Abstract
As a necessary precursor to a heliogyro solar sail flight demonstration, meaningful ground test experiments are necessary for predicting the linear and nonlinear structural dynamics of the heliogyro membrane blades in flight. This paper describes analytical comparisons of linear and nonlinear behavior of a multi-link discrete model of a heliogyro blade under 1-g gravitational and centrifugal loads, and one setup for experimental validation of 1-g out-of-plane motion. Linear system-identification is performed on the multi-link experimental data to validate the 1-g multi-link model of a heliogyro membrane blade.
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Abbreviations
- A :
-
= discrete-time state matrix
- B :
-
= discrete-time input matrix
- C :
-
= output matrix
- D :
-
= direct transmission matrix
- \( \hat{e}_{x} (t) \) :
-
= unit vector pointing to the direction of the gravitation field
- \( \hat{e}_{y} (t) \) :
-
= unit vector perpendicular to \( \hat{e}_{x} (t) \) and \( \hat{e}_{x} (t) \) obeying the usual ordering of the axes
- \( \hat{e}_{z} (t) \) :
-
= unit vector perpendicular to the plane of the chain in still motion
- l:
-
= total length of the membrane blade, meter
- m :
-
= total mass of the membrane blade, gram
- m i j :
-
= discretized mass of the membrane blade; i = 1,2,…n; j = 1,2
- n :
-
= degree of freedom (number of discretized sectors of the membrane blade)
- s :
-
= half width of the membrane, meter
- \( \theta_{i} \) :
-
= ith angular displacement of in-plane motion, radian; i = 1,2,…n
- \( \phi_{i} \) :
-
= ith angular displacement of out-of-plane/bending motion, radian; i = 1,2,…n
- \( \varphi_{i} \) :
-
= ith angular displacement of twisting motion, radian; i = 1,2,…n
- \( \tau_{{\theta_{i} }} \) :
-
= torque for the ith angular displacement of in-plane motion; i = 1,2,…n
- \( \tau_{{\phi_{i} }} \) :
-
= torque for the ith angular displacement of out-of-plane/bending motion; i = 1,2,…n
- \( \tau_{{\phi_{i} }} \) :
-
= torque for the ith angular displacement of twisting motion; i = 1,2,…n
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Acknowledgments
This research was supported in part by (received funding from) the Headquarters of University Advancement at the National Cheng Kung University, which is sponsored by the Ministry of Education, Taiwan, ROC.
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Huang, YR., Juang, JN., Hung, CH., Keats Wilkie, W. (2014). Dynamics of a Coupled Pendulum Model of a Heliogyro Membrane Blade. In: Macdonald, M. (eds) Advances in Solar Sailing. Springer Praxis Books(). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34907-2_42
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DOI: https://doi.org/10.1007/978-3-642-34907-2_42
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