Deployment of a Membrane Attached to Two Axially Moving Beams Articles uri icon

publication date

  • March 2019

start page

  • 1

end page

  • 12

issue

  • 3, 031003

volume

  • 86

International Standard Serial Number (ISSN)

  • 0021-8936

Electronic International Standard Serial Number (EISSN)

  • 1528-9036

abstract

  • 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.

subjects

  • Aeronautics
  • Mechanical Engineering
  • Physics

keywords

  • finite-element analysis; flexible sliding beams; nonlinear vibration; transverse vibrations; dynamic-analysis; part ii; stability; energetics; satellites; extension