Mathieu's Equation and its Generalizations: Overview of Stability Charts and their Features

Ivana Kovacic, Richard H. Rand, Si Mohamed Sah

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Abstrakt

This work is concerned with Mathieu's equation - a classical differential equation, which has the form of a linear second-order ordinary differential equation with Cosine-type 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.
OriginalsprogEngelsk
Artikelnummer020802
TidsskriftApplied Mechanics Reviews
Vol/bind70
Udgave nummer2
Antal sider22
ISSN0003-6900
DOI
StatusUdgivet - 2018
Udgivet eksterntJa

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