基于机器学习的动力学环境预测方法

为了研究建立同一结构在两个不同系统中振动响应之间的映射关系模型的基本问题,以两种边界条件组成的两个系统为例,从其动力学方程出发,建立了基于时域、频域描述的映射关系的力学模型.为求解两个系统的映射关系模型,引入以统计学习理论为基础的机器学习方法——支持向量机法,借助于决策函数可以从一种边界条件预测同一结构在另一种边界条件下结构的响应,并通过实验证明了该方法的有效性.     

功能梯度材料梁自由振动的线性与非线性振动

基于数值模拟和理论分析两种方法,研究了功能梯度材料(functional gradient materials,FGM)梁自由振动下的线性与非线性振动问题。通过解析法求解了FGM梁在经典理论下以及一阶剪切理论下的力学行为,得到了FGM梁在简支和固端约束下的固有频率。理论分析了不同边界条件、不同梁理论下、梯度指数、长细比等因素对于FGM梁固有频率的影响;不论经典梁理论还是一阶剪切理论,随着梯度指数的增加,FGM梁的固有频率都随之减小。通过ABAQUS仿真模拟,得到FGM梁数值模拟下的非线性固有频率。将理论解与数值解进行对比,完善力学模型。在多种理论下,利用解析法和数值模拟的方法,给出FGM梁结构振动响应的线性与非线性解。     

正弦电磁场中磁性材料力学特性分析

将电磁场理论与弹性力学理论相结合，分析了磁性材料在正弦电磁场中的力学特性。首先，介绍磁场力的一般数学表达式，随后依据电力设备磁路的对称性给出其磁场力简化数学模型，再根据电力设备中磁性材料的物理和几何特点建立其力学模型，最后将上述两种模型相结合导出描述正弦电磁场中磁性材料力学特性的数学模型，并给出其数值计算方法。这些数学模型可用于对由于磁路中存在涡流而产生的大型电力变压器铁心及其它电力设备振动和噪声进行定性和定量分析。     

轴对称压电圆板的非线性动力响应

基于Von Karman板理论和压电材料力学,考虑横向剪切变形,建立了轴对称压电圆板的非线性运动方程,提出了相应的力学与电学边界条件.求解时,首先应用Galerkin方法,将非线性偏微分运动方程转化为仅含时间变量的非线性常微分方程.然后,应用Newmark-β方法将时间函数离散,整个问题应用Newtoni迭代法求解.算例中,求得了压电圆板线性振动基频,验证了方程和求解方法的可靠性,讨论了压电效应、几何非线性、结构尺寸、力学和电学荷载等因素对板非线性动力响应的影响.     

稳恒扩展裂纹尖端的弹粘塑性场

采用弹粘塑性力学模型代替通常的弹塑性模型，对于I型和Ⅱ型问题，分别求得了不可压缩材料中平面应变动态扩展裂纹尖端的指数奇异性场和对数奇异性场，消除了弹塑性解中存在的塑性激波。通过数值计算，分别求得了两种奇异属性的分界线，建立起统一的裂纹尖端奇异性场。     

三参数粘弹性地基上层合板的自由和强迫振动

基于三参数粘弹性地基模型及Reddy高阶剪切变形板理论,用双重Fourier级数形式解求得粘弹性地基上四边简支对称正交及反对称斜交层合板的各模态自由振动频率的解析解,以及这两种层合板在任意横向动荷载作用下动力响应的半解析解。通过参数分析讨论了粘弹性地基参数、边厚比等因素对自振频率及动力响应的影响。结果表明,地基的剪切刚度和压缩刚度提高了板的自振频率而降低了板的振动幅值,地基的粘性作用不可忽略。     

结构非线性振动及其控制系统的等效力学模型研究

研究了结构非线性振动及其控制系统的等效力学模型建立问题,对结构进行等效线性化处理;对状态变量的观测,仅测量结构的前几个位移。将随机激励和观测噪声等维化处理后,导出了结构非线性振动及其控制系统的等效力学模型。通过等效力学模型的应用研究,得出了多高层结构在风与地震作用下的多维与一维等效力学模型、等效振型力学模型及其线性力学模型,给出了等效力学模型在多高层结构自适应抗风抗震控制中的应用。     

磁饱和时发电机组转子轴系电磁激发参数共振

应用机电分析动力学的方法和推广的撙和良日－麦克斯收方程找到了发电机气隙磁场能的解析式，建立了具有周期系数横、扭耦合振动的非线性常微分方程组，求得了一性方程组满足参数共振时的解，分析了发电机组参数对共振特性的影响，揭示了一些新现象。     

集簇式组合梁桥振动特性的弹性力学解

基于二维弹性力学理论,研究了集簇式组合梁桥的自由振动特性。将组合梁桥等效为二维的层合梁模型,分别建立了各单层梁的自由振动微分方程,求得了简支边界条件下各层梁的弹性力学解。假定集簇式剪力件是刚性连接件,用待定集中力代替其提供的水平剪力,根据组合梁上、下表面的边界条件和层间应力、位移的协调关系,得到了简支组合梁桥自由振动特性的精确解析解,通过数值计算分析了簇钉间距对组合梁桥固有频率的影响。研究结果表明:理论结果与有限元ABAQUS解具有较好的一致性,最大误差仅为2.3%;组合梁桥的固有频率随着簇钉间距的减小而增大,当簇钉间距较小时,频率变化趋势不明显。其结果可为组合梁桥的合理设计提供参考。     

一种旋转载体用角速率传感器模型

提出了一种利用旋转载体自身的旋转作为驱动，从而敏感旋转载体横滚或俯仰的角速率传感器模型，并运用陀螺力学理论建立传感器的动力学方程、求得解析解，对传感器进行动力学误差分析。     

Model reduction for reacting flow applications

A model reduction approach based on Galerkin projection, proper orthogonal decomposition (POD), and the discrete empirical interpolation method (DEIM) is developed for chemically reacting flow applications. Such applications are challenging for model reduction due to the strong coupling between fluid dynamics and chemical kinetics, a wide range of temporal and spatial scales, highly nonlinear chemical kinetics, and long simulation run-times. In our approach, the POD technique combined with Galerkin projection reduces the dimension of the state (unknown chemical concentrations over the spatial domain), while the DEIM approximates the nonlinear chemical source term. The combined method provides an efficient offline–online solution strategy that enables rapid solution of the reduced-order models. Application of the approach to an ignition model of a premixed H₂/O₂/Ar mixture with 19 reversible chemical reactions and 9 species leads to reduced-order models with state dimension several orders of magnitude smaller than the original system. For example, a reduced-order model with state dimension of 60 accurately approximates a full model with a dimension of 91,809. This accelerates the simulation of the chemical kinetics by more than two orders of magnitude. When combined with the full-order flow solver, this results in a reduction of the overall computational time by a factor of approximately 10. The reduced-order models are used to analyse the sensitivity of outputs of interest with respect to uncertain input parameters describing the reaction kinetics.     

Similarity solutions for the evolution of polydisperse droplets in vortex flows

A new mathematical analysis of the dynamics of evaporating sprays in the vicinity of a vortex flow field is presented. The governing equations for a polydisperse spray evaporating in an unsteady viscous vortex flow are formulated using the sectional approach. First, new similarity solutions are found for the dynamics of the spray in a mono-sectional framework. It is shown that similarity for the droplets’ drag term exists, and an explicit model for the drag is found using perturbation theory. Numerical simulations are conducted to validate the main assumptions of the analytic approach adopted in this study. An extension of the mono-sectional solution of the spray equations to a polydisperse spray solution is then derived and the dynamics of polydisperse spray in an Oseen type vortex are presented. It is shown that for a given radial location, the droplets in each section reach a maximal radial velocity due to the effect of vorticity. A simple model is derived for the prediction of this maximal radial velocity of the droplets using perturbation theory, which agrees very well with the full similarity solution. The present study shows that spray dynamics is highly affected by the droplets’ size, but also by the spray initial size distribution, even when the same Sauter mean diameter is considered. This may have far reaching implications, especially in spray combustion applications.     

Error estimate for influence of model reduction of nonlinear dissipative autonomous dynamical system on long-term behaviours

Introduction Forsomenonlineardynamicalsystems,especiallyincomplexmechanicalvibrationand fluid structureinteractionsystems,thefiniteelementmethodisoftenusedtoapproachthe solutionofthegoverningequationduetothedifficultyofdescribingsysteminanalyticalform.Asa…     

Criticality of bifurcation in the tuned axial–torsional rotary drilling model

We study the bifurcation characteristics of a lumped-parameter model of rotary drilling with 1:1 internal resonance between the axial and the torsional modes which leads to the largest stability thresholds. For this special case, the two-degree-of-freedom model for the drill-string reduces to an effectively single-degree-of-freedom system facilitating further analysis. The regenerative effect of the cutting action due to the axial vibrations is incorporated through a delayed term in the cutting force with the delay depending on the torsional oscillations. This state dependency of the delay introduces nonlinearity in the current model. Steady drilling loses stability via a Hopf bifurcation, and the nature of the bifurcation is determined by an analytical study using the method of multiple scales. We find that both subcritical and supercritical Hopf bifurcations are present in this system depending on the choice of operating parameters. Hence, the nonlinearity due to the state-dependent delay term could both be stabilizing or destabilizing in nature, and the self-interruption nonlinearity is essential to capture the global behavior. Numerical bifurcation analysis of a global axial–torsional model of rotary drilling further confirms the analytical results from the method of multiple scales. Further exploration of the rotary drilling dynamics unravels more complex phenomena including grazing bifurcations and possibly chaotic solutions.     

热化学非平衡辐射流场数值研究

从耦合辐射的轴对称热化学非平衡N-方程出发,采用双温度、11组元反应气体模型,耦合“线-线”精细辐射模型,利用隐式NND有限差分格式和时间预处理技术数值求解了FIREII飞船热化学非平衡辐射流场,得到了有关辐射和辐射光谱计算结果,并与有关文献的实验结果和计算结果进行了比较。     

认识稀薄气体动力学

以通俗易懂的方式介绍了空气动力学当气体间断分子效应显著时发展起来的特殊分文——稀薄气体动力学、讨论了非平衡现象与稀薄气体动力学的关系．通过与8速度气体模型的间断Boltzmann方程的对比，解释了Boltzmann方程碰撞项的物理意义和数学困难，简要综述了其一般解法、讨论了分子在物体表面的反射和问题的边界条件，着重介绍了直接模拟Monte Carlo(DSMC)方法和为克服低速稀薄流动(如MEMS中流动)中模拟困难的信息保存(IP)方法。     

One-dimensional dynamically consistent gradient elasticity models derived from a discrete microstructure: Part 1: Generic formulation

This paper is the first in a series of two that focus on gradient elasticity models derived from a discrete microstructure. In this first paper, a new continualization method is proposed in which each higher-order stiffness term is accompanied by a higher-order inertia term. As such, the resulting models are dynamically consistent. A new parameter is introduced that accounts for the nonlocal interaction between variables of the discrete model and of the continuous model. When this parameter is set to proper values, physically realistic behavior is obtained in statics as well as in dynamics. In this sense, the proposed methodology is superior to earlier approaches to derive gradient elasticity models, in which anomalies in the dynamic behavior have been found. A generic formulation of field equations and boundary conditions is given based on Hamilton's principle. In the second paper, analytical and numerical results of static and dynamic response of the second-order model and the fourth-order model will be treated.     

Direct sensitivity analysis of multibody systems with holonomic and nonholonomic constraints via an index-3 augmented Lagrangian formulation with projections

Optimizing the dynamic response of mechanical systems is often a necessary step during the early stages of product development cycle. This is a complex problem that requires to carry out the sensitivity analysis of the system dynamics equations if gradient-based optimization tools are used. These dynamics equations are often expressed as a highly nonlinear system of ordinary differential equations or differential-algebraic equations, if a dependent set of generalized coordinates with its corresponding kinematic constraints is used to describe the motion. Two main techniques are currently available to perform the sensitivity analysis of a multibody system, namely the direct differentiation and the adjoint variable methods. In this paper, we derive the equations that correspond to the direct sensitivity analysis of the index-3 augmented Lagrangian formulation with velocity and acceleration projections. Mechanical systems with both holonomic and nonholonomic constraints are considered. The evaluation of the system sensitivities requires the solution of a tangent linear model that corresponds to the Newton–Raphson iterative solution of the dynamics at configuration level, plus two additional nonlinear systems of equations for the velocity and acceleration projections. The method was validated in the sensitivity analysis of a set of examples, including a five-bar linkage with spring elements, which had been used in the literature as benchmark problem for similar multibody dynamics formulations, a point-mass system subjected to nonholonomic constraints, and a full-scale vehicle model.     

Multi-layer analytic solution for k-ω model equations via a symmetry approach

Despite being one of the oldest and most widely-used turbulence models in engineering computational fluid dynamics (CFD), the k-ω model has not been fully understood theoretically because of its high nonlinearity and complex model parameter setting. Here, a multi-layer analytic expression is postulated for two lengths (stress and kinetic energy lengths), yielding an analytic solution for the k-ω model equations in pipe flow. Approximate local balance equations are analyzed to determine the key parameters in the solution, which are shown to be rather close to the empirically-measured values from the numerical solution of the Wilcox k-ω model, and hence the analytic construction is fully validated. The results provide clear evidence that the k-ω model sets in it a multilayer structure, which is similar to but different, in some insignificant details, from the Navier-Stokes (N-S) turbulence. This finding explains why the k-ω model is so popular, especially in computing the near-wall flow. Finally, the analysis is extended to a newly-refined k-ω model called the structural ensemble dynamics (SED) k-ω model, showing that the SED k-ω model has improved the multi-layer structure in the outer flow but preserved the setting of the k-ω model in the inner region.