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I would like to gather ideas to model the dynamic behaviour of a plate with variable thickness. The assumption are:

  • Small deformations.
  • The plate is all made of the same material with variable thickness.
  • Boundary condition can be: free edge or fixed force profile.

My goal is to have a model as simple as possible and solve it with a Matlab script. The desired input are plate physical properties and boundary conditions. The desired output is the dynamics of each point of the plate.

The main ideas I am pursuing right now are:

  • Write the differential equation and solve using finite differences.
  • Simplify the whole model with equivalent springs and point masses.
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  • $\begingroup$ If you qualify for a student license (to keep the cost down), don't waste your time writing your own code - get the Partial Differential Equations toolbox instead. $\endgroup$
    – alephzero
    May 8, 2021 at 22:14
  • $\begingroup$ Or you might find something in Octave for free. Octave is made to be very similar to MATLAB but open source. $\endgroup$
    – DKNguyen
    May 9, 2021 at 7:03
  • $\begingroup$ Another option is to use python. But my question is not really about the coding part. What I am seeking are ideas on how to treat / discretize / sinplify the system in an effective way. $\endgroup$
    – Worldsheep
    May 9, 2021 at 16:00

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