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.