Mathieu's equation and its generalizations: Overview of stability charts and their features

Abstract

Copyright © 2018 by ASME. This work is concerned with Mathieu's equation-a classical differential equation, which has the form of a linear second-order ordinary differential equation (ODE) with Cosinetype periodic forcing of the stiffness coefficient, and its different generalizations/extensions. These extensions include: the effects of linear viscous damping, geometric nonlinearity, damping nonlinearity, fractional derivative terms, delay terms, quasiperiodic excitation, or elliptic-type excitation. The aim is to provide a systematic overview of the methods to determine the corresponding stability chart, its structure and features, and how it differs from that of the classical Mathieu's equation.