Nonlinear Dynamics

Automatic Ball Balancers

DJ Rodrigues, AR Champneys, MI Friswell & RE Wilson, Automatic Two-Plane Balancing for Rigid Rotors. International Journal of Non-linear Mechanics, 43(6), July 2008, 527-541.

K Green, AR Champneys, MI Friswell & AM Munoz, Investigation of a Multi-ball Automatic Dynamic Balancing Mechanism for Eccentric Rotors. Royal Society Philosophical Transactions A, 366(1866), March 2008, 705-728.

K Green, AR Champneys & MI Friswell, Analysis of the Transient Response of an Automatic Dynamic Balancer for Eccentric Rotors. International Journal of Mechanical Sciences, 48(3), March 2006, 274-293.

Dynamics of Structures with Local Nonlinearities and Model Reduction

The analysis of nonlinear models with a large number of degrees of freedom requires considerable computational effort and therefore models of nonlinear systems are generally restricted to a low number of degrees of freedom. In structural dynamics finite element analysis is often used to obtain accurate discretised models of continuous systems, usually with hundreds if not thousands of degrees of freedom. If a nonlinear component, for example a joint or a crack, is added to the finite element model, then the calculation of the system response will require considerable computation. Nonlinearities in these large models are often local in the sense that the forces in the nonlinear components may be determined by a small number of degrees of freedom. This project reduces the number of degrees of freedom in the model, whilst retaining those coordinates that are important to specify the nonlinearity, and thus speed up the computation.

One important application is the effect of cracks in beams and shafts on the system dynamics. There is considerable interest in predicting the response of failed shafts and also detecting the presence of a crack. The usual model represents the crack as piece wise linear and switches between two stiffness matrices depending on whether the crack is open or closed.

MI Friswell, JET Penny & SD Garvey, The Application of the IRS and Balanced Realisation Methods to Obtain Reduced Models of Structures with Local Nonlinearities. Journal of Sound and Vibration, 196(4), October 1996, 453-468.

MI Friswell, JET Penny & SD Garvey, Using Linear Model Reduction to Investigate the Dynamics of Structures with Local Non-linearities. Mechanical Systems and Signal Processing, 9(3), May 1995, 317-328.

MI Friswell & JET Penny, The Accuracy of Jump Frequencies in Series Solutions of the Response of a Duffing Oscillator. Journal of Sound and Vibration, 169(2), January 1994, 261-269.

Y Benhafsi, JET Penny & MI Friswell, A Parametric Identification Method for Discrete Nonlinear Systems Incorporating Cubic Stiffness Elements. International Journal of Analytical and Experimental Modal Analysis, 7(3), July 1992, 179-195.

MI Friswell & JET Penny, Crack Modelling for Structural Health Monitoring. Structural Health Monitoring: An International Journal, 1(2), October 2002, 139-148.

Rotating Discs with Friction Loading

This project builds on previous work on vibration phenomena in automotive brakes. Multiple scales analysis has been performed upon a fixed plate with a rotating system of mass/spring/damper forces and a frictional follower force. The analysis has shown that forward and backward travelling waves can be developed in the plate (or disc) and that merely the presence of friction (not its magnitude) is sufficient to destabilise the forward travelling wave and, conversely, to stabilise the backward travelling wave. Further initial work on flutter and parametric instabilities has also been carried out. This requires the analysis of parametric resonance under both linear and nonlinear friction conditions, the application of critical speed analysis to squeal instability, the development of Finite Element and Analytical models for frictional follower loads, the investigation of regular and chaotic motions, and finally to validate theoretical predictions by experiments.

H Ouyang, JE Mottershead, MP Cartmell & MI Friswell, Friction Induced Parametric Resonances in Discs: The Effect of a Negative Friction-Velocity Relationship. Journal of Sound and Vibration, 209(2), January 1998, 251-264.

JE Mottershead, H Ouyang, MP Cartmell & MI Friswell, Parametric Resonances in an Annular Disc, with a Rotating System of Distributed Mass and Elasticity; and Effects of Friction and Damping. Proceedings of the Royal Society of London, Series A, 453(1956), 1997, 1-19.

Q Cao, H Ouyang, MI Friswell & JE Mottershead, Linear Eigenvalue Analysis of the Disc-Brake Squeal Problem. International Journal for Numerical Methods in Engineering, 61(9), November 2004, 1546-1563

Dynamics of Nonlinear Systems

G Litak, M Borowiec, MI Friswell & W Przystupa, Chaotic Response of a Quarter-Car Model Forced by a Road Profile with a Stochastic Component. Chaos Solitons and Fractals.

G Litak, M Borowiec, MI Friswell & K Szabelski, Chaotic Vibration of a Quarter-Car Model Excited by the Road Surface Profile. Communications in Nonlinear Science and Numerical Simulations, 13(7), September 2008, 1373-1383.

G Litak, M Borowiec, M Ali, LM Saha & MI Friswell, Pulsive Feedback Control of a Quarter Car Model Forced by a Road Profile. Chaos Solitons and Fractals, 33(5), August 2007, 1672-1676.

K Worden, G Manson, TM Lord & MI Friswell, Some Observations on Uncertainty Propagation through a Simple Nonlinear System. Special Issue of the Journal of Sound and Vibration on Uncertainty, 288(3), December 2005, 601-621.

G Litak & MI Friswell, Dynamics of a Gear System with Faults in Meshing Stiffness. Nonlinear Dynamics, 41(4), September 2005, 415-421.

G Litak & MI Friswell, Vibration in Gear Systems. Chaos, Solitons and Fractals, 16(5), April 2003, 145-150.

Vibration of Nonlinear Composite Structures

Recent work has considered the vibration of multistable structures, and in particular identifying low order models that capture the strong non-linear dynamics of these structures.

A Carrella & MI Friswell, A Passive Vibration Isolator Incorporating a Composite Bistable Plate. Sixth EUROMECH Nonlinear Dynamics Conference, ENOC-2008, Saint Petersburg, Russia, 30 June - 4 July 2008.

A Carrella, F Mattioni, AA Diaz, MI Friswell, DJ Wagg & PM Weaver, Static and Dynamic Analysis of a Bistable Plate for Application in Morphing Structures. 7th European Conference on Structural Dynamics, EURODYN 2008, Southampton, 7-9 July 2008, paper 213.

A Carrella, MI Friswell, A Pirrera & GS Aglietti, Numerical and Experimental Analysis of a Square Bistable Plate. ISMA 2008, International Conference on Noise and Vibration Engineering, 15-17 September 2008, Leuven, Belgium, 3433-3440.

Last updated February 2009 by M I Friswell