基于质量阵Cholesky分解的发动机悬置系统优化

根据拉格朗日方程,建立发动机悬置系统的动力学模型;基于广义坐标下质量矩阵的Cholesky分解,设计正则模态矩阵;结合悬置系统的能量分布矩阵和工程约束条件,在最小二乘原则下,对支撑参数进行优化求解;在发动机的振动激励源分析的基础上,通过对悬置系统进行动力学仿真,证明了基于质量阵Cholesky分解的发动机悬置系统优化方法的可行性及有效性。     

求解结构动力学方程的一种辛格式及其优化

论文将四阶隐式高斯勒让德辛龙格库塔法应用于线性结构动力学方程,并对其进行了算法优化.针对n个自由度的动力学初值问题,先通过消元得到n阶线性代数方程组,利用其系数矩阵稀疏对称正定的性质,采用预处理共轭梯度法求解,其中预条件子由系数矩阵的不完全Cholesky分解得到.通过与中心差分法、Newmark-β法及Runge-Kutta法相比,论文方法在计算量未显著增加的前提下给出了更高的计算精度.     

广义特征值问题的Collatz包含定理

工程中已发展了许多矩阵特征值问题的近似求解方法,由Duncley法给出固有频率基频的下界,Rayleigh-Ritz近似法建立的方程,给出基频的上界,以及通常的矩阵迭代法给出的矩阵的固有频率程序中是以某一元素迭代前后比值确定的,这样实际上很难说是上界或下界。Collatz包含定理仅适用于对称标准特征值问题,可以给出特征值上、下界。采用矩阵Cholesky三角分解的原理,把Collatz包含定理推广到适用于具有对称矩阵的一般结构系统的广义征值问题,对于分解刚度矩阵或质量矩阵可给出基频,或最高因有频率。为了验证理论的正确性,给出了算例。     

发动机空间6DOF动力隔振拓扑模型仿真研究

汽车发动机悬置是典型的6DOF动力隔振系统,传统的动力隔振模型将动力机械整体视为刚体,而本文考虑运动零部件的影响,为汽车发动机悬置的结构设计带来了一种全新的视角。通过对发动机上运动零部件进行受力分析,找到引起发动机振动的最主要内在激励源;建立6DOF动力隔振空间拓扑模型,利用Simscape/Multibody仿真研究,验证了传统的动力隔振模型与空间拓扑模型之间存在理论误差;动力隔振拓扑模型更能准确描述6DOF动力隔振系统特性,所建立的汽车6DOF发动机Simscape/Multibody仿真模型可为后续的主动悬置设计提供重要基础。     

基于奇异值分解的多重渐消鲁棒Cubature卡尔曼滤波及在组合导航中的应用

为了提高标准Cubature卡尔曼滤波（CKF）的稳定性和鲁棒性,提出一种改进的多重渐消H∞滤波Cubature卡尔曼滤波算法。首先基于系统状态的可观测性给出多重渐消因子矩阵求解过程,提高滤波算法的稳定性,抑制滤波发散;其次,引入H∞鲁棒思想,构造多重渐消H∞滤波Cubature卡尔曼滤波器;最后,提出采用一种奇异值分解的矩阵分解策略代替标准Cubature卡尔曼滤波中的Cholesky分解,进一步提高算法的数值稳定性。实际GPS/INS组合导航实验表明,改进的多重渐消H∞滤波Cubature卡尔曼滤波算法不仅能有效抑制滤波发散提高算法的稳定性,而且对观测野值具有更高的鲁棒性;提出的新算法与标准CKF算法相比,XYZ三个方向的位置精度分别提高了55.8%,46.6%和39.7%。     

基于伪距的北斗双星/SINS组合导航系统可观测度分析

在连续的分段式定常系统模型基础上,证明了通过简化分段式定常系统的可观测矩阵来分析其离散化模型可观测性能的可行性;介绍了一种基于奇异值分解的系统状态可观测度分析方法.通过对一个分段间隔的条带化可观测矩阵进行奇异值分解来判断每一个奇异值对应的系统状态及每一个系统状态对应的可观测度;根据北斗双星定位系统的双伪距、高精度原子钟及气压高度信息,建立了北斗双星/SINS伪距组合滤波模型,并将可观测度分析方法应用于该模型中.仿真结果表明:在伪距组合模式下对简化的分段式定常系统可观测矩阵进行奇异值分解的方法能有效反映北斗双星/SINS组合导航系统的可观测程度.     

汽车动力总成悬置系统振动解耦计算方法研究

目前,汽车发动机动力总成悬置系统设计的主要任务是选择悬置元件的刚度、位置和角度,使悬置系统自由振动模态频率避开发动机怠速激励力频率与车身自振频率,并尽量提高各模态振型的解耦程度,从而提高悬置系统隔振效果。悬置系统按预定频率严格解耦设计是使设计出的悬置系统模态频率完全等于按汽车设计频率规划预定的频率,并使各模态的振型严格解耦,即各向振动能量的解耦度等于1。本文从悬置系统的自由振动方程出发给出了对悬置系统按预定频率严格解耦设计的方程组,通过方程组构造函数进而求出该方程组的解,从而提供比当前的悬置系统模态优化设计更为简便高效的优化设计方法。相应的算例验证了本文提出的按预定频率严格解耦设计方程和求解方法的正确性。     

树形多刚体系统的动力学普遍方程

本文继J.wittenburg,之后用图论的观点分析树形多刚体系统的结构,提出重叠子树结构的力学模型及脉络图定义,改进了增广体的概念从而使系统可以进行动力学等效分解。在规定一些符号及运算规则以后使用紧凑的矩阵形式导出树形多刚体系统动力学普遍方程组。在引进铰链矩阵以后系统的约束和运动学关系都写成矩阵形式,从而导出以广义坐标表出的动力学方程组,便于进行数值计算的程序设计。     

Matlab编程实现求解基于振型叠加法的多自由度动力学系统的时域和频域响应

给出了求解多自由度动力学系统响应的M atlab程序,这些程序基于振型叠加法可用于求解由质量矩阵M和刚度矩阵K以及常见阻尼矩阵描述的线性离散系统的时域和频域解.对于无阻尼系统,用户可以选择数值解或符号解析解(以时间或频率表示),并利用复模态叠加法计算了阻尼系统的数值解.总结了模态叠加方法下动力学响应的求解,并在简短的M atlab程序中实现.以三自由度系统和悬臂梁模型为例说明了程序的应用.这些程序也可用于工程应用中,通过对商用有限元软件包产生的质量和刚度进行后处理,产生感兴趣的时域和频域响应.     

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.      

Anti-plane time-harmonic Green's functions for a circular inhomogeneity in piezoelectric medium with a spring- or membrane-type interface

The present work focuses on the two-dimensional anti-plane time-harmonic dynamic Green's functions for a circular inhomogeneity immersed in an infinite matrix with an imperfect interface, where both the inhomogeneity and matrix are assumed to be piezoelectric and transversely isotropic. Two types of imperfect interface, the spring-type interface with electromechanical coupling and the membrane-type interface, are considered. The former type is often used to model the electromechanical damage along the interface while the latter is largely employed to simulate surface/interface effect of nano-sized inhomogeneity. By using the Bessel function expansions, explicit solutions for the electromechanical fields induced by a time-harmonic anti-plane line force and line charge located in an unbounded matrix as well as the circular inhomogeneity are respectively derived. The present solutions can recover the anti-plane Green's functions for some special cases, such as the dynamic or quasi-static Green's functions of piezoelectricity with perfect interface as well as the dynamic or quasi-static Green's functions of pure elasticity with imperfect interface. For detailed discussions, selected analytical results are presented. Dependence of the electromechanical fields on circular frequency as well as interface properties is examined. The size effect related to interfacial imperfection is also discussed.     

Dynamic-stress-data management for aeromechanical testing of turbomachinery

Aeromechanical testing of turbine engines is an important benchmark in the development of today's modern aircraft propulsion systems, and detailed dynamic-strain gaging of the engine's compressor and turbine are required to provide insight to the integrity of these engine components. Comprehensive real-time visualization of the compressor/turbine dynamic stress is necessary for safe engine operation and rapid posttest data-editing/processing systems are essential for day-to-day test-program direction. This paper reviews the evolution of on-line data-monitoring and posttest data-processing/analysis techniques that have been utilized at the Arnold Engineering Development Center to support dynamic strain-gage test programs. The transition from hardwire single-channel analog analysis equipment to the incorporation of digital computers for aiding on-line data monitoring, bulk processing of test data, and rapid editing/analysis of test results is discussed. The present on-line monitoring and posttest processing/analysis systems are presented, and refinements for improving the on-line data monitoring and posttest data-processing capabilities are discussed.     

碳纤维复合材料冲击模型率相关修正方法与试验研究

目前先进航空发动机的风扇叶片均采用复合材料结构,为了研究其在工作过程中可能受到的冲击损伤,即碳纤维增强树脂基复合材料受到高速冲击后的损伤与破坏过程,对其准静态下的正交各向异性本构模型和失效准则进行修正,建立了应变率相关的三维动态本构及损伤模型．该模型考虑了材料模量、强度和断裂韧性与应变率的相关性,并采用基于断裂韧性的渐进损伤模式对刚度进行折减来控制破坏过程．开展了不同应变率下的动态试验,得到基体方向拉伸与剪切的动态响应数据,拟合得到相应的动态修正因子．将该模型结合修正因子植入数值软件进行仿真计算,分析结果表明,所建立的率相关本构及损伤模型能够更准确地模拟层合板受冲击过程的损伤和破坏,与试验吻合较好．     

Dynamic system of an engine with spatially rocking links: a mathematical model

A mathematical model of a diesel with swashplates is proposed. The results of studying its design, kinematics, and dynamics are presented. The kinematic chain of the statically determinate mechanism of the engine is schematized. The kinematic relations are obtained taking into account the presence of Hooke’s joints and swashplates. A mathematical model of the dynamic system of the engine is described. A numerical example is given. The kinematics and dynamic processes of the engine are studied     

Dynamic analysis of beams on viscoelastic foundation

This study is intended to analyze dynamic behavior of beams on Pasternak-type viscoelastic foundation subjected to time-dependent loads. The Timoshenko beam theory is adopted in the derivation of the governing equation. Ordinary differential equations in scalar form obtained in the Laplace domain are solved numerically using the complementary functions method to calculate exactly the dynamic stiffness matrix of the problem. The solutions obtained are transformed to the real space using the Durbin's numerical inverse Laplace transform method. The dynamic response of beams on viscoelastic foundation is analyzed through various examples.     

Spectral element modelling and analysis of a pipeline conveying internal unsteady fluid

In this paper, a spectral element model is developed for the uniform straight pipelines conveying internal unsteady fluid. Four coupled pipe-dynamics equations are derived first by using the Hamilton's principle and the principles of fluid mechanics. The transverse displacement, the axial displacement, the fluid pressure and the fluid velocity are all considered as the dependent variables. The coupled pipe-dynamics equations are then linearized about the steady-state values of the fluid pressure and velocity. As the final step, the spectral element model represented by the exact dynamic stiffness matrix, which is often called spectral element matrix, is formulated by using the frequency-domain solutions of the linearized pipe-dynamics equations. The fast Fourier transform (FFT)-based spectral dynamic analyses are conducted to evaluate the accuracy of the present spectral element model and also to investigate the structural dynamic characteristics and the internal fluid transients of an example pipeline system.     

Strain-induced low-frequency relaxation in colloidal DGEBA/SiO2 suspensions

Diglycidyl ether of bisphenol A (DGEBA) is widely exploited as an epoxy resin in adhesives and coatings. In this paper, it is used as an oligomer matrix for silica-filled nanocomposites. Rheological measurements show that the pure matrix obeys power-law relaxation dynamics in the vicinity of the dynamic glass transition of this low-molecular-weight glass former. In the filled systems, a low-frequency relaxation appears additionally to the structural α-process of the matrix. Considering the nanocomposites as Newtonian hard-sphere suspensions at low angular frequencies (or high temperatures), the modified terminal regime behavior of the matrix can be linked to strain-induced perturbations of the isotropic filler distributions. While in the low-frequency regime hydrodynamic stresses relax instantaneously, the Brownian stress relaxation is viscoelastic and can be evidenced by dynamic rheological measurements. At higher angular frequencies, the α-process of the matrix superimposes on the Brownian stress relaxation. In particular, we were able to depict the low-frequency anomaly for concentrated, semi-dilute, and even for dilute suspensions.     

Nonlinear aeroelasticity of high-aspect-ratio wings excited by time-dependent thrust

Effects of engine placement on flutter characteristics of a very flexible high-aspect-ratio wing are investigated using the code NATASHA (Nonlinear Aeroelastic Trim And Stability of HALE Aircraft). Gravity for this class of wings plays an important role in flutter characteristics. In the absence of aerodynamic and gravitational forces and without an engine, the kinetic energy of the first two modes are calculated. Maximum and minimum flutter speed locations coincide with the area of minimum and maximum kinetic energy of the second bending and torsion modes. Time-dependent dynamic behavior of a turboshaft engine (JetCat SP5) is simulated with a transient engine model and the nonlinear aeroelastic response of the wing to the engine’s time-dependent thrust and dynamic excitation is presented. Below the flutter speed, at the wing tip and behind the elastic axis, the impulse engine excitation leads to a stable limit cycle oscillation; and for the ramp kind of excitation, beyond the flutter speed, at 75 % span, behind the elastic axis, it produces chaotic oscillation in the wing. Both the excitations above the flutter speed are stabilized, inboard of the wing.     

流体饱和多孔介质动力问题的显式时域解法

为了简化分析,Zienkiewicz等基于Biot理论,在忽略流体相对于土骨架运动的加速度条件下,建立了以土骨架位移u和孔隙流体压力p为基本变量的u-p格式饱和两相介质动力方程。针对该u-p方程,在空间上,采用伽辽金法有限元离散,并结合对角化形式的质量矩阵和流体压缩矩阵,忽略相邻结点间的惯性和流体压缩量间的耦合作用。在时域内,基于杜修力等提出的显式算法和Euler预估-校正法,建立了一种具有二阶精度的全显式时域积分法。采用一维饱和土模型,对比提出算法的数值解与Simon方法的解析解,发现两者吻合良好,验证了本文方法的正确性。并分析了饱和土二维动力问题,以及渗透系数和排水条件对饱和土动力响应的影响。     

绳牵引并联机器人弹性变形对动平台位姿精度的影响Influence of elastic deformation on pose precision of moving platform for wire-driven parallel robot

针对六自由度绳牵引并联机器人在风洞试验中的应用,分析了牵引绳弹性变形对动平台位姿精度的影响,其实质是运动学正解问题。鉴于牵引绳只能受拉力的特点,以及风洞试验的目的,须考虑系统的刚度和绳拉力的优化。基于系统运动学和动力学方程,推导了系统刚度矩阵;以提高系统主方向刚度为目标函数,对绳拉力进行了动态优化分布,以求解弹性变形;采用L‐M数值方法进行运动学正解,量化分析了两种不同弹性模量的牵引绳对系统刚度的影响,以及弹性变形引起的动平台位姿误差。研究结果表明,以刚度增强为优化目标,有利于提高系统稳定性;采用弹性模量较大的牵引绳,可以有效提高系统的刚度,减小绳长变形引起的飞行器模型位姿误差,满足风洞试验的精度要求。上述结果可为后续机构的改善和系统高精度的力位混合控制提供依据和指导。