A technique for increasing the accuracy of the FFT-based method of numerical inversion of Laplace transforms

AbstractThe FFT-based methods of numerical inversion of Laplace transforms use the trapezoidal rule to the Bromwich integral. We present in this paper a technique for reducing the truncation error in evaluating the Bromwich integral. The technique employs the differentiation property of the Laplace transform and performs the inversion on F(n)(s), the nth order derivative of the Laplace transform of a time function f(t). The improvement in the solution accuracy by incorporating the presented technique into the FFT-based numerical Laplace inversion method is demonstrated via numerical examples

A Model of Temporal Intensity Modulation for Laser Generated Ultrasound

Q-switched lasers are often used as a non-contact ultrasound source in non-destructive evaluation (NDE) of materials [1]. Q-switched lasers typically have ns pulse durations and generate broadband ultrasound waves, though longer laser pulses, of 100 microseconds or greater, have also been used [2] for NDE. These longer pulses tend to produce somewhat lower center frequencies than do Q-switched pulses, though they are still a broadband source. But it would be desirable in some NDE applications to narrow the signal bandwidth to improve the signal to noise ration (SNR), and also to have direct control over the center frequency of the generated ultrasound. In principle, this may be achieved by temporal [3,4] or spatial modulation [5,6] of the laser pulse, or both [7]. The purpose of this work was to develop a numerical model of a single, temporally modulated laser source of ultrasound in the thermoelastic regime, for isotropic metals

Análise viscoelástica de estruturas laminadas mediante emprego da inversao numérica da transformada de Laplace

Este trabalho focaliza a análise viscoelástica de estruturas laminadas em material compósito de matriz polimérica, propondo o emprego de métodos de inversa0 numérica da transformada de Laplace numa formulacao adaptada ao método dos elementos finitos. Nesta abordagem alternativa,as equacóes constitutivas viscoelásticas, formuladas no plano complexo da variável de transformacáo S , reduzem o problema a urna análise elástica equivalente. As solu~óesc omplexas sáo entiio retornadas ao plano físico para o valor de tempo desejado, dispensando processos incrementais. Exemplos de aplicaqóes siio executados comparando-se os resultados do Método da Transformada de Laplace com o Método das Variáveis de Estado que trata o problema viscoelástico de forma incremental.The viscoelastic analysis of laminated structures of polymeric matrix composite materials using Laplace transform is the objective of this work. The inverse of the Laplace transform is carried out using numerical methods adapted to a finite element method formulation. In this alternative aproach, as the constitutive equations are formulated on the complex plane in the transformation variable 'S', the viscoelasti~problemre duces to an equivalent elastic one. The complex solutions are then sent back to the physical plane for the desired time value, dispensing incremental processes. Examples of aplications compairing results obtained with the Laplace Transformation Method and the State Variables Method (that treats the viscoelastic problem in an incremental form) are presented.Peer Reviewe

Performance analysis of load based M/M/3 transient queueing system with finite capacity

This paper deals with the investigation of M/M/3 queueing model under the provision of service rates of jobs depend upon the load of the jobs arrived in the system. The customers (jobs) arrive in the system in Poisson fashion and they are served in the chronological order of their arrival. Differential equations of transient probability distribution functions by using a transition diagram have been set up. Laplace Transform, probability generating function, and Rouchey’s Theorem have been applied to get the probability of n customer in time t. Various performance indices such as the mean number of customers in the system, expected number of customers in a queue, probability that one has not to wait, expected mean time spent in a system, expected mean time spent in a queue, probability that the queue size being greater than or equal to N have been obtained analytically. Finally, the analytical results are validated graphically with the help of computing software.Publisher's Versio

Investigation on Transient Responses of a Piezoelectric Crack by using Durbin and Zhao Methods for Numerical Inversion of Laplace Transforms

[[abstract]]This study applies the numerical inversion of Laplace transform methods to study the piezoelectric dynamic fracture problem, recalculating Chen and Karihaloo's [1] analysis on the transient response of a impermeable crack subjected to anti-plane mechanical and in-plane electric impacts. Three numerical methods were adopted for calculating the dynamic stress intensity factor: Durbin method, Zhao method 1, and Zhao method 2. The results obtained were more accurate than the results in Chen and Karihaloo's [1] study. Through the calculation, this study presents a better range of parameters for the above three methods, and compares the advantages and disadvantages of each method in detail.[[notice]]補正完畢[[incitationindex]]SCI[[incitationindex]]EI[[booktype]]電子版[[booktype]]紙

Inversion of the Laplace transform from the real axis using an adaptive iterative method

In this paper a new method for inverting the Laplace transform from the real axis is formulated. This method is based on a quadrature formula. We assume that the unknown function $f(t)$ is continuous with (known) compact support. An adaptive iterative method and an adaptive stopping rule, which yield the convergence of the approximate solution to $f(t)$, are proposed in this paper.Comment: 38 pages, 12 figure

Estimating the Lead Time Distribution of Priority Lots in a Semiconductor Factory

We consider the lead time of priority lots in a semiconductor factory. The main cause of delays is waiting for repairs of failed machines, and the failures are mainly caused by power disturbances. This can be modeled as an exogenous time-dependent failure process, and we develop a probabilistic model of the system based on this. Using this model, a convolution algorithm for finding the lead time distribution is described. We describe a method of creating synthetic samples of the lead time from historical failure and repair data collected in the factory. Based on such a sample from the MIT Integrated Circuits Laboratory, we approximate the distribution of lead times by a gamma probability density function shifted by the smallest possible lead time for the product type. The parameters of the gamma distribution are found by using a maximum likelihood estimator. The resulting distribution gives good agreement with the synthetic data for values less than two standard deviations above the mean lead time. Since our procedure only depends on a description of the process and the failure and repair history of the factory, it can also be used to obtain lower bounds on the lead time for new product types

A model for the ultrasonic detection of surface-breaking cracks by the scanning laser source technique

    A model for the scanning laser source (SLS) technique is presented. The SLS is a novel laser-based inspection method for the ultrasonic detection of small surface-breaking cracks. The generated ultrasonic signal is monitored as a line-focused laser is scanned over the defect. Characteristic changes in the amplitude and the frequency content are observed. The modeling approach is based on the decomposition of the field generated by the laser in a cracked two-dimensional half-space, by virtue of linear superposition, into the incident and the scattered fields. The incident field is that generated by laser illumination of a defect-free half-space. A thermoelastic model has been used which takes account of the effect of thermal diffusion, as well as the finite width and duration of the laser source. The scattered field incorporates the interactions of the incident field with the surface-breaking crack. It has been analyzed numerically by a direct frequency domain boundary element method. A comparison with an experiment for a large defect shows that the model captures the observed phenomena. A simulation for a small crack illustrates the ability of the SLS technique to detect defects smaller than the wavelength of the generated Rayleigh wave. &nbsp