Dynamically Defined Dancing Pendulums

Following the previous post, I have re-created the animation using a non-linear dynamic analysis inside Strand7, rather than by feeding in the positions of each ball at each time step.  The input using this approach is much simpler; just set each pendulum with an equal angular off-set, and specify the direction of gravity, and then let the program work out where they go.  The first animation generated with this approach was visually nearly identical to the version generated with specified coordinates, which was encouraging, but didn’t make for a very interesting video.  To add a bit of variety, and to replicate the behaviour of real pendulums more closely, I have also added some “viscous damping”, which gradually reduces the amplitude of each pendulums movement:

Details of the Strand7 animations settings:

  • Analysis Type: Nonlinear transient dynamic analysis
  • Non-linear options: Nonlinear geometry selected (nonlinear materials and creep not required)
  • Time steps: 18,000 steps at 0.005 sec increments, save every 10 steps.
  • Viscous damping selected
  • Pendulum strings defined as steel wire with a diameter of 2 mm
  • Pendulum viscosity set at 25 kN.s/m/m^3 (set by trial and error to reduce amplitude by about half over 90 seconds)
  • Iteration limit = 20, Displacement Norm Tolerance = 1e-6, Residuals Norm Tolerance = 1e-5

First attempts had problems with the analysis becoming unstable after a few seconds, which were resolved by:

  • Reducing the time step
  • Reducing the displacement and residuals norms
  • Reducing the stiffness of the pendulum cables
This entry was posted in Finite Element Analysis, Newton and tagged , , . Bookmark the permalink.

2 Responses to Dynamically Defined Dancing Pendulums

  1. Pingback: Yet more pendulums | Newton Excel Bach, not (just) an Excel Blog

  2. Pingback: Dancing Pendulums Revisited | Newton Excel Bach, not (just) an Excel Blog

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