基于特征正交分解的非定常气动力建模技术

采用特征正交分解(proper orthogonal decomposition,POD)方法,建立了基于状态空间的非定常气动力降阶模型,并耦合结构方程,建立了降阶的气动弹性系统,开展了颤振分析的初步研究,计算效率提高了2～3个数量级.具体过程是:首先获取全阶系统的频域快照构成关联矩阵,通过对关联矩阵进行奇异值分解提取流场模态(或流场基),对低能量模态截断形成降阶子空间,并将其映射到全阶系统,从而形成基于状态空间的降阶非定常气动力模型.对气动弹性标模AGARD445.6进行算例验证,证明了降阶方法正确,可以提供高效、高精度的气动弹性分析.     

功能梯度材料动力学问题的POD模型降阶分析

为了快速分析非均质材料结构在复杂载荷作用下的动态响应,提出一种模型降阶方法,只需计算结构在简单均质材料情况下的动力学问题,进而用其计算结果对非均质材料结构进行分析.首先,采用结构内部任意一点处的材料参数值作为整个结构的材料参数,利用有限元分析软件计算该均质材料结构在动态载荷作用下的位移场建立数据库,该数据库包含计算模型各个节点(自由度为N)在某时间段内L个时刻的位移;其次,对数据库中的信息按照时间离散的特定方式组集成瞬像矩阵,并利用特征正交分解方法对其进行分解,得到该模型的L个特征正交基底,选取其中能反应模型主要特征的H个(其中HL?N)作为一组最优基底,通过这组基底建立模型的低阶离散控制方程;最后,求解低阶离散微分方程组,得到功能梯度材料结构在复杂载荷作用下的位移场.文中分别给出二维和三维算例,比较了降阶模型和全阶模型计算结果,验证了该方法的有效性,并且计算效率能提高1～2个数量级.     

基于特征正交分解的一类瞬态非线性热传导问题的新型快速分析方法

提出了一种基于特征正交分解(POD)和有限元法的瞬态非线性热传导问题的模型降阶快速分析方法, 建立了导热系数随温度变化的一类瞬态非线性热传导问题有限元格式的POD降阶模型. 在隐式时间推进方法的基础上有效结合单元预转换方法和多级线性化方法发展了一种加速求解瞬态非线性热传导降阶模型的新型计算方法,并通过二维和三维算例验证了该方法的准确性和高效性. 研究结果表明: (1)降阶模型解的均方根误差在经过初始时段轻微的脉动后稳定于0.01%以下, 而其计算效率比有限元全阶模型提高2$\sim $3个数量级, 并且自由度数量(DOFs)愈大提高的幅度也愈加显著; (2)新型算法解决了常规算法在计算非线性降阶模型时加速性能差的问题, 即使是在DOFs比较小的时候也能够明显提高计算效率; (3)常数边界条件下得到的POD模态可以用来建立相同求解域在各种复杂时变边界条件下的瞬态非线性热传导降阶模型, 并对其传热过程和温度场进行快速准确的分析与预测, 具有很好的工程应用价值.      

基于特征正交分解的一类瞬态非线性热传导问题的新型快速分析方法

提出了一种基于特征正交分解(POD)和有限元法的瞬态非线性热传导问题的模型降阶快速分析方法,建立了导热系数随温度变化的一类瞬态非线性热传导问题有限元格式的POD降阶模型.在隐式时间推进方法的基础上有效结合单元预转换方法和多级线性化方法发展了一种加速求解瞬态非线性热传导降阶模型的新型计算方法,并通过二维和三维算例验证了该方法的准确性和高效性.研究结果表明:(1)降阶模型解的均方根误差在经过初始时段轻微的脉动后稳定于0.01%以下,而其计算效率比有限元全阶模型提高2～3个数量级,并且自由度数量(DOFs)愈大提高的幅度也愈加显著;(2)新型算法解决了常规算法在计算非线性降阶模型时加速性能差的问题,即使是在DOFs比较小的时候也能够明显提高计算效率;(3)常数边界条件下得到的POD模态可以用来建立相同求解域在各种复杂时变边界条件下的瞬态非线性热传导降阶模型,并对其传热过程和温度场进行快速准确的分析与预测,具有很好的工程应用价值.     

基于边界元方法的气动弹性降阶模型及仿真

传统气动弹性的时域计算耗费了大量时间,为了提高计算效率,本文发展了基于边界元方法的降阶模型技术。首先基于边界元方法建立非定常流场的求解模型,结合特征值分析技术建立了非定常气动力的低阶模型;然后,利用边界元方法建立了气动网格和结构网格之间的信息转换矩阵;最后将非定常气动力降阶模型和结构动力学方程联合,建立了气动弹性系统的低阶状态空间模型。将所发展的降阶模型方法应用于NACA0012翼型的非定常气动力求解中,结果表明降阶模型可以在保证原系统计算精度的同时提高了计算效率;将降阶模型技术应用到三维机翼的气动弹性响应计算中,在系统阶数仅为12阶的情况下可以得到与原系统一致的极限环响应,说明降阶模型技术在求解气动弹性问题中的巨大优势。     

基于SCI/ERA方法的高效气动力降阶模型

由正交Walsh函数构造Walsh-单信号-复合-输入,对其作用下的计算流体力学响应采用单信号-复合-输入/特征系统实现算法SCI/ERA(Single-Composite-Input/Eigensystem Realization Algorithm)辨识得到离散时间非定常气动力状态空间降阶模型。通过对Isogai机翼剖面气动弹性算例的计算证明该方法具有和非定常计算流体力学方法相当的精度同时模型维数降低2个数量级;在模型构造时间上,SCI/ERA方法比脉冲/ERA方法计算效率提高24%,同时内存占用减小34%;由理论分析可知当耦合结构模态数目增加时,SCI/ERA方法所需的计算开销增幅远小于脉冲/ERA方法;采用频域平衡特征正交分解BPOD(Balanced Proper Orthogonal Decomposition)方法可以准确地从降阶模型中提取出一个低频二次降阶模型,同时保持与原模型相当的精度。二次降阶后模型维数进一步减小88%。     

应用POD和Padé拟合的线性动力学系统辨识

提出了一种线性动力学系统辨识方法.应用Padé多项式对系统的动刚度曲线进行拟合,通过最小二乘法确定Padé多项式中的系数矩阵,利用遗传算法确定出Padé拟合式中的参数.通过比较系统动刚度矩阵的理论公式和Padé拟合式,辨识得到系统的质量阵、刚度阵和阻尼阵.当系统阶数较高时,可结合POD降阶技术对系统进行辨识,该方法适用于全阶模型和降阶模型.数值仿真算例表明,论文方法具有较高的精度和较好的鲁棒性.     

一种高效的叶轮机叶片气动阻尼计算方法

运用叠加原理, 发展了一种可以运用于小振幅运动的叶 轮机叶片非定常气动力降阶模型, 并将该模型与传统的能量法相结合, 提出了一种叶轮机叶 片气动阻尼的高效求解方法. 运用该方法求解叶轮机叶片的气动阻尼系数, 对某个频率、某 个模态只需要进行一次非定常计算, 就可以求出所有叶间振动相角下的气动阻尼系 数, 提高了气动阻尼的求解效率. 在STCF4和NASA Rotor 67两个算例上运用非定常雷诺平均N-S(RANS)方程和提出的降阶模型进行了对比计算. 算例表明, 在小振幅下该方法的计算结果与RANS方程计算得到的气动阻尼系数能很 好地吻合, 而计算效率相比多通道非定常RANS方程计算提升了近一个数量级, 并且 该方法还可以运用于有失谐情况的颤振分析, 在工程上有较高的应用价值.     

尾流激励的叶片气动力降阶模型

气动力降阶模型是研究叶片气动弹性振动快速高效的新方法。现有气动力降阶模型的研究主要集中在叶片颤振方面，没有涉及更为常见的上游尾流激励的叶片振动问题。本文提出基于Volterra级数的尾流激励叶片气动力降阶模型，为尾流激励下叶片振动和动静叶干涉振动研究提供了新的思路。采用行波法简化尾流的参数个数，用阶跃信号法识别降阶模型的核函数。二维叶片的算例结果表明，本文方法可以较准确地描述尾流激励引起的叶片气动力振荡，而且计算效率极高。     

基于非线性状态空间辨识的气动弹性模型降阶

高维、非线性气动弹性系统的模型降阶是当前气动弹性力学与控制领域的研究热点之一.然而国内外现有的非线性模型降阶方法仍存在辨识算法复杂、精度有待提高等问题.本研究提出了一种基于非线性状态空间辨识的跨音速气动弹性模型降阶方法.首先,该方法基于非定常空气动力的单位脉冲响应数据,采用特征系统实现算法对非线性状态空间模型的线性动力学部分进行系统辨识.其次,引入状态和控制输入的非线性函数,采用优化算法对非线性函数的系数矩阵进行优化,进而得到考虑非线性效应的空气动力降阶模型.为了验证该降阶模型在预测跨音速气动弹性力学行为的精确性,本文以三维机翼为研究对象,分别从基于非线性降阶模型的气动力辨识、跨声速颤振边界计算和极限环振荡预测三方面进行了算例验证,并与现有的模型降阶方法进行了对比,进一步说明本文所提出方法的有效性.研究结果表明,该降阶模型对上述三类问题的计算精度与直接流-固耦合方法相吻合,可用于高效预测飞行器跨声速气动弹性力学行为.     

POD-identification reduced order model of linear transport equations for control purposes

Intrusive reduced order modeling techniques require access to the solver's discretization and solution algorithm, which are not available for most computational fluid dynamics codes. Therefore, a nonintrusive reduction method that identifies the system matrix of linear fluid dynamical problems with a least-squares technique is presented. The methodology is applied to the linear scalar transport convection-diffusion equation for a 2D square cavity problem with a heated lid. The (time-dependent) boundary conditions are enforced in the obtained reduced order model (ROM) with a penalty method. The results are compared and the accuracy of the ROMs is assessed against the full order solutions and it is shown that the ROM can be used for sensitivity analysis by controlling the nonhomogeneous Dirichlet boundary conditions.     

基于区域分解的环肋圆柱壳-圆锥壳组合结构振动分析

提出了一种区域分解法来分析不同边界条件下环肋骨圆柱壳-圆锥壳组合结构的振动特性.首先把组合壳体分解为自由的圆柱壳、圆锥壳段;视环肋骨为离散元件,根据肋骨与圆柱壳段之间的变形协调条件,将肋骨的动能和应变能附加于圆柱壳段能量泛函中.然后基于分区广义变分和最小二乘加权残值法将所有分区界面的位移协调方程引入到组合壳体的能量泛函中.圆柱壳段、圆锥壳段位移变量的周向和轴向分量分别采用Fourier级数和Chebyshev多项式展开.以自由-自由、自由-固支和固支-固支边界条件的环肋骨组合壳体为例,采用区域分解法分析了其自由振动及在不同激励下的振动响应.通过与有限元软件ANSYS结果进行对比,发现两种方法计算结果非常吻合,验证了区域分解方法的计算精度和高效性.     

Study of techniques for obtaining continuous models from 2D discrete reduced‐order state‐space CFD models

The application of unsteady computational fluid dynamics (CFD) codes to aeroelastic calculations leads to a large number of degrees of freedom making them computationally expensive. Reduced‐order models (ROMs) have therefore been developed; an ROM is a system of equations which is able to reproduce the solutions of the full set of equations with reasonable accuracy, but which is of lower order. ROMs have been the focus of research in various engineering situations, but it is only relatively recently that such techniques have begun to be introduced into CFD. In order for the reduced systems to be generally applicable to aeroelastic calculations, it is necessary to have continuous time models that can be put into discrete form for different time steps. While some engineering reduction schemes can produce time‐continuous models directly, the majority of methods reported in CFD initially produce discrete time or discrete frequency models. Such models are restricted in their applicability and in order to overcome this situation, a continuous time ROM must be extracted from the discrete time system. This process can most simply be achieved by inverting the transformation from continuous to discrete time that was initially used to discretize the CFD scheme. However an alternative method reported in literature is based on continuous time sampling, even when this is not used for the initial discretization of the CFD code. This paper focuses on one particular method for ROM generation, eigensystem realization algorithm (ERA), that has been used in the CFD field. This is implemented to produce a discrete time ROM from a standard CFD code, that can be used to investigate methods for obtaining continuous ROMs and the limitations of the resulting models. Copyright © 2006 John Wiley & Sons, Ltd.     

A genetic algorithm optimization of ring-stiffened cylindrical shells for axial and radial buckling loads

In this research, the general axial and radial buckling optimization of ring-stiffened cylindrical shells is implemented by the genetic algorithm (GA). The stiffened shell is subjected to four constraints including the fundamental frequency, the structural weight, the axial buckling load, and the radial buckling load. In addition, six design variables including shell thickness, number of stiffeners, stiffeners width and height, stiffeners eccentricity distribution order, and stiffeners spacing distribution order are considered. In analytical solution, the Ritz method is applied and stiffeners are treated as discrete elements. The effect of the weighting coefficients of the objective functions on the optimum solution is studied. The results show that optimized stiffening a cylindrical shell leads to a lower structural weight, higher natural frequencies, and larger axial and radial buckling loads, simultaneously. In addition, the upper and lower bounds of the design variables influence the optimum results considerably. It is also found that the distributions of eccentricity and spacing of the stiffeners influence the magnitudes of the axial and radial buckling loads considerably.     

曲线加筋Kirchhoff-Mindlin板自由振动分析

相比传统加筋板,曲线加筋板能够更充分地发挥材料力学性能.在加筋板力学分析中,厚板通常采用Reissner-Mindlin理论,然而当板厚较薄时易出现剪切自锁,离散的Kirchhoff-Mindlin理论采用假设剪切应变场可避免该问题.针对曲线加筋Kirchhoff-Mindlin板自由振动分析,采用离散的Kirchhoff-Mindlin三角形单元和Timoshenko曲梁单元分别模拟板和加强筋,根据板的位移插值函数及筋板交界面的位移协调条件,建立基于板单元位移自由度的有限元方程.为了验证方法的有效性和准确性,采用直线加筋薄板、曲线加筋薄板和厚板3种模型进行算例研究,通过收敛性和精度分析来选择合理的有限元网格密度.直线加筋薄板前20阶固有频率均与文献结果吻合良好;曲线加筋板算例中,本文方法满足收敛条件的板单元数目为2469,Nastran模型板单元数目为6243;本文所得曲线加筋板固有频率与Nastran计算结果最大误差为3.4%.研究结果表明,本文方法无需筋板单元共节点,可使用较少的有限元网格数量,并能够保证计算精度;在离散Kirchhoff-Mindlin三角形板单元基础上构造Timoshenko梁单元可同时适用于曲线加筋薄板与厚板自由振动分析.     

VIBRATION AND ACOUSTIC RADIATION FROM SUBMERGED STIFFENED SPHERICAL SHELL WITH DECK-TYPE INTERNAL PLATE

Based on the motion differential equations of vibration and acoustic coupling system for thin elastic spherical shell with an elastic plate attached to its internal surface, in which Dirac-δ functions are employed to introduce the moments and forces applied by the attachment on the surface of shell, by means of expanding field quantities as Legendre series, a semi-analytic solution is derived for the vibration and acoustic radiation from a submerged stiffened spherical shell with a deck-type internal plate, which has a satisfactory computational effectiveness and precision for an arbitrary frequency range. It is easy to analyze the effect of the internal plate on the acoustic radiation field by using the formulas obtained by the method proposed. It is concluded that the internal plate can significantly change the mechanical and acoustic characteristics of shell, and give the coupling system a very rich resonance frequency spectrum. Moreover, the method can be used to study the acoustic radiation mechanism in similar structures as the one studied here.     

Free vibrations of rotating composite conical shells with stringer and ring stiffeners

In this paper, an analytical solution for the free vibration of rotating composite conical shells with axial stiffeners (stringers) and circumferential stiffener (rings), is presented using an energy-based approach. Ritz method is applied while stiffeners are treated as discrete elements. The conical shells are stiffened with uniform interval and it is assumed that the stiffeners have the same material and geometric properties. The study includes the effects of the coriolis and centrifugal accelerations, and the initial hoop tension. The results obtained include the relationship between frequency parameter and circumferential wave number as well as rotating speed at various angles. Influences of geometric properties on the frequency parameter are also discussed. In order to validate the present analysis, it is compared with other published works for a non-stiffened conical shell; other comparison is made in the special case where the angle of the stiffened conical shell goes to zero, i.e., stiffened cylindrical shell. Good agreement is observed and a new range of results is presented for rotating stiffened conical shells which can be used as a benchmark to approximate solutions.     

基于非线性分析的加肋板肋条位置无网格优化

在加肋板无网格模型中, 肋条的位置对各种工况下加肋板受力性能的影响至关重要. 文章基于一阶剪切变形和移动最小二乘法理论提出一种考虑非线性影响的加肋板无网格模型, 并利用遗传算法优化肋条位置. 首先, 采用离散节点分别对平板和肋条进行离散, 得到加肋板的无网格离散模型; 其次, 通过冯·卡门大挠度理论得到非矩形板几何非线性问题的弯曲控制方程; 再次, 通过哈密顿原理得到加肋非矩形板自由振动问题的控制方程; 最后引入遗传算法, 以肋条的位置为设计变量、非矩形加肋板中心点挠度最小或自振频率最大为目标函数, 对肋条位置进行优化. 在考虑了几何非线性影响的肋条位置优化过程中, 肋条位置改变时只需重新计算位移转换矩阵, 避免了网格重构. 本文以全局荷载下单肋条菱形板为例与理论解进行对比, 进行有效性验证. 再以板的中点挠度最小和自振频率最大为优化目标, 对局部荷载作用下不同形状、不同肋条布置方式的加肋板进行优化, 分析方法的收敛性及稳定性.      

两端铰接的细长柔性圆柱体涡激振动响应特性数值研究

目前细长柔性圆柱体涡激振动响应的研究方法主要包括实验方法、计算流体动力学方法以及半经验模型方法. 鉴于实验方法研究成本较高、计算流体动力学方法计算时间较长,本文基于尾流振子模型对线性剪切来流下两端铰接的细长柔性圆柱体涡激振动响应特性进行了半经验模型方法研究. 先建立了柔性圆柱体结构振子以及尾流振子之间的耦合模型,紧接着基于二阶精度中心差分格式对耦合模型先离散后迭代进行求解. 对不同剪切参数下柔性圆柱体涡激振动响应的振动波长、振动频率、振动位移以及响应频率随时间的变化特性等参数进行了分析. 分析结果表明:圆柱体的涡激振动响应由驻波和行波混合组成. 当无量纲弯曲刚度较小时,在圆柱体两端附近,驻波占主导;而在圆柱体中间段附近,行波占主导. 当无量纲弯曲刚度较大时,在圆柱体整个长度区间上均为驻波占主导. 随着剪切参数的增大,振动位移以及振动波长均逐渐减小,而振动频率和频率带宽均逐渐增大.