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Statistical energy analysis of nonlinear vibrating systems.

Accepted version
Peer-reviewed

Repository DOI


Type

Conference Object

Change log

Authors

Spelman, GM 
Langley, RS 

Abstract

Nonlinearities in practical systems can arise in contacts between components, possibly from friction or impacts. However, it is also known that quadratic and cubic nonlinearity can occur in the stiffness of structural elements undergoing large amplitude vibration, without the need for local contacts. Nonlinearity due purely to large amplitude vibration can then result in significant energy being found in frequency bands other than those being driven by external forces. To analyse this phenomenon, a method is developed here in which the response of the structure in the frequency domain is divided into frequency bands, and the energy flow between the frequency bands is calculated. The frequency bands are assigned an energy variable to describe the mean response and the nonlinear coupling between bands is described in terms of weighted summations of the convolutions of linear modal transfer functions. This represents a nonlinear extension to an established linear theory known as statistical energy analysis (SEA). The nonlinear extension to SEA theory is presented for the case of a plate structure with quadratic and cubic nonlinearity.

Description

Keywords

energy cascades, nonlinear vibration, statistical energy analysis

Journal Title

Philos Trans A Math Phys Eng Sci

Conference Name

Journal ISSN

1364-503X
1471-2962

Volume Title

373

Publisher

The Royal Society
Sponsorship
Engineering and Physical Sciences Research Council (EP/K003836/1)
The authors would like to acknowledge the ‘Engineering Nonlinearity’ Program Grant, funded by EPSRC that has funded the research content of this paper. We have no competing interests.