非均匀变截面梁动力响应的一般解

本文利用精确解析法[1]给出非均匀变截面梁在任意谐振荷载和边界条件下的动力响应的一般解.问题最后归结为求解一个非正定微分方程.对于这一问题用一般变分法求解失败,利用本文的方法,这个问题的一般解可以写成解析的形式.因此对优化特别方便.本文给出收敛性证明.文末给出的算例表明本文的方法可获得满意的结果.     

Fastiterative methods for least squares estimations

Least squares estimations have been used extensively in many applications, e.g. system identification and signal prediction. When the stochastic process is stationary, the least squares estimators can be found by solving a Toeplitz or near-Toeplitz matrix system depending on the knowledge of the data statistics. In this paper, we employ the preconditioned conjugate gradient method with circulant preconditioners to solve such systems. Our proposed circulant preconditioners are derived from the spectral property of the given stationary process. In the case where the spectral density functions() of the process is known, we prove that ifs() is a positive continuous function, then the spectrum of the preconditioned system will be clustered around 1 and the method converges superlinearly. However, if the statistics of the process is unknown, then we prove that with probability 1, the spectrum of the preconditioned system is still clustered around 1 provided that large data samples are taken. For finite impulse response (FIR) system identification problems, our numerical results show that annth order least squares estimator can usually be obtained inO(n logn) operations whenO(n) data samples are used. Finally, we remark that our algorithm can be modified to suit the applications of recursive least squares computations with the proper use of sliding window method arising in signal processing applications.Research supported in part by HKRGC grant no. 221600070, ONR contract no. N00014-90-J-1695 and DOE grant no. DE-FG03-87ER25037.     

关于虚拟激励法的一个注记

从具有随机频率与随机相位的随机谐和函数出发,证明了当随机频率与相位均为均匀分布而随机幅值与功率谱密度平方根成正比时,该随机过程的功率谱即精确地等于目标功率谱.进而表明:只需遍历频率区间,即可由单一谐和函数激励下的响应幅值给出响应的功率谱密度,从而揭示了虚拟激励法的物理意义.研究还表明:为了给出结构响应的功率谱密度,实际...     

The optical nonreciprocal response based on a four-mode optomechanical system

We propose a scheme for realizing the optical nonreciprocal response based a four-mode optomechanical system,consisting of two charged mechanical modes and two linearly coupled optical modes. Two charged mechanical modes are coupled by Coulomb interaction, and two optical modes are coupled to one of mechanical modes by radiation pressure. We numerically evaluate the transmission probability of the probe field to obtain the optimum optical nonreciprocal response parameters. Also, we show that the optical nonreciprocal response is caused by the quantum interference between the optomechanical couplings and the linearly coupled interaction that breaks the time-reversal symmetry.     

高功率微波作用下限幅器尖峰泄漏特性

针对限幅器在高功率微波（HPM）作用下的尖峰泄漏问题,基于搭建的HPM注入实验平台和电路仿真开展了研究。研究结果表明：当注入功率超过6 dBm时,限幅器会出现尖峰泄漏现象,限幅器泄漏尖峰的上升沿与脉宽随着注入功率的增加而减小,而绝对尖峰泄漏功率随注入功率的增加呈增长趋势,平顶泄漏功率呈近似“线性增加-缓慢下降-小幅增长”趋势。并且,实验结果显示：HPM脉宽与重频对限幅器尖峰泄漏特性基本无影响,其泄漏特性变化规律与单次脉冲的基本一致;尖峰泄漏能量随注入功率的增加而降低。     

注汽油井蒸气汽液比的折射率法测量研究

给油田的油井中注入高温高压蒸气时,从井口到井底连续地查明汽液比对节省能源和提高产出率意义重大。由于干蒸气和水的折射率不同,汽液的比例可以从汽液两相流的折射率响应特性反映出来。研制的测量装置采用蓝宝石作为折射率敏感的探测头,直接对汽液两相流的比例变化产生响应,能够应用于高温高压及狭窄工作空间的输汽环境中。装置在锅炉输汽管道中的实测响应曲线反映了输汽过程中汽液比的真实变化。该装置还在井深800m,井口蒸气温度270℃、压力10Mpa的油田注汽井中进行测量,测得的结果对注汽法采油的井况分析具有一定的作用。     

Simulation of Lamb wave reflections at plate edges using the semi-analytical finite element method

In typical Lamb wave simulation practices, effects of plate edge reflections are often not considered in order to simplify the wave signal interpretations. Methods that are based on infinite plates such as the semi-analytical finite element method is effective in simulating Lamb waves as it excludes the effect of plate edges. However, the inclusion of plate edges in a finite plate could render this method inapplicable, especially for transient response simulations. Here, by applying the ratio of Lamb mode reflections at plate edges, and representing the reflection at plate edges using infinite plate solutions, the semi-analytical finite element method can be applied for transient response simulation, even when the plate is no longer infinite.     

大型粮仓温度分布反演数学模型的研究

采用有限元数值模拟方法,以响应面模型RSM(Response surface model)理论为基础对大型粮仓冬、夏两季的温度分布进行了深入分析,推导了粮仓温度反演数学模型。将采集的温度值导入RSM模型中,并结合单因素轮换法、正交实验和统计方法,通过构造一个具有明确表达形式的多项式来预测粮仓温度分布反演数学模型。在数学模型的基础上给出各因子交互作用下的设计空间、各因素对粮温影响的主效应及交互效应。实验证明该数学模型误差小,精度高,具有良好的计算性能,在大型粮仓温度监控系统中采用该模型能够解决布线少、预测空间范围广的问题。     

煤质硫含量紫外差分吸收测量方法研究

快速准确地测定煤质硫含量,可为企业、环境监督部门提供重要的技术依据。国内外已有多种煤质硫含量分析仪器,但或多或少存在令操作人员不满意的地方。提出一种基于紫外(UV)差分吸收光谱(DOAS)的煤质硫含量测量方法。针对分子数分数测量范围宽、光程短等问题,在传统算法的基础上,提出基于有限脉冲响应(FIR)滤波和四阶多项式非线性补偿的改进DOAS算法。搭建了实验测量系统,对5种标准煤样进行了实验研究。结果表明,测量系统的下限为0.014%,能够去除烟尘和背景气体的影响,降低系统的维护量,单次测量时间在4min左右,测量系统的重复性满足国家标准的要求。