A non‐linear inverse vibration problem of estimating the time‐dependent stiffness coefficients by conjugate gradient method

An iterative regularization method, i.e. the conjugate gradient method (CGM) is applied to an inverse non‐linear force vibration problem to estimate the unknown time‐dependent stiffness coefficients (or spring constants) in a damped system by using the measured system displacement. It is assumed that no prior information is available on the functional form of the unknown stiffness coefficients in the present study, thus, it is classified as the function estimation in inverse calculation. The accuracy of the inverse analysis is examined by using the simulated exact and inexact displacement measurements. The numerical simulations are performed to test the validity of the present algorithm by using different types of stiffness coefficients and measurement errors. Results show that an excellent estimation on the time‐dependent spring constants can be obtained with any arbitrary initial guesses within a couple of seconds of CPU time at Pentium III‐500 MHz PC. Copyright © 2001 John Wiley & Sons, Ltd.     

铸铝ZL101与树脂砂型之间等效换热系数的数值模拟

采用ZL01铝合金作为成型材料,用呋喃树脂砂作为造型材料,采用24通道的数据采集系统采集了然件凝固与冷却过程中铸型,铸件内和铸件表面温度与时间的变化规律,从而为等效换热系数的反问题数值计算提供了一第一手的数模拟。对两平板铸件进行换热反问题的计算,其结果得出了两板件上下表面的等效换系数KE与时间的变化关系,可以看出等效换热系数在凝固开始时达到一个峰值,而后逐渐减小,并且其大小与铸 的模截面积有关,这些为今后的数值模拟中确定交换系数KE提供了科学的计算数据。     

An inverse solution for reconstruction of the heat transfer coefficient from the knowledge of two temperature values in a solid substrate

Reconstruction of the heat transfer coefficient from the knowledge of temperature distribution is an inverse problem. The main focus of this study was to develop an inverse model that could be used to determine the heat transfer coefficient associated with a fluid in contact with a solid surface from the knowledge of two measured temperature values (T₁ and T_M) in the solid substrate. The temperature distribution for the inverse problem was numerically generated, for a situation with a known heat transfer coefficient, using an implicit finite-differencing scheme. The solution domain was first discretized in to finite number of small regions and nodes. Conservation of energy was then applied to each of the control volume about the nodal regions. This approach resulted in a set of linear equations that was solved simultaneously. Two nodal temperatures in the substrate, from the direct solution, were then used in the inverse problem to reconstruct the heat transfer coefficient. To solve the inverse problem, the solution domain was divided into two distinct regions (Region I and Region II). Region I contained the solution domain between the two known temperatures (T₁ and T_M), and Region II included the region between T_M and the surface with the convective boundary condition. Again, a finite-differencing scheme was employed to generate a set of linear equations in each region. First, the set of linear equations in Region I was solved simultaneously and the results were then used to reconstruct the nodal temperatures in Region II. The convective surface temperature was then utilized to determine the heat transfer coefficient. A series of numerical experiments were conducted to test the validity of the inverse model. Comparison of the inverse solutions with the direct solutions confirms that the heat transfer coefficient can be reconstructed, with good accuracy, from the knowledge of two temperature points in the solid substrate.     

模拟退火算法在线热源反问题数值求解中的应用

提出采用模拟退火算法(simulated annealing,SA)来数值求解线热源反问题.探讨了如何设计算法使之适合反问题求解,并给出了算法求解的伪代码;通过线源正问题的模拟数据,使用设计的SA算法进行反问题求解,以此来验证算法求解的准确性和可靠性,并对一组实测数据进行了计算.结果表明,该算法不但可以实现两个参数同时、快速反演,而且具有求解精度高,对初始条件依赖少,编制容易等优点.     

基于声辐射逆问题的故障诊断与噪声分析的研究

本文采用全特解场边界元求解声辐射逆问题的方法,通过对故障诊断和噪声源分析、相位分析、声环境设计的仿真计算与讨论,初步揭示了声源与其所发生声场的逆关系。计算结果可为噪声控制、故障诊断、声环境设计等工程实际应用提供有价值的参数。     

The conjugate problem of the thermal elasticity theory with imperfect heat contact between substances

In this paper, the one-dimensional mathematical formulation of the conjugate coupling problem of the thermal elasticity theory with non-ideal contact between substances is suggested. The approximate analytical solution of the problem is received for both quasi-static and dynamic formulations. The integral transformation method of Laplace is used together with asymptotic representation of solution in the transformation space. The fields of the temperatures, stresses, strains and displacements are found. It is demonstrated with the help of some examples that the region near the interface may be the cause of the localization of stresses. The numerical solution of the quasi-static problem is in a qualitative agreement with the analytical estimations.     

Mathematical analysis and solution methodology for an inverse spectral problem arising in the design of optical waveguides

We analyse mathematically the problem of determining refractive index profiles from some desired/measured guided waves propagating in optical fibres. We establish the uniqueness of the solution of this inverse spectral problem assuming that only one guided mode is known. We then propose an iterative computational procedure for solving numerically the considered inverse spectral problem. Numerical results are presented to illustrate the potential of the proposed regularized Newton algorithm to efficiently and accurately retrieve the refractive index profiles even when the guided mode measurements are highly noisy.     

直接冷却中氮化铝与无氧铜低温真空接触热导的实验研究

以5W／20K小型G-M制冷机为冷源,对低温下氮化铝（AlN）与无氧铜（OFHC）界面的接触热导进行了实验研究和分析。在45～140K内,氮化铝／无氧铜界面接触热导随温度的升高而增大,同时亦随接触压力的增加而增大。实验中同时得到了氮化铝在低温下的热导率,随温度的升高,氮化铝热导率值逐渐增大。就氮化铝低温热导率及氮化铝／无氧铜接触界面热阻随温度变化规律进行了微结构机理分析。     

用有限元分析和DICM确定纸浆模塑材料弹性常数的逆问题

用有限元法分析纸浆模塑包装结构,需要事先确定纸浆模塑材料的弹性常数.基于纸浆模塑薄壁圆锥筒的压缩试验,讨论了可以利用有限元分析和数字相关测量方法(DICM)来识别纸浆模塑材料弹性常数的逆问题.     

Effect of crack shape,inclination angle,and friction coefficient in crack surface contact problems

In rolling/sliding contact fatigue, it is known that the crack propagates at a characteristic angle =15–30 deg to the surface. To analyze the mechanism, however, the body force method has been widely used assuming 3D crack models for =45–90. In this study, therefore, the unknown body force densities are newly approximated by using fundamental density functions and polynomials. Then, a semi-elliptical crack model is analyzed for =15–90 under compressive residual stresses and Hertzian contact loads. The stress intensity factors K _II, K _III are calculated with varying the crack shape b/a, inclination crack angle , and crack face friction coefficient . The calculations show that the present method is useful for the analysis for =15–30 deg with high accuracy. It is seen that the K _II-values when b/a0 are larger than the ones when b/a=1 by 0–24% for both under compressive residual stress and Hertzian contact load. Regarding the maximum K _II values under Hertzian contact load, the results of =15 deg are smaller than the ones of =45 deg by 23–34%. Regarding the amplitude of (K _{II max}–K _{II min}), the results of =15 deg are smaller than the ones of =45 deg by 4–24%. With increasing the value of friction coefficient for crack faces the value of K _II decreases significantly. When the crack is short and the inclination angle is small, the value of friction coefficient f for Hertzian contact load largely affect the K _II value.