Practical insight through perturbation analysis

Tanya Tarnopolskaya, Frank de Hoog


Though industrial processes are perceived to be dauntingly complex from a mathematical modelling perspective, simple mathematical models often provide remarkable insight. One of the reasons behind this apparent contradiction is that the mathematical models often involve small and/or large non-dimensional parameters and therefore are amenable to simplification through the use of perturbation analysis. In many cases, the leading order perturbation approximation provides the bulk of the information about the structure and behaviour of the solution and is often sufficient to obtain profound insight into the phenomenon under examination. This article illustrates such utility of the perturbation analysis by using examples in which leading order perturbation approximations provide substantial insight into the mode transition phenomena in the vibrational behaviour of curved beams and helices. The methodology described in this article can be used in a wide range of applications to reveal the simplest possible structure of the mathematical model that answers the question under examination.

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Perturbation analysis, singular perturbation, regular perturbation, leading-order perturbation approximation

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