Session: 05-02: Guided Waves II

Paper Number: 98050

98050 - Application of Mindlin Theory to Describe the Scattering of Guided Waves From Notches in a Plate 

The corrosion of pipes, pressure vessels, and storage tanks is a significant challenge to the oil, gas, and petrochemical industries causing unscheduled shutdowns and costly accidents of the assets. Guided wave tomography (GWT) is an attractive method to locate and determine the thickness of a corroded surface in the pipe by processing the waves excited and received by transducer arrays. Principally, it is an inversion method that collects the set of ultrasonic guided wave measurements from transducers and inverts them by appropriate tomography algorithms.

The main challenge associated with the GWT is the development of an efficient forward model to handle the wave propagation in a complex model. The 3D equations for electrodynamics have been proven to be an accurate model for describing the interactions between guided waves and defects but the computational effort required to solve these equations on computer hardware is not viable. Therefore, 2D acoustic forward models are usually preferred in many tomographic algorithms as they allow the easy mapping of the defect from the wave velocity. However, the acoustic forward models proved to be less accurate to describe the scattering of guided waves if the defect is smaller than 2 wavelengths of the probing wave. Also, they do not mimic the wave reflections from the defect which are important to build up higher tomographic resolution.

This paper investigates the accuracy of Mindlin plate theory to describe the scattering of low-frequency A0 mode from the defects smaller than 2 wavelengths of probing wave. Mindlin’s plate theory incorporates two adjustable parameters shear deformation and rotary inertia in the equations of motion which allows to model flexural modes in the 2D plane. The defects considered are small-sized symmetric and non-symmetric V-shaped notches in aluminum plate, which in real structures usually occurs as a result of localized corrosion. The Finite Difference (FD) method is used to analyze the scattering of A0 mode from defects with changing depth and width in a plane strain setting. In addition, the Pseudospectral method (PsM) is implemented to study the scattering from a complex 3D defect. The results are compared with the results from Finite Element (FE) simulations. The results of the Mindlin forward model are found to be in good agreement with the results from the FE model. The proposed numerical model leads to a better understanding of the interaction of guided waves with smaller defects and may improve the application of GWT to form a wall thickness map of the corroded surface, which is not possible using acoustic methods.

Presenting Author: Usman Rasheed Tallinn University of Technology (Taltech)