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Approximate analytical solutions of an axially moving spacecraft appendage subjected to tip mass

Ghaleh, P. B ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1177/0954410013494140
  3. Abstract:
  4. Approximate solutions for vibrations of flexible beam-type appendages subjected to tip mass are studied while uniform and exponential profiles for arm deployment are simulated. Applying an equivalent dynamical system and following Lagrangian approach, the equations of motion of the system are derived as nonlinear ordinary differential equations (ODEs) (with time-varying coefficients), in which the effect of the tip mass can be considered as some nonlinearity added to the 'no tip mass' case dynamics. The approximate closed-form solutions are obtained through a novel methodology using a computer algorithm, in which the solutions of the 'no tip mass' case are expanded by imposing quadratic perturbations on the independent variable. The mean square of errors (MSEs) for the obtained approximate analytical solution is computed. Using this method, the amplitude and frequency of the arm response are presented by the algebraic equations, which help the parametric design of such systems. In addition, effects of tip mass as an indicator of nonlinearities added to the system dynamics, on the amplitude and frequency of the beam response, are investigated during arm deployment
  5. Keywords:
  6. Algorithms ; Dynamical systems ; Equations of motion ; Flexible structures ; Lagrange multipliers ; Ordinary differential equations ; Approximate analytical solutions ; Approximate solution ; Deployment profile ; Flexible arm ; Nonlinear ordinary differential equation ; Perturbation ; Quadratic perturbation ; Time-varying coefficient ; Algebra
  7. Source: Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering ; Vol. 228, issue. 9 , 2014 , pp. 1487-1497 ; ISSN: 09544100
  8. URL: http://pig.sagepub.com/content/228/9/1487