Dynamic analysis and drilling degrees of freedom

Finite element methods for dynamic analysis employing elements with drilling degrees of freedom are presented. The formulation is based on a variational principle in which displacements and rotations are interpolated independently. The issue of zero masses corresponding to rotational degrees of freedom is addressed and techniques for defining consistent and lumped rotational mass matrices are presented.     

Dynamics Modelling of Hexaslides using the Decoupled Natural Orthogonal Complement Matrices

In this paper, dynamic model of a class of parallel systems, namely, the hexaslides, is proposed. The model developed is based on the concept the decoupled natural orthogonal complement (DeNOC) matrices, introduced elsewhere. The dynamic model of hexslides, though complex due to the existence of multi-loop kinematic chains, is required for actuator power estimation, computed-torque control, optimum tool trajectory generation, etc. The use of DeNOC offers many physical interpretations, recursive algorithms, and parallel computations. Using the proposed dynamic model, a parallel inverse dynamics algorithm has been presented to compute the actuator forces. This is useful to choose suitable motors for an application. An illustration is provided using an existing machine tool based on hexaslides, namely, the HexaM, while it is carrying out a circular contouring. Secondly, the effect of leg and slider inertias is also studied, which clearly suggests that neither of these can be neglected while finding the actuator forces.     

Inversion of confluent Vandermonde matrices

This paper is concerned with the inversion of confluent Vandermonde matrices. A novel and simple recursive algorithm for inverting confluent Vandermonde matrices is presented. The algorithm is suitable for classroom use in both numerical as well as symbolic computation. Examples are included to illustrate the proposed algorithm.     

Transient Green’s Tensor for a Layered Solid Half-Space With Different Interface Conditions

Pulsed ultrasonic techniques can be and have been used to examine the interface conditions of a bonded structure. To provide a theoretical basis for such testing techniques we model the structure as a layer on top of a half-space, both of different elastic properties, with various interface bonding conditions. The exact dynamic Green’s tensor for such a structure is explicitly derived from the three-dimensional equations of motion. The final solution is a series. Each term of the series corresponds to a successive arrival of a “generalized ray” and each is a definite line integral along a fixed path which can be easily computed numerically. Willis’ method is used in the derivation. A new scheme of automatic generation of the arrivals and ray paths using combinatorial analysis, along with the summation of the corresponding products of reflection coefficients is presented. A FORTRAN code is developed for computation of the Green’s tensor when both the source and the detector are located on the top surface. The Green’s tensor is then used to simulate displacements due to pulsed ultrasonic point sources of known time waveform. Results show that the interface bonding conditions have a great influence on the transient displacements. For example, when the interface bonding conditions vary, some of the first few head waves and regular reflected rays change polarities and amplitudes. This phenomenon can be used to infer the quality of the interface bond of materials in ultrasonic nondestructive evaluation. In addition the results are useful in the study of acoustic microscopy probes, coatings, and geo-exploration.     

The stability robustness determination of state space models with real unstructured perturbations

This paper considers the robust stability of a linear time-invariant state space model subject to real parameter perturbations. The problem is to find the distance of a given stable matrix from the set of unstable matrices. A new method, based on the properties of the Kronecker sum and two other composite matrices, is developed to study this problem; this new method makes it possible to distinguish real perturbations from complex ones. Although a procedure to find the exact value of the distance is still not available, some explicit lower bounds on the distance are obtained. The bounds are applicable only for the case of real plant perturbations, and are easy to compute numerically; if the matrix is large in size, an iterative procedure is given to compute the bounds. Various examples including a 46th-order spacecraft system are given to illustrate the results obtained. The examples show that the new bounds obtained can have an arbitrary degree of improvement over previously reported ones. This work has been supported by the Natural Sciences and Engineering Research Council of Canada under Grant No. A4396.     

Eigensolution of specially structured matrices with hyper‐symmetry

Recently, four canonical forms have been developed and applied to the dynamics and stability analysis of symmetric frames. In this paper, hyper‐symmetric matrices and specially structured matrices are defined and efficient methods are proposed for the eigensolution of such matrices. Applications are extended to hyper‐graphs and specially structured graphs. Simple methods are developed for calculating the eigenvalues of the Laplacian matrices of such graphs. The developments presented in this paper can also be considered as generalization of Form II and Form III symmetry, previously defined by the authors. Copyright © 2006 John Wiley & Sons, Ltd.     

An Implementation of Bouchouev's Method for a Short Time Calibration of Option Pricing Models

We analyse the Bouchouev integral equation for the deterministic volatility function in the Black–Scholes option pricing model. We areable to reduce Bouchouev's original triple integral equation to a single integral equation and describe its numerical solution. Moreover we show empirically that the most complex term in the equation may often be safely ignored for the purposes of numerical calculations. We present a selection of numerical examples indicating the range of time values for which we would expect the equation to be valid.     

浅谈2000版IS09000族质量管理体系标准的结构与特点

结合对2000年版ISO9000族质量管理体系标准的理解和分析,对标准的结构和特点进行了探讨。     

Determining the characteristics of systems with multiple inputs and multiple outputs

A simple and computationally efficient method of determining the transfer function and other characteristics of systems with multiple inputs and multiple outputs (MIMO systems) described by autoregression equations is proposed. The method is based on the use of the discrete Fourier transformation. The algorithm is highly suitable for computer implementation. The efficiency and simplicity of the method are illustrated using the example of a system with three inputs and three outputs. The proposed concept may be applied to systems described by the autoregression sliding mean.