Summary

Proceedings of the 2013 International Symposium on Nonlinear Theory and its Applications

2013

Session Number:A1L-D

Session:

Number:26

Linear and passive control method for the steady state amplitude in a parametrically excited hinged-hinged beam

Hiroshi YABUNO,  Hajime OHISHI,  

pp.26-29

Publication Date:

Online ISSN:2188-5079

DOI:10.15248/proc.2.26

PDF download (324.4KB)

Summary:
Linear and passive control method for the steady state amplitude in a parametrically excited hinged-hinged beam is proposed theoretically. In general, the magnitude of steady state amplitude in parametrically excited system is determined by the effect of cubic nonlinearity in the system. By changing the boundary condition due to the attachment of a linear spring, we modify the magnitude of the cubic nonlinearity in the lateral direction and control the response amplitude of the parametrically excited hinged-hinged beam.

References:

[1] A. H. Nayfeh and D. T. Mook, Nonlinear oscillations, 1979, Wiley New York.

[2] K. L. Turner, S. A. Miller, P. G. Hartwell, N. C. Mac-Donald, S. H. Strogatz, S. G. Adams, “Five parametric resonances in a microelectromechanical system,” Nature (London), vol.396, pp.149-152, 1998.

[3] J. F. Rhoads, S. W. Shaw, K. L. Turner, and R. Baskaran, “Tunable microelectromechanical filters that exploit parametric resonance,” Journal of Vibration and Acoustics, vol.127, pp.423-430, 2005.

[4] Z. Yie, M. Zielke, C. Burgner, and K. Turner, “Comparison of parametric Tunable microelectromechanical filters that exploit parametric resonance,” Journal of Micromechanics and Microengineering, vol.21, 2011.

[5] M. V. Requa and K. I. Turner, “Precise frequency estimation in a microelectromechanical parametric resonator,” Applied Physics Letters, vol.90, 1733508, 2007.

[6] M. Daqaq and D. Bode, “Exploring the parametric amplification phenomenon for energy harvesting,” Proceedings of the Institution of Mechanical Engineers Part I-Journal of Systems and Control Engineering, vol. 225, pp.456-466, 2011.

[7] S. Crespo and C. Glynn, “Nonlinear flexural-frexural-torsional dynamics of inextensional beams I,” Journal of Structural Mechanics, vol.6, pp. 437-448.

[8] W. Lacarbonara and H.Yabuno, “Refined models of elastic beams undergoing large in-plane motions: Theory and experiment,” International Journal of Solids and Structures, vol.43, pp.5073-5074, 2006.

[9] I. Son, Y. Uchiyama, W. Lacarbonara, H. Yabuno, “Simply supported elastic beams under parametric excitation,” Nonlinear Dynamics, vol. 53, pp.129-138, 2008.