本文分析了液体边界层对平板振动的阻尼效应，基于液体的Stokes边界层理论，建立了考虑液体边界层阻尼效应的平板振动单自由度系统运动方程，利用Laplace变换方法求解了运动方程，得到了平板结构的位移响应解答，制作了一个单自由度质量-弹簧系统来测量水体粘滞阻尼效应，并将理论与试验结果进行了对比分析，表明Stokes边界层理论能较好模拟水体的粘滞阻尼特性，边界层阻尼明显减小了结构的动力响应，本文最后讨论了所提的分析方法的适用范围．     

离散型设置粘弹阻尼结构的复模态综合法

本文利用粘弹材料的本构方程,对粘弹阻尼结构的模态分析表达式进行了理论推导,进而将Craig的复模态综合法推广到粘弹阻尼系统.本文还发展了一种处理刚体模态的方法,从而克服了Craig法的不足,解决了含粘性阻尼、粘弹阻尼的复杂结构的隔振设计问题.     

组合结构振动的等效阻尼比

本文采用滞后阻尼的假定，在获得组合结构含有滞后阻尼系数的复频率方程后，进而导出了一种分析组合结构体系效阻尼比的方法，只要在实数范围内，采用通常的特征值方法或所选用２的软件。便可获得各种组合结构任一阶等铲阻尼比，简单且实用，本文最后给出了一个组合悬臂结构和组合高层建筑筒体结构的实例。     

The auto-adjustable damping method for solving nonlinear equations

I.IntroductionTherearealotofnonlinearproblemsinengineering.Forexamples,theheattrallsfel'with'nonlinearradiation-convectionboundaryalldlimitedheatcapacity,thenonlinearhydrodynamicsandaerodynamics,thenonlillearstrtlcturaldynamicresponsesandtheIihe.Itisalmostimpossibletosolvethe11onlinearequationsbydirectmethodexceptfi)rsomespecialnonlinearequations.Thegeneralapproachislinearizingtheequationsandformingvariousiterationprocedures.Forthestronglynonlillearproblems,thesolutionobtainedintheitcrativep…