压电弹性层合梁-板结构中SH波的传播

建立了压电层合梁-板结构的压电-弹性动力学基本方程式，在给定压电层合梁-板结构形式和波传播方向的情况下，对基本方程式进行了简化；利用连续性条件和边界条件，建立了波传播的特征方程式，并对波动方程式进行求解；得到了前三阶频散关系曲线。通过实例数值计算，讨论了弹性层、压电层的厚度比与频散关系的影响，得出了SH波在压电层合梁-板结构中传播的基本特性。     

具有初应力的多层空心圆柱体中的导波

基于“增量变形力学”理论,研究了轴向初应力和径向初应力对多层空心圆柱体中导波传播特性的影响,应用Legendre多项式方法求解了耦合波动方程,并通过数值算例讨论了该方法的收敛性,分析了初应力对纵向波和扭转波的影响,数值分析结果表明初应力对两者的影响是非常不同的。此外,轴向初应力对频散曲线的影响与径向初应力的影响也非常不同。     

应力波在基桩中的传播特性

将基桩简化为一维弹性杆，研究了位移波和应力波在不同类型的基桩中的传播特性。同时，本文分析了位移波和应力波在固定端、自由端和弹性支承端的反射特点。在固定端，位移为零而应力加倍；在自由端，应力为零而位移加倍。通过对应力波在基桩中的传播特性的分析，不仅有利于提高基桩动测的理性认识，而且为实测响应的解释和参数的估计提供了较为严格的理论依据。     

粘弹性岩体中的爆炸应力波

本文从理论上研究了粘弹性岩体中爆炸应力波的传播规律,建立了粘弹性应力波传播的数值计算方法.研究表明,由于粘滞数应,应力波波阵面的不连续性已不复存在,低应力的传播速度高于高应力的传播速度,应力波的上升时间越来越大,且应力波的衰减指数与装药直径有关.     

非均质岩体中一维应力波演化过程分析

地下球形药包爆轰后将产生很强的地震波，其传播受到多种因素的影响。把岩石介质的弹塑性帽盖模型耦合到有限差分法程序中，对一维爆轰波在非均质岩石体中的传播、演化机理进行了数值模拟与分析；着重探讨了一维应力波从“硬”岩石层进入“软”岩石层、从“软”岩石层进入“硬”岩石层时，波在形状和强度等方面的变化规律；同时探讨了岩石介质中存在的“软弱夹层”对一维应力波传播的影响。     

接触爆炸荷载下金属管道中应力波数值分析

以大口径金属管道为对象,通过数值模拟研究了金属管道在局部外接触爆炸荷载作用下的应力波对其的效应。根据管道应力波传播过程的数值模拟结果,分析了管壁中应力波产生、发展和传播的过程及应力波形特点;比较了管道发生破坏前后应力状态的变化;阐述了管壁各观测点切向、径向与轴向应力随时间的变化特征,并探讨了其中的原因。     

系泊缆松弛-张紧状态应力波的特性分析

从应力波的自由传播特性出发,分析在系泊缆绳松弛-张紧问题研究中需要考虑的因素。引入缆绳单位长度的重力与缆绳水平张力的比值λ,利用泰勒级数展开,将平衡张力和曲率表示为λ和缆绳弧长坐标s的函数。研究了缆绳出现松弛-张紧状态时应力波的自由传播特性,分析缆绳内水平张力、缆绳弧长坐标等参数对缆绳内应力波传播特性的影响。结果表明:缆绳处于松弛-张紧状态时,缆绳内应力波传播特性与张力、曲率和缆绳自重等因素密切相关。该文的工作为缆绳松弛-张紧条件下冲击载荷问题的研究奠定了基础。     

层状板中Lamb波的频散特性研究

利用矩阵递推方法，建立了层状板中Ｌａｍｂ波的特征方程以及相应的位移和应力分布计算公式，由此分析了双层板、软夹层板和硬夹层板中Ｌａｍｂ波的频散特性，特别指出软夹层的存在对Ｌａｍｂ波的频散特性有显著影响。该结论对工程测试分析有一定指导意义。     

曲率波前传感器波前重构算法的研究

运用衍射理论计算出两个离焦面上的光强分布,从而获得波前曲率和孔径边缘的波前径向倾斜。根据Zernike多项式的微分特性,采用两种不同的方法分别处理曲率和倾斜,使用积分的方法解决了在边界上δ函数很难处理的问题。由探测器的几何分布预先算出控制矩阵,用Zernike多项式曲线拟合的方法重构出波前。计算机仿真表明,波前残差小于5％,验证了此波前重构算法的可行性。     

基于特征线的杆波阻特性两点应变法反演研究

在冲击凿岩机械系统中,钻头对岩石的作用力与凿深的关系曲线反映了钻头与岩石相互作用机理,而钻头波阻特性是获取这种关系曲线的前提.提出了一种基于特征线和两点应变测试法来反演计算钻头波阻的方法.首先应用特征线网格,描述应力波在变波阻杆中的传播规律,分别建立依空间和依时间波动分析方程;然后提出了根据弹性杆上一点状态矢量依次计算钻头波阻的反演原理,介绍了由弹性杆两点应变求解任意一点状态矢量的方法;最后对基于特征线的杆波阻特性两点应变反演方法进行了验证和讨论.     

Wave propagation in multilayered piezoelectric spherical plates

This paper proposes an improvement of the Legendre polynomial series method to solve the harmonic wave propagation in multilayered piezoelectric spherical plates, which are used in point-focusing transducers. The conventional Legendre polynomial method can deal with the multilayered structures only when the material properties of two adjacent layers do not change significantly and cannot obtain correctly normal stress and normal electric displacement shapes unlike the proposed improved orthogonal polynomial approach which overcomes these drawbacks. Detailed formulations are given to highlight its differences from the conventional Legendre polynomial approach. Through the comparisons of numerical results given by an exact solution (obtained from the reverberation-ray matrix method), and by the conventional polynomial approach and the improved polynomial approach, the validity of the proposed approach is illustrated. The influences of the radius-to-thickness ratio on dispersion curves, stress and electric displacement distributions are discussed. It is found that three factors determine the distribution of mechanical energy and electric energy at higher frequencies: radius-to-thickness ratio, wave speed, and position of the component material.     

Matrix method to find a new set of Zernike coefficients from an original set when the aperture radius is changed

A matrix method is developed that allows a new set of Zernike coefficients that describe a surface or wave front appropriate for a new aperture size to be found from an original set of Zernike coefficients that describe the same surface or wave front but use a different aperture size. The new set of coefficients, arranged as elements of a vector, is formed by multiplying the original set of coefficients, also arranged as elements of a vector, by a conversion matrix formed from powers of the ratio of the new to the original aperture and elements of a matrix that forms the weighting coefficients of the radial Zernike polynomial functions. In developing the method, a new matrix method for expressing Zernike polynomial functions is introduced and used. An algorithm is given for creating the conversion matrix along with computer code to implement the algorithm.     

An alternative definition of material properties

The stresslstrain relation is initially discussed in general form. The normal matrix formulation employing the Lamé Constants and the more 'practical' formulation based on the Elastic Modulus and Poisson's Ratio are detailed.
An alternative approach employing the wave speeds of the material as the basic material parameters is discussed. This approach has a number of advantages over the present tensile testing methods. The main advantages are that the properties can be obtained on the actual part or specimen without resorting to destructive testing means, and the data can be collected with the same strain gauge equipment that is to be employed in subsequent testing procedures.
The problem associated with the measurement of short duration, low amplitude pulses is discussed and the broad details of the required instrumentation are given.
Two simple experiments are illustrated in which firstly, the wave velocity in a bar is obtained and secondly, the dilatational and shear wave speeds are obtained in a plate structure.     

Testing degenerate polynomials

Two methods to test whether a given polynomial has two distinct roots whose quotient is a root of unity are discussed.     

BATCH SEQUENCING

Consider the single machine scheduling problem where there are a number of part types to be processed. A part type is defined as follows: Two parts are of the same part type if the machine does not require a setup in between the processing of these parts. The problem investigated in this paper is to find a sequence of batches of parts (if there are any) where all the requirements for parts are met. A heuristic and an exact algorithm are developed, and computational analysis is performed to measure the performance of the heuristic. The time complexity function of the heuristic is O(n²), and the exact algorithm runs in polynomial time given a fixed upper bound on the number of setups.     

Analytical extraction of leaky modes in circular slab waveguides with arbitrary refractive index profile

Circular slab waveguides are conformally transformed into straight inhomogeneous waveguides, whereupon electromagnetic fields in the core are expanded in terms of Legendre polynomial basis functions. Thereafter, different analytical expression of electromagnetic fields in the cladding region, viz. Wentzel-Kramers-Brillouin solution, modified Airy function expansion, and the exact field solution for circular waveguides, i.e., Hankel function of complex order, are each matched to the polynomial expansion of the transverse electric field within the guide. This field matching process renders different boundary conditions to be satisfied by the set of orthogonal Legendre polynomial basis functions. In this fashion, the governing wave equation is converted into an algebraic and easy to solve eigenvalue problem, which is associated with a matrix whose elements are analytically given. Various numerical examples are presented and the accuracy of each of the abovementioned different boundary conditions is assessed. Furthermore, the computational efficiency and the convergence rate of the proposed method with increasing number of basis functions are briefly discussed.     

基于双变量无单元法的欧拉梁动力特性计算与分析

以广义移动最小二乘法为理论基础,将同时考虑挠度和转角双变量的无单元法运用于欧拉梁的动力特性计算与分析。以罚函数法引入位移边界,建立欧拉梁无单元法质量矩阵和刚度矩阵的计算方法。运用双变量无单元法计算了四种不同边界条件欧拉梁的自振圆频率和振型,通过与理论解、有限元解、单变量无单元解的比较,表明该法较单变量无单元法具有更高的插值精度,在各种复杂边界条件下均能获得准确的计算结果。特别是在高阶振型中,计算精度明显优于有限元解。最后,通过试算法对多项式基的阶次进行了讨论,给定了在动力计算中的合理取值。     

Tsallis Distribution-Based Fractional Derivative Method for Lamb Wave Signal Recovery

A new fractional derivative method based on the Tsallis distribution function is developed to recover the Lamb wave signals from the noisy Lamb wave signals. After the fractional derivative of the amplitude spectrum of the noisy Lamb signal at different derivative orders, the quartic polynomial function between the peak amplitude and the derivative order as well as that between the peak frequency and the derivative order is proposed based on the Tsallis distribution function. Then, the characteristic parameters of the amplitude spectrum are deduced by using the proposed polynomial relationship. Finally, the noise-free Lamb wave signal is recovered based on the characteristic parameters. Simulated results indicate that the Lamb wave signals can be recovered in the case of the white noise, the transient noise and the sine wave signal. Experimental results confirm the validity of the method. Consequently, the developed method can recover the Lamb wave signals effectively.     

Propagation of uncertainties in unfolding procedures

A review of methods currently used to unfold particle spectra from measured pulse height distributions or other detector readings is given. It is pointed out that most of the measurements in particle spectrometry reveal ill-conditioned or ill-posed problems. The presentation which is given here for examples of such inverse problems is focussed on the algorithms used in the HEPRO unfolding program package of PTB. The question of uncertainty propagation is discussed for least-squares algorithms as well as for those based on maximum entropy. A first attempt has been made to quantify generally the “ambiguity” in ill-posed unfolding problems. The maximum entropy algorithm realized in the MIEKE code allows a clear distinction to be made between two parts of uncertainty, one part coming from ambiguity and one part coming from the usual uncertainty propagation. The resulting uncertainty matrix of the MIEKE code provides these two parts.