During swimming in dogfish sharks, Squalus acanthias, both the intervertebral joints and the vertebral centra undergo significant strain. To investigate this system, unique among vertebrates, we cyclically bent isolated segments of 10 vertebrae and nine joints. For the first time in the biomechanics of fish vertebral columns, we simultaneously characterized non-linear elasticity and viscosity throughout the bending oscillation, extending recently proposed techniques for large-amplitude oscillatory shear (LAOS) characterization to large-amplitude oscillatory bending (LAOB). The vertebral column segments behave as non-linear viscoelastic springs. Elastic properties dominate for all frequencies and curvatures tested, increasing as either variable increases. Non-linearities within a bending cycle are most in evidence at the highest frequency, 2.0 Hz, and curvature, 5 m−1. Viscous bending properties are greatest at low frequencies and high curvatures, with non-linear effects occurring at all frequencies and curvatures. The range of mechanical behaviors includes that of springs and brakes, with smooth transitions between them that allow for continuously variable power transmission by the vertebral column to assist in the mechanics of undulatory propulsion.
The authors declare no competing or financial interests.
M.E.P. and J.H.L. designed the experiments and collected data. All authors analyzed these data using an approach developed by R.H.E. All authors contributed to manuscript preparation and editing prior to submission.
This work was supported by the US National Science Foundation [DBI-0442269, IOS-0922605, and grant no. 1344227, INSPIRE, Special Projects].
Supplementary information available online at http://jeb.biologists.org/lookup/doi/10.1242/jeb.135251.supplemental
- Received November 30, 2015.
- Accepted July 7, 2016.
- © 2016. Published by The Company of Biologists Ltd