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As a student I came across an amazing lab experimentA T-type structure with two masses attached to it showed a sudden change in oscillation mode.  

 

With MapleSim I was able to reproduce the experiment.

At the time I was told that this perplexing phenome happens because there are always imperfections. 

 

Today we would probably say that the symmetry has to be broken. The attached example has two parameter sets that a) break symmetry of boundary conditions and b) by structural asymmetry (i.e imperfection). Asymmetry in the initial conditions should also be possible (but I could make work with flexible beams). 

Compared to coupled oscillators that exchange energy via a coupling spring, this example exchanges energy via masses. In fact in its simplest implementation only one mass and two elastic structures are required for this type of mode coupling. MapleSim multibody library offers plenty of possibilities to demonstrate thisFlexible beams are not required. However, flexible beams show mode coupling beautifully and allow a simple reproduction in real life. For that the worksheet contains a parameter set to build a real model with steel wires. Tuning by adjusting the length of the vertical post is required since nonlinearities already shift frequencies in the model. 

 

I would be interested in other cool examples of mode coupling. I am also interested in solutions for flexible beams that impose asymmetry in the initial conditions. To keep it realistic at the start, the T should be bend as one would bend it with a fingertip in x direction. It would be even more realistic if the arms are flexed by gravity with zero velocity at the start of the simulation. How can this be done? 

 

Flexible_beam_mode_coupling.msim

Featured Post

Dear all,

Recently I discovered the noncommuting variables in the Physics package due to Edgardo Cheb-Terrab; doubtless there are many posts here on Maple Primes describing them.  Here is one more, which shows how to use this package to prove the Schur complement formula.

https://maple.cloud/app/6080387763929088/Schur+Complement+Proof+in+Maple

I guess I have a newbie's question: how well-integrated are Maple Primes and the Maple Cloud?  Anyway that seemed the easiest way to share this.

-r



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