两种模态理论时域解的数学关系

当阻尼满足一定条件时,一个有阻尼的n个自由度的线性振动系统在其主空间的运动仍可解耦。解决以上系统的振动问题的理论和方法被称之为实模态理论。若振动系统的阻尼不满足解耦条件,则研究此类问题的理论和方法被称之为复模态理论。在讨论这两种理论的兼容性的时候,则多是在频域内从传递函数出发去认识它。事实上,我们也可以在时域内,从具有一般阻尼的n个自由度的线性振动系统的状态方程出发,借助于一阶线性微分方程组的exp(At)形式解和矩阵函数理论来进一步认识两种模态理论的     

采用界面单元协调子结构方法研究

子结构混合试验在研究复杂工程时,需要针对不同物理的物理性质划分子结构,比如土和结构,这些子结构的单元类型和网格划分通常不同,为了使混合试验更灵活地划分子结构,该文提出利用界面单元方法,基于广义变分原理,将两子域凝聚在边界上的刚度矩阵与界面单元刚度矩阵组装成耦合结构的整体刚度矩阵,进而求解新的平衡方程即可得到各个耦合子域的位移。同时,将传递函数的概念引入界面单元方法中,通过二维自由度和三维自由度之间的传递函数,解决了具有不同自由度单元的子结构之间的耦合问题。最后,利用板梁受竖向地震动作用的案例验证了界面单元和传递函数结合的方法的可行性和精确性。     

关于复模态理论的几个问题

对一个具有一般粘性阻尼的n个自由度的线性振动系统的研究需要用到复模态理论。本文论述了复模态理论中的若干问题,证明了复模态参数的一些重要性质,定义了实广义参数(广义质量,广义阻尼率等),导出了实系数矩形式的系统传递函数,还定义了系统的共振频率。所有这些定义和公式都兼容实模态理论中对应的定义和公式。     

非自伴随动力学系统的工况模态分析

非自伴随动力学系统主要存在于转子动力学、自激颤振和反馈控制中,伴随着系数矩阵的对称性破坏而出现。非自伴随系统动力学特征信息的辨识在颤振的预测、控制律的识别、结构动力学特性的优化等方面尤为重要。然而工程中的非自伴随动力学系统,如受稳流风载的大跨度桥梁、高速飞行的飞行器、转子动力学系统、汽车的制动系统,由于系统的激励信息未知,只能依靠系统的响应信号对系统进行辨识。该研究围绕非自伴随动力学系统的工况模态分析展开,首先推导了非自伴随动力学系统在白噪声激励下响应的相关函数与系统自由衰减响应之间的等价关系;继而将迭代整体最小二乘算法引入到相关函数的辨识中;最后通过两自由度桥梁节段模型和多自由度系统的算例验证了方法的有效性。     

航空发动机风扇管道径向声模态模拟与识别技术

针对航空发动机风扇管道径向声模态模拟与测试问题,研究了径向声模态模拟技术以及径向声模态识别技术。采用基于径向排布的声源阵列形式,调节阵列预设的各扬声器幅值及相位实现径向模态声源模拟。建立声源管道下游多圈环形阵列,根据阵列位置信息构造求解模态的传递函数矩阵,运用Tikhonov正则化方法减小传递函数矩阵的条件数,从而实现径向声模态识别能力。通过理论推导和数值计算,设计风扇管道径向声模态试验装置,并在消声室进行试验验证。通过试验验证了该系统具备周向4阶以内,径向2阶以内的径向声模态模拟与识别能力。     

单自由度系统某些理论在多自由度系统上的推广

本文给出了多自由度系统临界阻尼矩阵、阻尼比矩阵及模态阻尼比矩阵的定义。并由此给了两种判定系统模态阻尼状态的判据。本文还举例说明了临界阻尼和模态阻尼比矩阵之间的应用及意义。     

二自由度参数振动自由响应逼近

对二自由度参数振动问题,应用反馈调制概念,将参数振动的自由振动响应表示成为以振荡频率和参数激励频率的线性组合,用矩阵三角级数进行逼近。应用谐波平衡,将二自由度参数振动方程转化为无限阶线性代数方程组;从齐次方程非零解得到特征方程,通过数值解得到主振荡频率;引入归一化模态,求解出模态、系数矩阵及自由响应通解,由初始条件确定自由响应的任意常数;定义一个计算误差函数,将该方法和龙格-库塔法进行比较,当逼近级数项数大于一定项时,计算误差值比龙格-库塔法要小的多。因此,所给的矩阵三角级数表达为二自由度参数振动自由响应逼近提供了一种有效的解析分析工具,它具有理论研究和工程应用的价值。     

粘弹结构动力学分析

本文研究由单一粘弹材料构成的粘弹结构的振动.在时间域和拉氏域内建立了它的动力学方程.给出了粘弹结构的"对偶弹性结构"概念,并用来讨论了粘弹结构的模态特性,证实位移形态可由实模态向量张成的向量空间内加以描述,它就是"对偶弹性结构"的模态向量,无需增广坐标.每个模态自由度含有数个反映蠕变的实特征值和一对反映衰减振动的复共轭特征值.分析了在模态向量空问内的动响应,给出了传递函数(频率响应)和脉冲响应.从而揭示了粘弹结构的动力学特性.     

基于试验模态参数的结构有限元模型修正

本文利用动力缩聚方法研究在结构模态试验的测量自由度小于有限元模型自由度时的模型修正问题,给出了一种利用非完备试验模态参数修正有限元模型的质量和刚度矩阵的方法,该方法可使修正后的模型保持原有的自由度相稀疏特性。     

时滞作用下切削系统的时频响应特性研究

在车削、铣削、钻镗孔等机械加工过程中,由于再生切削效应,刀具-工件系统的运动方程存在时滞环节,导致系统的动力学特性发生改变。以车削过程为工程背景,定量研究了单自由度二阶线性时滞微分系统在受到外激励时的动力学响应。通过推导系统输入输出随时滞刚度及时滞量大小变化的传递函数关系,在参数空间得到了系统的幅频响应曲面。结果显示时滞将使得系统的工作模态发生改变,幅频响应出现多个共振峰,其中时滞刚度主要影响共振峰的峰值,而时滞量则主要影响共振峰的数量。同时,通过解析求解共振峰的脊线簇的方程,得到了共振峰在参数空间的分布规律。此外,数值求解得到了共振峰数目的定量分布图,结果显示,随着时滞刚度与时滞量的增大,共振峰的数目从1呈连续整数增加直至无穷,而系统阻尼对这一增长趋势无明显影响。通过车削试验平台上的模态锤击试验,验证了理论推导的时滞系统时频响应特性的相关结论。该研究在机床工作模态分析、整机动力学响应分析等方面具有潜在的学术与应用价值。     

充砂振动柱动态特性预估

本文对充砂振动柱在基础激励下的动态特性进行了理论和实验研究。把砂作为一种具有均匀密度的连续体,假设砂的弹性模量是砂柱高度的幂函数和砂柱中只存在纵向波,建立了波动方程,导出了原点导纳和传递导纳的理论公式。这个公式亦适用于非常短的砂柱。同时采用阻抗方法推导了充砂振动柱的结构损耗因子表达式。实验值和预估值基本相符。     

结构多轴抗震试验加载系统开发及控制策略研究

开发基于液压伺服作动器的高性能三自由度结构动力试验加载系统,该系统特点为控制精确、功能全面。建立力控制下位移加载混合控制方法,提出拟静力试验中多作动器耦合控制策略。以足尺钢结构立柱为试件,研究应用三自由度结构动力试验系统进行拟静力试验与混合试验具体方法,验证该试验系统在结构动力试验中应用的可行性、有效性。结果表明,通过对多作动器的耦合控制,该试验系统可在拟静力试验中同时实现对立柱试件恒定的竖向力控制及精确剪切型加载。通过基于α-OS法的混合试验证明该加载系统可精确模拟单柱子结构复杂边界条件,对整体坐标与作动器局部坐标变换,可实现多作动器位移协调加载。该结论可推广至多自由度试验系统研究中。     

Experimental Investigation of Wire Arrangements for Narrow-Gap Triple-Wire Gas Indirect Arc Welding

A new narrow-gap welding process is proposed by applying triple-wire gas indirect arc (TW-GIA). There are double power supplies and triple wires in this system. Power supplies are only connected between electrode wires and base materials are not linked to power supplies. Since there are different wire arrangements with TW-GIA, this article studies these wire arrangements and their effects on sidewall fusion for narrow-gap welding. Results show that different wire arrangements lead to variant arc behaviors and metal transfer, and consequently they lead to different situation of sidewall fusion. The heat to melt sidewalls is mainly from the indirect arc column and metal transfer with narrow-gap TW-GIA. When side wires deviate from the main wire to opposite directions, heat from arc columns and metal transfer can concentrate toward groove sidewalls. When the whole weld torch is lowered, heat from the indirect arc column and metal transfer increases at the weld bead root.     

采用四象限探测器的双轴跟踪控制技术

采用四象限探测器作为位置传感器，设计出以DSP作为控制器的双轴跟踪控制试验演示系统。通过误差数据采样、计算和比较，在反馈作用下对误差修正，以快速扫描系统和大范围扫描系统构成的双轴联合机构实现运动目标的捕获跟踪。试验结果表明，该系统能够快速捕获并平稳跟踪合作目标，且调试方便，可靠性好，为下一步工程化奠定了基础。     

多级齿轮传动转子系统的模态缩减与振动特性分析

提出了一种适用于多级齿轮传动转子系统的模态缩减法,以某透平驱动水泵系统为研究对象,采用有限元法建立了系统的动力学模型,并利用模态缩减法减少了系统自由度.在此基础上研究了系统的固有特性、不平衡量与静态传递误差引起的稳态响应、启动状态下的瞬态响应以及稳定运转下突加不平衡时的瞬态响应.结果表明,在计算系统的固有频率和稳态响应...     

Analytical optimal solution of the extension of the depth of field using cubic-phase wavefront coding. Part I. Reduced-complexity approximate representation of the modulation transfer function

In this paper we derive an approximate analytical representation for the modulation transfer function (MTF) of an imaging system possessing a defocused cubic-phase pupil function. This expression is based on an approximation using the Arctan function and significantly reduces the computational time required to calculate the resulting MTF. We derive rigorous bounds on the minimum and average accuracy of our approximation. Using this approximate representation of the MTF, the analytical solution of the problem of calculating the extension of the depth of field for a circular aperture with a cubic phase mask becomes possible. We also comment on how one can modify our method to construct a lower-bound or an upper-bound approximate analytical expression for the MTF.     

Evaluation of the column components size on the vapour enrichment and system performance in small power NH3–H2O absorption refrigeration machines

This paper presents an analysis of the influence of the distillation column components size on the vapour enrichment and system performance in small power NH₃–H₂O absorption machines with partial condensation. It is known that ammonia enrichment is required in this type of systems; otherwise water accumulates in the evaporator and strongly deteriorates the system performance and efficiency. The distillation column analysed consists of a stripping adiabatic section below the column feed point and an adiabatic rectifying packed section over it. The partial condensation of the vapour is produced at the top of the column by means of a heat integrated rectifier with the strong solution as coolant and a water cooled rectifier. Differential mathematical models based on mass and energy balances and heat and mass transfer equations have been developed for each one of the column sections and rectifiers, which allow defining their real dimensions. Results are shown for a given practical application. Specific geometric dimensions of the column components are considered. Different distillation column configurations are analysed by selecting and discarding the use of the possible components of the column and by changing their dimensions. The analysis and comparison of the different column arrangements has been based on the system COP and on the column dimensions.     

Longitudinally modulated cryogenic system. A generally applicable approach to solute trapping and mobilization in gas chromatography

This paper describes a novel approach to solute trapping and remobilization. It involves the use of a subambient trap, with a narrow capillary column passing through the cooled region. A mechanism allows for longitudinal movement of the trap relative to the chromatographic column or narrow transfer line through which analytes travel. Either the trap or the column can be moved, and the frequency or manner of relative movement determines the type of result obtained. A series of preliminary studies are described that define the general approach to using this device and demonstrate the unique benefits that may arise from the modulation movement. Significant improvement (reduction) in peak width occurs if the device is placed immediately prior to the detection system, and consequently a great increase in detection limits results. With a 25 cm length of capillary column between the trap and detector, it is calculated that the plate height of dodecane is 0.082 mm, equivalent to 12?100 plates/m. This was found to be much greater than that for dodecane analyzed on a 25 m column. By slow displacement of the column through the trap, it is demonstrated that the solute is trapped in the first 1 cm (or less) of the column located in the cold trap.     

Coupled simultaneous heat and mass transfer in multicomponent two-phase mixtures

A method is proposed for calculating the parameters of simultaneous heat and mass transfer in a multicomponent two-phase gas-liquid system, this method being based on solving the system of differential equations of convective heat transfer and convective diffusion.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 49, No. 3, pp. 421–428, September, 1985.     

低频水声声压校准测试系统的设计

水声声压是声学测量中应用最广泛的参数，对声压的测量又是通过测量水听器的声压灵敏度来完成的。声学计量检定系统中对低频水声声压灵敏度的校准有多种方法，应用振动液柱法校准低频水听器的声压灵敏度是常用方法之一。伴随着新型器件、新材料和数据采集器的应用，笔者根据振动液柱法的数学模型，初步设计了一套测试系统。本文给出测试系统实现原理和系统框图，并对其不确定度进行了分析评定，同时给出测试系统能达到的技术指标。