The performance requirements of flexible structures are continually increasing. Often structures are required to have integrated control and sensor systems to carry out tasks such as limiting unwanted vibrations, detecting damage and in some cases changing the shape of the structure. These types of structures have become known as smart structures (sometimes called adaptive or intelligent structures). The ability to perform multiple tasks means that the smart structure is multifunctional. By their nature, these structures are typically highly flexible and are required to operate in a dynamic environment. As a result, the vibration behaviour of the structure is of critical importance. Not only is vibration important, it is often nonlinear, due to a range of effects which naturally arise in flexible structural dynamics. Applying control to the structure to limit unwanted vibration and to effect any shape changes also requires detailed knowledge of the vibration characteristics. This chapter introduces the basic ideas of nonlinear vibration and control, which will be used in later chapters to underpin the analysis of more complex structural elements.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Beards, C. F. (1981). Vibration analysis and control system dynamics. Ellis Horwood.
Bishop, R. E. D. and Johnson, D. C. (1960). The mechanics of vibration. Cambridge University Press.
Brogliato, B. (1999). Nonsmooth mechanics: Models, dynamics and control. Springer-Verlag.
Cartmell, M. (1990). Introduction to linear, parametric and nonlinear vibrations. Chapman and Hall.
Clark, R. L., Saunders, W. R., and Gibbs, G. P. (1998). Adaptive structures; dynamics and control. John Wiley.
Clough, R. W. and Penzien, J. (1993). Dynamics of Structures. McGraw-Hill. Second edition.
Den Hartog, J. P. (1934). Mechanical Vibrations. McGraw-Hill: New York.
di Bernardo, M., Budd, C. J., Champneys, A. R., and Kowalczyk, P. (2007). Piecewise-smooth dynamical systems: theory and applications. Springer-Verlag.
Ewins, D. J. (2000). Modal Testing. Research Studies Press.
Frish-Fay, R. (1962). Flexible Bars. Butterworths: London.
Fuller, C. R., Elliot, S. J., and Nelson, P. A. (1996). Active control of vibration. Academic Press.
Géradin, M. and Rixen, D. (1997). Mechanical Vibrations: Theory and Application to Structural Dynamics. Wiley Blackwell.
Goodwin, G. C., Graebe, S. F., and Salgado, M. E. (2000). Control System Design. Pearson. Inman, D. J. (2006). Vibration with control. Wiley.
Inman, D. J. (2007). Engineering vibration. Prentice Hall. Jordan, D. W. and Smith, P. (1999). Nonlinear ordinary differential equations; an introduction to dynamical systems. Oxford University Press. Third Edition. Krauskopf, B. (2005). Unlocking Dynamical Diversity: Optical Feedback Effects on Semiconductor Lasers, chapter; Bifurcation analysis of lasers with delay, pages 147–183. Wiley.
Leo, D. J. (2007). Smart material systems. Wiley.
McLachlan, N. W. (1950). Ordinary non-linear differential equations. Oxford University Press.
Meirovitch, L. (2001). Fundamentals of vibration. McGraw-Hill: New York.
Moheimani, S. O. R., Halim, D., and Fleming, A. J. (2003). Spatial control of vibration. World Scientific.
Moon, F. C. (1987). Chaotic vibrations: An introduction for applied scientists and engineers. John Wiley: New York.
Moon, F. C. and Shaw, S. W. (1983). Chaotic vibrations of a beam with non-linear boundary conditions. International Journal of Non-Linear Mechanics, 18(6), 465–477.
Nayfeh, A. H. and Mook, D. T. (1995). Nonlinear oscillations. John Wiley: New York.
Neill, D., Livelybrooks, D., and Donnelly, R. J. (2007). A pendulum experiment on added mass and the principle of equivalence. American Journal of Physics 75, 226–229.
Nelkon, M. (1969). Mechanics and properties of matter. Heinemann.
Preumont, A. (2002). Vibration control of active structures. Kluwer: Dordrecht.
Rayleigh, J. W. S. (1894a). Theory of sound: Volume 1. Macmillan and Co: London.
Rayleigh, J. W. S. (1894b). Theory of sound: Volume 2. Macmillan and Co: London.
Slotine, J.-J. E. and Li, W. (1991). Applied nonlinear control. Prentice Hall.
Srinivasan, A. V. and McFarland, D. M. (2001). Smart structures. Cambridge.
Thompson, J. M. T. and Champneys, A. R. (1996). From helix to localized writhing in the torsional post-buckling of elastic rods. Proceedings of the Royal Society A 452, 117–138.
Thompson, J. M. T. and Stewart, H. B. (2002). Nonlinear dynamics and chaos. John Wiley: Chichester.
Timoshenko, S. P. (1953). History of strength of materials. McGraw-Hill.
van der Heijden, G. H. M. (2008). The nonlinear mechanics of slender structures undergoing large deformations. Available for download from G. H. M. van der Heijden's website.
Virgin, L. N. (2007). Vibration of Axially-Loaded Structures. Cambridge.
Weaver Jr, W., Timoshenko, S. P., and Young, D. (1990). Vibration problems in engineering. Wiley.
Worden, K. and Tomlinson, G. R. (2000). Nonlinearity in structural dynamics. IOP.
Worden, K., Bullough, W. A., and Haywood, J. (2003). Smart Technologies. World Scientific.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Canopus Academic Publishing Limited
About this chapter
Cite this chapter
(2010). Introduction to Nonlinear Vibration and Control. In: Wagg, D., Neild, S. (eds) Nonlinear Vibration with Control. Solid Mechanics and Its Applications, vol 170. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-2837-2_1
Download citation
DOI: https://doi.org/10.1007/978-90-481-2837-2_1
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-2836-5
Online ISBN: 978-90-481-2837-2
eBook Packages: EngineeringEngineering (R0)