Applications of Transmission Line Matrix Method For NDT

The Transmission Line Matrix ( TLM ) is a physical discretization approach used to solve the wave equation numerically. The method replaces a continuous system by a network or an array of lumped elements. The TLM method involves dividing the solution region into a rectangular mesh of the transmission line segments. The nodes of the mesh are the points of discontinuity for acoustic impedances. A computer program based on transmission-line matrix (TLM) model was developed to simulate the ultrasound propagation media with different acoustic impedances. The numerical model provides both frequency and time domain responses. The influence of variations in the shape of the incident pulse is discussed. The numerical results are compared with those obtained from experiments. Introduction To improve the results obtained in ultrasonic NDT , considerable theoretical effort is involved in developing reliable mathematical models of wave propagation in different media. Due to the complexity of the problems, numerical methods have proven to be an appropriate approach. Among other numerical methods applied in the time domain, the TLM was found to be suitable for complex geometries and various types of input signals. These advantages make this method a suitable method for ultrasonic NDT. The transmission line method was proposed by Johns (1). The method is a direct numerical implementation of the Huygens principle (2). The wave front at each iteration (instant in time) for a certain point is a result made of the waveforms generated at a neighbouring point in the previous iteration. The TLM is a physical discretization approach and this method does not require the solution of the differential equation. A continuous system is replaced by a network or an array of lumped elements. The TLM requires division of the solution region into a rectangular mesh of the transmission lines. The nodes of the mesh are points of discontinuity for impedances. To solve a problem using the TLM, a set of boundary conditions and material constituents must be provided. An initial excitation must also be given. Then the impulses are propagated throughout the mesh using scattering theory on transmission lines. There is no limitation regarding the frequency of interest, but the size of the mesh imposes an upper limit on the frequency response analysis. Model Description 5/4/04 12:01 PM Applications of Transmission Line Matrix Method For NDT Page 1 of 7 http://www.ndt.net/article/ecndt02/319/319.htm Considering Kirchhoff’s laws for a shunt transmission the wave equation for the voltage can be written (3): TLM algorithm