Dynamic analysis of shear deformable plates using the Dual Reciprocity Method

The Dual Reciprocity Method is a popular mathematical technique to treat domain integrals in the boundary element method (BEM). This technique has been used to treat inertial integrals in the dynamic thin plate bending analysis using a direct formulation of the BEM based on the elastostatic fundamental solution of the problem. In this work, this approach was applied for the dynamic analysis of shear deformable plates based on the Reissner plate bending theory, considering the rotary inertia of the plate. Three kinds of problems: modal, harmonic and transient dynamic analysis, were analyzed. Numerical examples are presented to demonstrate the efficiency and accuracy of the proposed formulation.     

Some comments on the use of Radial Basis Functions in the Dual Reciprocity Method

We comment on the use of radial basis functions in the dual reciprocity method (DRM), particularly thin plate splines as used in Agnantiaris et al. (1996). We note that the omission of the linear terms could have biased the numerical results as has occurred in several previous studies. Furthermore, we show that a full understanding of the convergence behavior of the DRM requires one to consider both interpolation and BEM errors, since the latter can offset the effect of improved data approximation. For a model Poisson problem this is demonstrated theoretically and the results confirmed by a numerical experiment.     

Three-dimensional structural vibration analysis by the Dual Reciprocity BEM

The dual reciprocity boundary element method (DR/BEM) is employed for the analysis of free and forced vibrations of three-dimensional elastic solids. Use of the elastostatic fundamental solution in the integral formulation of elastodynamics creates an inertial volume integral in addition to the boundary ones. This volume integral is transformed into a surface integral by invoking the reciprocal theorem. A general analytical method is described for the closed form determination of the particular solutions of the displacement and traction tensors corresponding to any radial basis function employed in the transformation process. The simple but effective 1+r radial basis function is used in the applications of this paper. Quadratic continuous and discontinuous 9-noded boundary elements are used in the analysis. Free vibrations are studied by solving the corresponding eigenvalue problem iteratively. Harmonic forced vibration problems are solved directly in the frequency domain. Transient forced vibration problems are solved by integrating the equations of motion stepwise with the aid of various algorithms. Interior collection points are also used for assessing the accuracy of the method. Two numerical examples involving free and forced vibrations of a sphere and a cube are presented in detail.     

Dual reciprocity BEM: local versus global approximation functions for diffusion, convection and other problems

The use of the global approximation functions (elements of Pascal's triangle, sine expansions and others) in the dual reciprocity boundary element method is compared to the better known local radial basis functions for convection, diffusion and other problems in which the volume integrals considered contain first and second derivatives of the problem variables, time derivatives and sums and products of functions, including nonlinear terms. It will be shown that whilst it is possible to obtain accurate solutions to the problems considered using the global functions, a successful solution to a given problem depends very much on the function chosen, as well as other factors.     

Information criteria for the choice of parametric functions formeasurement

This paper deals with the problem of nonlinear reconstruction of a measurand or the so-called nonlinear inverse problem. Some criteria leading to the choice of the parametric models to be used in inverse problems are presented. It is demonstrated that some parametric functions are “better” than others when the final goal is an accurate estimate of some unknown quantity. Examples dealing with analytical functions or with a more realistic heat conduction problem are given     

The problem of selecting the shape functions for a p-type finite element

The paper addresses the question of the optimal selection of the shape functions for p-type finite elements and discusses the effectivity of the conjugate gradient and multilevel iteration method for solving the corresponding linear system.     

Transient Non-linear Heat Conduction Solution by a Dual Reciprocity Boundary Element Method with an Effective Posteriori Error Estimator

A Dual Reciprocity Boundary Element Method is formulated to solve non-linear heat conduction problems. The approach is based on using the Kirchhoff transform along with lagging of the effective non-linear thermal diffusivity. A posteriori error estimate is used to provide effective estimates of the temporal and spatial error. A numerical example is used to demonstrate the approach.     

粘弹性薄板动力响应问题的多重互易法

本文给出了粘弹性薄板动力响应问题的多重互易法（MRM）.首先在Laplace变换区域中得到了由重调和算子基本解序列给出的粘弹性板动力响应问题的MRM方法,再利用改进的Bellman反变换技术,求得原问题的解.讨论了MRM方法中的迭代误差估计.文末给出了数值算例,计算表明该方法具有较高精度和较快收敛性.适用于长时间的动力问题的计算.     

A new method for selecting calf pericardium for use in cardiac bioprostheses on the basis of morphological and mechanical criteria

The durability of existing calf pericardium bioprostheses is limited by phenomena such as mechanical stress and calcification, the factors most frequently implicated in valve failure. Varying the preferred direction of the collagen fibers influences the mechanical behavior of the pericardial membrane. Given this possible variation, a strict control of the selection of the biomaterial employed in the construction of valve leaflets is essential, but a reliable method of selection has yet to be established.This study describes the development of a new system of in vitro selection involving a hydraulic simulator that reproduces the mechanical behavior of pericardial membranes subjected to the stress of continuous flow.By combining morphological criteria such as thickness and homogeneity with those of mechanical behavior, and by selecting paired samples from different parts of the pericardium, we obtained excellent mathematical fits. Linear regression analysis provided the mode of predicting the tensile strength in a given sample when this value had been determined in its twin. The upper zones of calf pericardium, corresponding to either right or left ventricle but at a distance from ligamentous structures, showed the best mean results at rupture (60 MPa) and permitted the most reliable prediction. The expected stress for an elongation of 30% was 1.12 MPa, as was previously observed, with a 95% confidence interval of between 1.11 and 1.14 MPa.These trials, together with the careful selection of the pairs, should help to establish definitive selection criteria. © 2001 Kluwer Academic Publishers     

Limitations of the Petroski-Achenbach crack opening displacement approximation for the calculation of weight functions

The displacement fields of edge cracks under tensile stress can be described by an approximation given by Petroski and Achenbach. Using this approximation and the weight function method, the displacement fields for single forces and varying stress distributions can be obtained. This is done for the examples of an edge cracked and a through cracked plate, showing good agreement with FE and analytical calculations, respectively.     

Analysis of the Effect of Microphone Parameters in Reciprocity Calibrations Using Taguchi Method

The paper presents parametric study investigating the relative influence of the various microphone parameters affecting the closed coupler reciprocity measurements while computing the sensitivity of reference standard microphones using the well known MP.EXE program used by National Metrology Institutes of various countries. A design of experiments perspective using L ₉ (3⁴) orthogonal array and analysis of variance (ANOVA) method is presented for LS1P and LS2P microphones. The relative importance of microphone parameters on its sensitivity is evaluated in terms of percentage contribution using ANOVA methodology.     

Algorithms for choosing weighting characteristics for approximation of functions with the method of least squares

Proposals are presented for new approaches to selection of the weighting characteristics (weights) in the method of least squares with allowance for not only the stochastic characteristics of measurement errors, but for the coefficients of the quadrature formulas used for transition to discrete analysis of a continuous process; the case of nonuniformities in the distribution of locations of quantization points for measurements is also considered. Translated from Izmeritel’naya Tekhnika, No. 8, pp. 5–10, August, 1996.     

周期函数的Lagrange型插值逼近

求文构造了一类Lagrange型插值三角多项式．并给出以高阶模为阶的逼近偏差估计．     

Minimizing the Effects of Reflections by Using a Virtual Pulse Method, for Free-Field Reciprocity Calibration

The National Metrology Institute of Japan has developed a free-field reciprocity calibration system for type WS3 microphones as acoustic standards in the airborne ultrasonic range between 20 and 100 kHz, because numerous instruments radiate airborne ultrasound. Precise calibration of these microphones requires minimizing the influence of sound reflected from the objects such as absorbing wedges and supporting rods within the acoustic chamber. To minimize this influence, we applied the virtual pulse method, which is a signal processing technique used in the audible frequency to airborne ultrasonic range. Experimental and analytical results validated this method. Use of this method in the calibration of type WS3 microphones will decrease the calibration uncertainty in the free-field sensitivity level.     

两换能器互易法校准高频水听器若干影响因素的研究

两换能器互易法由于将校准归结到若干电学量的测量,目前是校准高频水听器的主要方法之一。校准水听器过程中,在保证电学量测量精度的情况下,开展了诸多影响因素的研究,主要包括辅助换能器有效直径、声场中心对称性,水听器浸泡时间,水含氧量及衰减修正等引起的影响研究等。研究表明,在准确计算出衍射修正参数G1、平均效应修正参数G2的前提下,辅助换能器有效直径、衰减修正等引入的影响较大,而声场的非中心对称性、水听器浸泡时间及水含氧量带来的影响较小。结果表明,所建立的高频水听器校准装置,在0.5～15 MHz的频率范围内,校准结果与英国国家物理实验室的校准结果非常接近,结果准确可靠。     

Application of variational mesh generation approach for selecting centers of radial basis functions collocation method

In this paper, a two-dimensional variational mesh generation method is applied to obtain adaptive centers for radial basis functions (RBFs). At first, a set of uniform centers is distributed in the domain, then mesh generation differential equations are used to move the centers to region with high gradients. An iterative algorithm is introduced to solve steady-state mesh generation differential equations with RBFs. Functions with steep variation in the domains are used to validate the adaptive centers generation method. In addition to the centers adaption process is applied to solve elliptic partial differential equations via RBFs collocation method. Numerical results of Helmholtz differential equation show a clear reduction in the error, when the adaptive centers are used for RBFs.     

New Measurement Service for Determining Pressure Sensitivity of Type LS2aP Microphones by the Reciprocity Method

A new National Institute of Standards and Technology (NIST) measurement service has been developed for determining the pressure sensitivities of American National Standards Institute and International Electrotechnical Commission type LS2aP laboratory standard microphones over the frequency range 31.5 Hz to 20 000 Hz. At most frequencies common to the new service and the old service, the values of the expanded uncertainties of the new service are one-half the corresponding values of the old service, or better. The new service uses an improved version of the system employed by NIST in the Consultative Committee for Acoustics, Ultrasound, and Vibration (CCAUV) key comparison CCAUV.A-K3. Measurements are performed using a long and a short air-filled plane-wave coupler. For each frequency in the range 31.5 Hz to 2000 Hz, the reported sensitivity level is the average of data from both couplers. For each frequency above 2000 Hz, the reported sensitivity level is determined with data from the short coupler only. For proof test data in the frequency range 31.5 Hz to 2000 Hz, the average absolute differences between data from the long and the short couplers are much smaller than the expanded uncertainties.     

Dual bases and discrete reproducing kernels: a unified framework for RBF and MLS approximation

Moving least squares (MLS) and radial basis function (RBF) methods play a central role in multivariate approximation theory. In this paper we provide a unified framework for both RBF and MLS approximation. This framework turns out to be a linearly constrained quadratic minimization problem. We show that RBF approximation can be considered as a special case of MLS approximation. This sheds new light on both MLS and RBF approximation. Among the new insights are dual bases for the approximation spaces and certain discrete reproducing kernels.     

基于频响函数辨识鼓筒-轮盘结合部连接参数的选点原则

基于频响函数的辨识方法被广泛用于识别结合部动态参数,其中如何选择频响数据是关键问题。本文针对结合部采用弹簧和阻尼器连接的鼓筒-轮盘模型提出了频响数据选取原则和对应于该原则的量化标准。具体选点原则为所选取的局部信噪比最高的频点所对应的模态对连接刚度的综合灵敏度应该最高。为了定量比较不同模态对连接刚度的综合灵敏度,建立了具体的量化指标和标准。理论分析表明本文所提出的频响数据选取原则和量化标准是有效的,具有一定的工程应用价值。