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Research Papers

Deployment of a Membrane Attached to Two Axially Moving Beams

[+] Author and Article Information
Behrad Vatankhahghadim

Institute for Aerospace Studies,
University of Toronto,
Toronto, ON M3H 5T6, Canada
e-mail: behrad.vatankhahghadim@mail.utoronto.ca

Christopher J. Damaren

Professor and Director
Institute for Aerospace Studies,
University of Toronto,
Toronto, ON M3H 5T6, Canada
e-mail: damaren@utias.utoronto.ca

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received September 12, 2018; final manuscript received November 28, 2018; published online December 24, 2018. Assoc. Editor: Ahmet S. Yigit.

J. Appl. Mech 86(3), 031003 (Dec 24, 2018) (12 pages) Paper No: JAM-18-1531; doi: 10.1115/1.4042134 History: Received September 12, 2018; Revised November 28, 2018

The deployment dynamics of a simplified solar sail quadrant consisting of two Euler–Bernoulli beams and a flexible membrane are studied. Upon prescribing the in-plane motion and modeling the tension field based on linearly increasing stresses assumed on the attached boundaries, the coupled equations of motion that describe the system's transverse deflections are obtained. Based on these equations and their boundary conditions (BCs), deployment stability is studied by deriving simplified analytic expressions for the rate of change of system energy. It is shown that uniform extension and retraction result in decreasing and increasing energy, respectively. The motion equations are discretized using expansions in terms of “time-varying quasi-modes” (snapshots of the modes of a cantilevered beam and a clamped membrane), and the integrals needed for the resulting system matrices are rendered time-invariant via a coordinate transformation. Numerical simulation results are provided to illustrate a sample deployment and validate the analytic energy rate expressions.

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Figures

Grahic Jump Location
Fig. 1

Spatial distribution of (a) velocity field and (b) stress field

Grahic Jump Location
Fig. 2

Comparison of present deployment results (with negligible membrane effects) against beam-only deployment simulations of Refs. [16] and [69]: (a) backward and (b) forward simulation from t0 = 0.5 s

Grahic Jump Location
Fig. 3

Boom tip deflections during deployment with L˙=0.1 m/s

Grahic Jump Location
Fig. 4

Membrane deflections during deployment L˙=0.1 m/s at times (a) 0 s, (b) 1 s, (c) 2 s, (d) 3 s, (e) 4 s, and (f) 5 s

Grahic Jump Location
Fig. 5

Rate of change of vibration energy, E˙v, during (a) L˙=0.1 m/s and (b) retraction with L˙=−0.1 m/s

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