Investigating modal contributions using a Galerkin model

Elliott, A.J. , Cammarano, A. and Neild, S.A. (2019) Investigating modal contributions using a Galerkin model. In: Kerschen, G. (ed.) Nonlinear Dynamics, Volume 1: Proceedings of the 36th IMAC, A Conference and Exposition on Structural Dynamics 2018. Series: Conference proceedings of the Society for Experimental Mechanics series. Springer: Cham, pp. 199-210. ISBN 9783319742793 (doi: 10.1007/978-3-319-74280-9_22)

Abstract

The ability to accurately model the behaviour of a mechanical structure using a fraction of the original number of degrees of freedom is pursued throughout the study of dynamics and, in recent years, this has been key in the study of nonlinear systems. One of the first ways in which this was implemented was through the Galerkin method, and it has been continually used since its original derivation due to the fact that it does not require the use of any commercial finite element packages. In fact, the modeshapes of the system have been previously calculated analytically and the linear natural frequencies calculated numerically, leading to large reductions in the amount of time needed to develop the model. This paper considers the modal reduction of a Galerkin clamped-clamped beam model, first deriving the equations of motion and introducing analytical terms for orthogonality, then comparing the behaviour it predicts with that from commercial finite element software for a range of forcing frequencies and amplitudes. Finally, the model can be used to derived the backbone curves of the system.

• Item Type: Book Sections
• Status: Published
• Glasgow Author(s) Enlighten ID: Cammarano, Dr Andrea and Elliott, Mr Alexander
• Authors: Elliott, A.J., Cammarano, A., and Neild, S.A.
• College/School: College of Science and Engineering > School of Engineering > Systems Power and Energy
• Publisher: Springer
• ISBN: 9783319742793
• Published Online: 07 June 2018