Mathematical model of distribution of ultrasonic waves directed into the pipeline with welded joints
Keywords:
mathematical model, Weld, pipeline, multi–layered medium, guided wave, transfer matrix coefficients, general matrix.Abstract
A mathematical model describing the propagation of ultrasonic guided waves in a multi–layered medium is proposed. Weld of the pipeline is proposed to consider as multi–layered elastic medium. Presented equations that describe the displacement field and stress created by bulk ultrasonic waves. The mathematical description of the formation of guided waves in the plate is presented. The formation is described by a system of equations each describes a bulk wave. For solving this system of equations is constructed a determinant and are shown equations for each element. For the mathematical description of the propagation of ultrasonic guided waves in a multi–layered media offers two approaches transfer matrix coefficients and a general matrix. In the method of transfer matrix coefficients the inner layers will be part of the equations that describe guided waves through the distribution of wave field (elementary volume displacement and stress) at the top and bottom interfaces of external layers. General matrix approach consists in collecting all the layers of media in a matrix.
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