Hello!

I'm currently studying the influence of adding a mass in a cantilever tip, near to a bifurcation.

In order to do it, I simplified a model of the cantilever to a 1DOF mass(m)-spring(k)-damper(b) system, where there is a stiffness linear and nonlinear (koX + k1X^3) so the system can be descrived as a Duffing like behavior ( for large amplitudes).

I wrote the equation of motion of the system as in the Image I annexed and then I made it nondimensional.

Now I wrote the differential equations (velocity, position) just to look at the phase portrait and the poincaré mapping. (For analyse the reponse frequency I have to apply Method of multiple scales and obtain amplitude and phase but for now just want to analyse the system before it).

In order to analyse the phase portrait, etc. I used a matlab program made by Housam Binous, for forced Duffing systems and I tried to adapt to my case ( Basically instead of Force*cos(Wt) and used the electrostatic force as described in the image) but I am not getting the results I expected in the plots, they are very strange).

Could you help me solving this challenge? I'm struggling with it, but It should be simple .

I annexed the matlab files and the image.

Thank you very much !

Kind Regards,

Bruno Silva

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