Using frequency detuning to compare analytical approximations for forced responses

Elliott, A., Cammarano, A. , Neild, S.A., Hill, T.L. and Wagg, D.J. (2019) Using frequency detuning to compare analytical approximations for forced responses. Nonlinear Dynamics, 98, pp. 2795-2809. (doi: 10.1007/s11071-019-05229-6)

Abstract

It is possible to use numerical techniques to provide solutions to nonlinear dynamical systems that can be considered exact up to numerical tolerances. However, often, this does not provide the user with sufficient information to fully understand the behaviour of these systems. To address this issue, it is common practice to find an approximate solution using an analytical method, which can be used to develop a more thorough appreciation of how the parameters of a system influence its response. This paper considers three such techniques—the harmonic balance, multiple scales, and direct normal form methods—in their ability to accurately capture the forced response of nonlinear structures. Using frequency detuning as a method of comparison, it is shown that it is possible for all three methods to give identical solutions, should particular conditions be used.

• Item Type: Articles
• Additional Information: This research was supported by EPSRC (Grant no EP/K005375/1).
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Cammarano, Dr Andrea and Elliott, Mr Alexander
• Authors: Elliott, A., Cammarano, A., Neild, S.A., Hill, T.L., and Wagg, D.J.
• College/School: College of Science and Engineering > School of Engineering > Systems Power and Energy
• Journal Name: Nonlinear Dynamics
• Publisher: Springer
• ISSN: 0924-090X
• ISSN (Online): 1573-269X
• Published Online: 05 September 2019
• Copyright Holders: Copyright © The Authors 2019
• First Published: First published in Nonlinear Dynamics 98:2795–2809
• Publisher Policy: Reproduced under a Creative Commons license