We derive the exact dispersion relations for flexural elastic wave motion in a beam under finite deformation. We employ the Euler-Bernoulli kinematic hypothesis. Focusing on homogeneous waveguides with constant cross-section, we utilize the exact strain tensor and retain all high order terms. The results allow us to quantify the deviation in the dispersion curves when exact large deformation is considered compared to the small strain assumption. We show that incorporation of finite deformation shifts the frequency dispersion curves downwards. Furthermore, the group velocity increases with wavenumber but this trend reverses at high wavenumbers when the wave amplitude is sufficiently high. At sufficiently high wave amplitudes, the group velocity becomes negative at high wavenumbers. This study on nonlinear homogeneous beams lays the foundation for future development to nonlinear periodic beams.
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ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
August 28–31, 2011
Washington, DC, USA
Conference Sponsors:
- Design Engineering Division and Computers and Information in Engineering Division
ISBN:
978-0-7918-5478-5
PROCEEDINGS PAPER
Analysis of Elastic Wave Propagation in Nonlinear Beams
Mohammad H. Abedinnasab,
Mohammad H. Abedinnasab
Sharif University of Technology, Tehran, Iran
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Mahmoud I. Hussein
Mahmoud I. Hussein
University of Colorado at Boulder, Boulder, CO
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Mohammad H. Abedinnasab
Sharif University of Technology, Tehran, Iran
Mahmoud I. Hussein
University of Colorado at Boulder, Boulder, CO
Paper No:
DETC2011-48672, pp. 207-212; 6 pages
Published Online:
June 12, 2012
Citation
Abedinnasab, MH, & Hussein, MI. "Analysis of Elastic Wave Propagation in Nonlinear Beams." Proceedings of the ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 1: 23rd Biennial Conference on Mechanical Vibration and Noise, Parts A and B. Washington, DC, USA. August 28–31, 2011. pp. 207-212. ASME. https://doi.org/10.1115/DETC2011-48672
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