最小能量多重仿射紧框架的特征

引入多个加细函数生成的最小能量多重仿射框架的概念.运用矩阵理论和时频分析方法,给出对应于最小能量多重仿射框架的多重加细函数所满足的条件.得到最小能量多重仿射紧框架的特征与构造方法.对原多重加细函数和最小能量多小波仿射框架做正交变换,得到新的多重加细函数和对应的最小能量多重仿射框架.     

非线性振动系统周期解的数值分析

用直接数值积分法求非线性振动系统的周期解,求解时对初始条件进行迭代,使它与终点条件相一致.积分时间区间(即周期)或运动方程中的某些参数,也可在迭代过程中随同变化,积分方法是变步长的. 用这种“打靶”法求周期解,所需计算工作量相对较少.其中误差主要来源于数值积分,故不难估计并控制它足够小.这种方法可处理各种类型的振动问题,如单自由度和多自由度系统的自由无阻尼振动、强迫振动、自激振动和参数振动等等;也能求得不稳定解和那些对参数变动十分敏感的解.解的稳定性根据相关的周期系数微分方程来研究.求共振曲线或其他振动特性曲线时,利用插值方法并自动调节步长来定出迭代始值. 为了阐明这种方法的通用性,计算了若干例子.非线性的描述可用解析函数或任何其他形式,例如分段线性函数.文中还就所得周期解指出了非线性振动的一些值得注意的性质.部分计算结果与已有的近似解或实验结果作了比较.     

三维横向流体诱发直管振动的数值模拟

基于有限体积法和有限元法,结合动网格控制技术,建立了横向流体作用下三维弹性直管流致振动计算的数值模型,实现了计算结构动力学与计算流体力学之间的联合仿真．首先,通过对刚性管的静止绕流计算,研究了网格离散方式和不同湍流模型对圆柱类结构静止绕流流场特征的影响和预测能力,得到了适用于双向耦合分析的CFD模型;其次,利用基于双向流固耦合方法的流致振动模型,计算并分析了流体力与结构位移间的相位关系,指出流体力与位移间的相位差是由流体力引起的,同时对双向耦合和单向耦合进行了比较分析;最后通过对直管流致振动的数值计算,联合管表面压力、尾流区时均速度、分离角等时均量,分析了尾流区的流场特征.     

任意边界条件下圆柱厚壳自由振动分析的空间变量变换法

本文提出一种一般解析方法——空间变量变换法,用以求解任意边界条件下圆柱厚壳自由振动问题.运用本文方法对悬臂圆柱厚壳的自振特性作了计算,计算结果与薄壳理论相应结果及试验值作了比较.理论分析和计算结果表明,本文方法具有很好的收敛性和精确性,可以推广用于分析梁、板、壳的自由振动.     

非线性振动分析的均向量场法

通过构造向量形式的振动微分方程组，利用均向量场（AVF）法得到振动响应的向量差分迭代格式.该离散格式能够保能量，同时具有二阶精度的特征，从而给出非线性振动问题的均向量场法.介绍了均向量场法的基本步骤.在建立AVF格式时，对于微分方程中若干常见的项，直接给出相应的映射项.应用均向量场法研究了非线性单摆问题和Kepler(开普勒)问题，数值结果说明了该方法保能量和具有长时间求解能力的特性.     

基于Bootstrap方法的VaR区间估计

本文介绍了非参数方法中基于自助法的三种区间的估计方法,并将它们应用到金融资产的VaR计算上.自助法很好地克服了历史模拟法的一些局限性.本文对上证综合指数(IA0001)进行了VaR计算的实证分析,计算了VaR点估计和区间估计,并比较了几种计算方法各自的特点,得出了一些有意义的结果.     

基于非线性能量阱的双频激励非线性系统减振

针对某型民用航空发动机双频带激励特点,建立了单自由度线性振子耦合非线性能量阱（nonlinear energy sink,NES）的动力学模型.根据典型双转子发动机在巡航状态下低、高特征频率比（1∶4.74）,为系统设定双频带简谐外激励.利用四阶Runge-Kutta算法,研究了耦合NES振子时系统的振动抑制特征,并从外激励频率对系统主振子动能、系统总体能量的影响等方面,与未耦合NES系统、耦合线性动力吸振器两种情况下的数值计算结果进行对比分析.研究结果表明NES对双频带外激励具有更好的振动抑制效果,用NES降低航空发动机振动有可行性.     

基于GMRES算法的弹性结构强耦合小变形流激振动分析

使用混合广义变分原理,将基于Lagrange表述的小位移变形结构振动问题与基于Euler描述的不可压缩粘性流动问题,统一在功率平衡的框架下建立流固系统的耦合控制方程．用有限元格式做空间离散后,再用广义梯形法将有限元控制方程转化为增量型的线性方程组,该方程组的系数矩阵具有非对称性,其中元素含对流效应和时间因子．将GMRES算法与振动分析的Newmark法和流动分析的Hughes预测多修正法结合,发展成一种基于GMRES-Hughes-Newmark的稳定算法,用于计算具有复杂几何边界的强耦合流激振动问题．以混流式水轮机叶道为数值算例的计算表明,模拟结果与试验实测结果吻合较好．     

弹性约束边界条件下矩形蜂窝夹芯板的自由振动分析

蜂窝夹芯板在飞行器、高速列车等领域有广泛的用途，对其开展振动分析具有明确的科学价值及工程意义.为区别于诸简支等传统约束边界，提出了弹性约束边界下蜂窝夹芯板结构的自由振动特性分析方法.具体来说，首先通过将蜂窝夹芯层等效为各向异性板，将夹芯板问题转变为三层板结构.进一步地，将板结构的位移场函数由改进的二维Fourier级数表示，并基于能量原理的Rayleigh Ritz法得到结构的固有频率和固有振型，理论预测结果与数值模拟分析吻合较好.提出的理论模型可用于系统讨论约束边界对蜂窝夹芯结构自由振动特性的影响，为此类结构的约束方案设计提供理论依据.     

模糊集对分析用于脱硫除尘器的综合评价

提出了锅炉脱硫除尘器综合评价的模糊集对分析方法.评述了方法的基本原理和计算步骤,通过实例介绍了方法的应用.评价实例结果表明模糊集对分析用于脱硫除尘器综合评价是可行的.与密切值法相比,所得评价结果相同.该法具有计算简便和实用的特点.     

高精度参数估计问题

对高精度参数的估计问题进行了研究.在观测数据无误差的情况下,将微分方程组转化为线性方程组,利用矩阵的奇异值分解给出了参数的最优解.在有观测数据误差的情况下,采用高斯-牛顿迭代法进行求解,给出了改进的高斯-牛顿法和阻尼最小二乘算法;通过灰色估计法给出了模型的初始解,通过微分方程数值解法计算模型迭代过程中误差和偏导数.最后,通过对迭代过程中的状态变量引入误差项,导出了基于总体最小二乘的高斯-牛顿迭代法,从系统的角度解决了观测时间有误差下的参数估计问题.     

Statistical energy analysis by finite elements for middle frequency vibration

Statistical energy analysis (SEA) is commonly used in industry to predict high-frequency vibrational response of structures. Since only local modes are used in SEA, only high-frequency responses can be predicted. This study extends SEA to the middle-frequency region by additionally using global modes. Methods using impedance matrices that can be found by NASTRAN are developed. Then the results are post processed to determine coupling loss factors.     

Stabilization of the wave equation with acoustic and delay boundary conditions

In this paper, we consider the wave equation on a bounded domain with mixed Dirichlet-impedance type boundary conditions coupled with oscillators on the Neumann boundary. The system has either a delay in the pressure term of the wave component or the velocity of the oscillator component. Using the velocity as a boundary feedback it is shown that if the delay factor is less than that of the damping factor then the energy of the solutions decays to zero exponentially. The results are based on the energy method, a compactness-uniqueness argument and an appropriate weighted trace estimate. In the critical case where the damping and delay factors are equal, it is shown using variational methods that the energy decays to zero asymptotically.     

A matrix-splitting method for symmetric affine second-order cone complementarity problems

The affine second-order cone complementarity problem (SOCCP) is a wide class of problems that contains the linear complementarity problem (LCP) as a special case. The purpose of this paper is to propose an iterative method for the symmetric affine SOCCP that is based on the idea of matrix splitting. Matrix-splitting methods have originally been developed for the solution of the system of linear equations and have subsequently been extended to the LCP and the affine variational inequality problem. In this paper, we first give conditions under which the matrix-splitting method converges to a solution of the affine SOCCP. We then present, as a particular realization of the matrix-splitting method, the block successive overrelaxation (SOR) method for the affine SOCCP involving a positive definite matrix, and propose an efficient method for solving subproblems. Finally, we report some numerical results with the proposed algorithm, where promising results are obtained especially for problems with sparse matrices.     

几何耦合对直升机桨叶液压减摆器等效线性阻尼的影响研究

建立了直升机前飞时,计入变距/挥舞/摆振几何耦合和力-速度非线性关系的液压减摆器分析模型;用4阶龙格-库塔法在时域内计算减摆器的轴向速度;根据减摆器轴向速度的瞬态响应成分,利用基于富里叶级数的移动矩形窗方法计算了减摆器等效线性阻尼。结果表明,存在变距/挥舞/摆振几何耦合的液压减摆器,在直升机前飞时其等效线性阻尼将大幅度下降。     

Damping properties of composites based on interpenetrating polymer networks formed in the presence of compatibilizing additives

From the results of an analysis of the viscoelastic characteristics of semi-interpenetrating polymer networks (semi-IPNs) that are based on a crosslinked polyurethane and a linear polystyrene and are formed in the presence of compatibilizing additives (oligourethane dimethacrylate and ethylene glycol monomethacrylate), their damping ability is est mated. Such parameters as the tangent of mechanical loss (tan δ) at the glass-transition temperature, the temperature interval of effective damping (where tan δ > 0.3), and the loss area under the loss modulus vs. temperature plots are used as the criteria of damping ability. It is shown that the introduction of the compatibilizing additives to the semi-IPNs extends the interval of their effective damping temperature. By varying the composition of the material and the amount of the compatibilizing additives, it is possible to realize a purposeful selection of vibration-damping materials for solving specific technological problems. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 4, pp. 545–558, July–August, 2006.     

Guaranteed affine lower bound functions for multivariate polynomials

The construction of affine lower bound functions for multivariate polynomials based on Bernstein polynomials is presented. These bound functions are guaranteed also in the presence of rounding errors and (interval) data uncertainties. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Residual saturated porous media – from oscillating water blobs to waves in ground earth

A model for wave propagation in residual saturated porous media is presented distinguishing enclosed fluid clusters with respect to their eigenfrequency and damping properties. The additional micro-structure information of cluster specific damping is preserved during the formal upscaling process and allows a stronger coupling between micro- and macro-scale than characterisation via eigenfrequencies alone. A numerical example of sandstone filled with air and liquid clusters of different eigenfrequency and damping distributions is given. If energy dissipation due to viscous damping dominates energy storage due to cluster oscillations, the damping distribution is more influential than the eigenfrequency distribution and vice versa. Spreading the damping distribution around a constant mean value supported the effect of capillary forces and spreading the eigenfrequency distribution around a constant mean value supported the effect of viscous damping in the investigated samples. For a wide distribution of the liquid clusters' damping properties, two damping mechanisms of propagating waves occur at the same time: damping due to viscous effects (for highly damped clusters) and energy storage by cluster oscillations (for underdamped clusters). (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Comparison of numerical homogenization techniques in BT-CFO multiferroic particle composites

This work is restricted to linear material behavior, i.e. the structure is considered to be in a perfectly poled state. Different numerical homogenization methods are investigated and used to calculate effective properties of a 0-2 composite modelled in reprensentative volume elements. Bariumtitanate (BT) and cobaltferrite (CFO) are employed in the Finite Element model, where the roles of matrix and inclusion are mutable in principle. Mixed magnetoelectromechanical boundary conditions based on different homogenization theories are applied to the model. The calculated macroscopic behaviors described by the different approaches are compared and presented in the paper. The special focus is on the prediction of coefficients of magnetoelectric coupling with respect to an optimization of the structural arrangement of the composite. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Principal component analysis on interval data

Summary  Real world data analysis is often affected by different types of errors as: measurement errors, computation errors, imprecision related to the method adopted for estimating the data. The uncertainty in the data, which is strictly connected to the above errors, may be treated by considering, rather than a single value for each data, the interval of values in which it may fall: the interval data. Statistical units described by interval data can be assumed as a special case of Symbolic Object (SO). In Symbolic Data Analysis (SDA), these data are represented as boxes. Accordingly, purpose of the present work is the extension of Principal Component analysis (PCA) to obtain a visualisation of such boxes, on a lower dimensional space pointing out of the relationships among the variables, the units, and between both of them. The aim is to use, when possible, the interval algebra instruments to adapt the mathematical models, on the basis of the classical PCA, to the case in which an interval data matrix is given. The proposed method has been tested on a real data set and the numerical results, which are in agreement with the theory, are reported.