Modal Analysis of Transient Ultrasonic Guided Waves in a Cylinder

Abstract

Loaded cylinders are ubiquitous in industrial applications (e.g., pipes carrying pressurized fluids). Defects in a cylinder reduce the load that can be carried safely; catastrophic failure of a cylinder can be costly in terms of both economics and loss of life. An apparent dichotomy exists presently in the literature. To date, analyses are performed predominantly in the wave number-frequency domain and tend to focus on a single mode or relatively few modes (e.g., [1] – [3]) to minimize computational requirements. Excitation of a single mode, while permitting straightforward interpretations, is difficult to achieve in practice, requires specialized transducers (see, e.g., [2]), and potentially limits the types of defects that can be detected (see, e.g., [4]). Waves generated and subsequently scattered by a transient multi-modal excitation, on the other hand, are much easier to excite practically and have the potential to quickly detect and characterize more defects, albeit with more interpretation effort. An understanding of the behaviour of multi-modes excitations is of great interest in Non-Destructive Testing (NDT). While direct time integration is capable of considering multiple modes in a single analyses, it sheds little insight into modal interactions. A Semi-Analytic Finite Element (SAFE) computational approach [5] is adopted here that ameliorates the shortcomings of single mode and direct time integration analyses and provides information on the relative contribution of each mode. This approach, while computationally expensive, allows many “what if? ” questions to be posed that give insight into the sensitivity from variations, for example, in material properties and cylinder geometries. This understanding is a prerequisite for developing and understanding solutions to inverse problems, including the development of robust artificial intelligence that can automate the interpretation. To overcome the difficulties with computational expense, parallel computing techniques are applied, that are implemented on readily available personal and high performance micro-computers. Practical implementation difficulties, including vast storage requirements, numerical artifacts arising from the use of finite memory widths, and minimization of waiting times, are overcome by adopting appropriate computer science techniques. The ultimate feasibility and field applicability of ultrasonic inspection of structures using elastic waves depends upon a meaningful interpretation of measured data which can come only from knowledge of the physics of guided wave propagation and scattering that is presently unavailable. The approach presented here is a first step in this direction.