基于Volterra积分方程Taylor展开的卷积型非粘滞阻尼系统响应的时程分析方法

考虑一个具有卷积型非粘滞阻尼特性的多自由度系统响应的时程分析问题。非粘滞阻尼模型假设阻尼力与质点速度的时间历程相关,数学表达式为阻尼力等于质点速度与某一核函数的卷积,该模型为常用的粘滞阻尼模型的一般化形式。以一种在特定区间内求解第二类Volterra方程的Taylor展开法为基础,对所分析时段中各时间点的响应函数逐步作Taylor展开,代入卷积核来消去运动方程的积分项,通过求解推导出的时变线性方程组完成对卷积型阻尼模型系统的时程响应分析。数值算例验证了该方法的有效性。该方法增大时间步长可以大幅减少计算量,计算精度有所下降。     

基于微分求积法求解非粘滞阻尼系统的时程响应

研究一种含有指数型非粘滞阻尼线性多自由度振动系统的时程分析问题。该非粘滞阻尼模型假设阻尼力与质点速度的时间历程相关,数学表述为质点速度与核函数的卷积。由于阻尼模型的改变,常用的数值积分方法（如Newmark-β法、Wilson-θ法）不能直接应用于这种非粘滞阻尼系统。基于一种无条件稳定的微分求积方法,给出了这种非粘滞阻...     

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。     

非平稳随机激励下结构体系动力可靠度时域解法

将结构动力方程写成状态方程形式,采用精细积分法对其进行数值求解,导出了非平稳激励下结构随机响应的时域显式表达式,该过程的计算量仅相当于两次确定性时程分析的计算量.基于该显式表达式,结合首次超越失效准则,提出了非平稳随机激励下结构体系动力可靠度的数值模拟算法.与功率谱方法相比,该方法无需同时在时频域内进行大量数值积分,也无需引入关于响应过程跨越界限次数概率分布,以及各失效模式相关性等方面的假定.通过数值算例,对比了该方法与泊松过程法、马尔可夫过程法、传统蒙特卡罗法的计算精度和计算效率,结果显示该方法具有理想的精度和相当高的效率.     

大型非经典阻尼系统的动态解耦方法

提出了大型非经典阻尼系统动力分析的动态解耦方法，同时在特征值问题的求解和动力响应的计算中完全避免复数运算．方法适用于无阻尼陀螺系统、非经典阻尼系统（包括阻尼陀螺系统），且不论系统亏损与否．得到了揭示阻尼作用的有趣的理论结果和实用的数值方法     

非参数概率系统非平稳随机响应研究

对复杂系统的测量和知识的有限性造成的不确定很难完全由随机参数模型进行描述,采用随机矩阵模型更具有一般性和合理性.本文应用随机矩阵模拟不确定线性动力系统有限元模型中质量阵、阻尼阵和刚度阵的概率不确定性.综合运用虚拟激励法和精细时程积分法建立了非参数概率系统非平稳随机响应的有效计算方法.数值模拟结果表明,对于高精度制造,模型的不确定性是不能忽略的.本文提出的算法为此类问题求解提供了一条有效途径.     

结构非平稳随机响应分析的快速虚拟激励法

虚拟激励法能够方便地应用于结构非平稳随机响应分析,但在每个离散频点处都涉及到虚拟激励作用下动力方程的时程积分,对于大型复杂结构,其计算量是难以接受的。将结构动力方程写成状态方程形式,采用精细积分法对状态方程进行数值求解,导出了结构动力响应关于离散时刻处激励的显式线性表达式。利用这一显式表达式,只需要变换离散时刻处的激励数值,就可以方便快捷地求出新的激励作用下的结构动力响应。效率分析和数值算例表明,相对于传统虚拟激励法,本文提出的改进算法在求解非平稳激励下结构随机振动方面具有更高的计算效率。     

含分数阻尼特性元件的多体系统动力学研究

在绝对节点坐标体系下研究了具有分数导数阻尼特性元件的多体系统动力学建模、求解 问题. 采用基于绝对节点坐标的无闭锁效应剪变梁单元离散柔性构件，建立了含常数质量矩 阵的系统动力学方程, 并采用数值耗散可控的广义a方法求解. 通过数值算 例计算，对比研究了算法参数与阻尼项的分数指数对系统动力学响应的影响规律. 该方法可以进一步扩展到众多工程实际问题研究中.     

转子系统的平稳／非平稳随机地震响应分析

应用虚拟激励法结合精细时程积分计算了转子系统受平稳／非平稳随机地震激励的动力响应。采用虚拟激励分析将平稳随机激励转化为稳态简谐激励，将非平稳随机激励转化为瞬态确定性激励，即使对于非对称的油膜刚度阵和阻尼阵，算法仍然简单高效，并得到精确的结果。     

串联电气设备支架隔震体系地震响应半解析法

通过并联橡胶隔震支座，建立串联高架电气设备支架隔震体系及力学模型，应用分布参 数梁振动理论, 通过边界条件引入集中参数，推导其频率方程，并用数值方法求得 频率及振型. 应用Betti定律，推导具有集中分布参数柔性节点的多节电瓷型高压电 气设备的正交条件，得到广义质量及广义载荷. 将该串联隔震体系的非比例阻尼分 解为比例阻尼部分和非比例阻尼部分，应用Hamilton原理推导出非比例阻尼部分等效振型阻 尼比，实现串联电气设备支架隔震体系振动方程的解耦，然后通过振型叠加法求得结构 的地震响应. 最后应用该半解析法与有限元数值积分法对一330kV电压互感器地震响应进行 分析. 结果表明:该隔震体系能显著减小电气设备的地震响应，同时该半解析法求解的地震响 应与有限元数值积分求解的结果相一致，说明该隔震体系的有效性与该半解析方法求解非 比例阻尼串联电气设备支架隔震体系地震响应的正确性.     

A Galerkin method for distributed systems with non-local damping

In this paper, a non-local damping model including time and spatial hysteresis effects is used for the dynamic analysis of structures consisting of Euler–Bernoulli beams and Kirchoff plates. Unlike ordinary local damping models, the damping force in a non-local model is obtained as a weighted average of the velocity field over the spatial domain, determined by a kernel function based on distance measures. The resulting equation of motion for the beam or plate structures is an integro-partial-differential equation, rather than the partial-differential equation obtained for a local damping model. Approximate solutions for the complex eigenvalues and modes with non-local damping are obtained using the Galerkin method. Numerical examples demonstrate the efficiency of the proposed method for beam and plate structures with simple boundary conditions, for non-local and non-viscous damping models, and different kernel functions.     

黏性阻尼系统时域响应灵敏度及其一致性研究

时域响应灵敏度分析是时域梯度优化算法的基础. 灵敏度分析通常只涉及对设计变量的微分运算, 但时域响应灵敏度问题还涉及时间域的离散化. 因此, 微分和离散的先后顺序可能对时域响应灵敏度结果产生影响. 针对黏性阻尼系统时域响应灵敏度求解问题, 基于改进精细积分方法, 分别推导了先微分后离散和先离散后微分两种伴随变量方法. 其中, 先微分后离散法首先对由伴随变量构造的增广函数微分, 再利用改进精细积分方法在各离散时间点求解时域响应灵敏度; 而先离散后微分方法则首先在各离散时间点引入残值方程构造增广函数, 再对各增广函数进行微分以求解时域响应灵敏度. 通过数值算例验证了所提出方法的有效性和准确性, 并与传统基于Newmark的方法进行比较. 结果表明, 积分方案、数值离散误差以及离散和微分的先后顺序共同影响灵敏度的一致性误差. 综合考虑精度、效率和一致性问题, 基于改进精细积分的先微分后离散伴随变量法表现更优, 最适合应用于黏性阻尼系统时域梯度优化算法.      

力锤敲击作用下内嵌自主移动钢球欧拉梁碰撞减振性能研究

结合内嵌自主移动质量子系统梁／板实验平台实验结果,对力锤敲击作用下,内嵌自主移动钢球欧拉梁碰撞减振系统进行研究。采用线性弹簧-阻尼模型模拟钢球与梁之间的碰撞机制,通过分析建立了整个碰撞系统的分段线性动力学方程;运用无量纲化、假设模态法及高阶模态截断等方法导出系统的状态空间方程。数值计算结果表明,内嵌自主移动钢球对欧拉梁...     

The analysis of arbitrarily-damped linear mechanical systems

Summary The analysis of arbitrarily-damped linear mechanical systems is the subject of this paper, the main issue being the analysis of nondecouplable systems. It is well known that decouplable systems occur when the damping matrix happens to be a linear combination of the mass and stiffness matrices. Systems with this type of damping are said to have proportional damping, which nevertheless seldom occurs in practice, but many a damped system is analyzed under the assumption that it is proportionally damped. In fact, this property allows the analyst to study these systems using the same approach as that applicable to their undamped counterparts. In this paper, we show that proportional damping need not be assumed in order to analyze the system at hand with the same approach as used to analyze undamped systems. Moreover, we propose an algorithm to determine the natural frequencies, the damped frequencies and the damping ratios of an n-degree-of-freedom damped system, that does not require the casting of the system into first-order form. In this way, the characteristic equation is derived naturally as a 2n-degree polynomial, computing its roots being then straightforward. Furthermore, we propose a semigraphical method to ease this calculation, which should be attractive to practicing engineers. Received 5 April 1999; accepted for publication 7 May 1999     

Wave dispersion and dissipation performance of locally resonant acoustic metamaterials using an internal variable model

Engineering structures for different dispersion and dissipation levels of wave propagation use internal variable models, which may enhance the performance of acoustic metamaterials (AMMs). In this study, the wave dispersion and dissipation performance of AMMs is studied using an anelastic displacement fields (ADF) model. A symmetric state-space method based on Floquet-Bloch’s theorem for a nonviscously damped unit cell is developed. The study also constructs Bloch’s eigenvalue problems built from the symmetric state-space formulation to obtain the wavevector-dependent damped frequency and damping ratio for wave propagation analysis of periodic structures. The effects of wave dispersion and dissipation on the performance of AMMs are studied by using two numerical examples of mass-in-mass lattice systems containing multiple resonators. It is shown that nonviscous damping increases the wave dispersion performance of AMM. It is also shown that the metadamping phenomenon enhances the wave dissipation performance of AMM. It is demonstrated that the new method in symmetric form is applicable for performance analysis of periodic phononic crystal.     

MOTION OF THE DAMPED FOUCAULT PENDULUM

本文建立运动方程,得到了阻尼傅科摆的解析解,并对解的性质进行了一些探究.文中建立的模型是在理想单摆的基础上增加了科里奥利力和与速度成正比的阻尼力.     

结构动力响应数值算法耗散和超调特性设计

对结构动力响应数值计算问题提出引入多个自由参数来获得所希望的算法特性. 多参数的一个明显的好处就是在算法设计上有更大的自由空间. 利用这些自由参数获得了两个新的无条件稳定、有二阶精度的、有好的耗散和没有超调的单步时间直接积分算法. 在存在阻尼情况下基于有限差分分析理论证明了新算法的这些特性. 其中一个有高频渐进消去特性，且在有阻尼情况下与Houbolt方法相比对高频有更强的耗散. 另一个在低频极限无耗散，高频耗散可以用一自由参数控制. 超调分析结果显示两个新算法都不显示超调，而HHT方法不仅有速度超调，还有位移超调. 最后使用一些算例并通过与传统方法的比较数值地验证了理论分析结果.     

Interaction of a Traveling Pressure Perturbation with a Boundary Layer

The interaction between a traveling pressure perturbation and a laminar compressible boundary layer is investigated for a perturbation level higher than that needed to initiate steady-state flow separation. It is found that if the velocity of the pressure perturbation is fairly high the flow may remain unseparated and its direction of motion determines the nature of the perturbation propagation in the boundary layer. It is shown that even in the linear approximation the perturbations are mainly induced by the linear wall layer and not by the critical layer, which always remains nonlinear. It is also found that in the unsteady case shortwave perturbation oscillations are damped with time while the longwave ones grow and that the growth of the perturbations with time amplifies their damping along the streamwise coordinate while damping reduces it.     

Equivalent linearizations for practical hysteretic systems

Experimental testing of a friction damped base isolation system has indicated a need for a new model of friction damping and for an appropriate equivalent linearization technique. The model for the damping adopted is a combination of viscous damping, constant Coulomb friction and linear Coulomb friction.This model is incorporated into the equation of motion for a single-degree-of-freedom system and the exact solutions are given for free vibrations and for steady-state vibrations excited by a harmonic force. The exact solution is taken as a basis for an equivalent linearization technique that can be used in conjunction with conventional design spectra for a practical design of such a system.