Dear Stack Exchange Community,
I am in the process of attempting to recreate the nonlinear resonance plots of a paper in relation to nonlinear dynamics of 'Micro Electromechanical Systems', namely this paper:
http://link.springer.com/article/10.1007/s00542-016-2947-7
The system looks at the typical nonlinear mechanical system where it behaves as a linear resonant system for low excitation amplitudes but soon becomes nonlinear for large input amplitudes and displays the 'fold over' effect, for example:
The polynomial in question is of the form:
$$ \left[\dfrac{3}{4}k_3z^3+\left(\lambda^2-\omega^2\right)z\right]^2+\left[\mu\omega z\right]^2=K^2 $$
Where $k_3$, $\lambda$, $\mu$ and $K$ are all constants.
I wish to solve for the amplitude '$z$' for a specific angular frequency '$\omega$'. As of right now I am looking for appropriate methods with which to solve this system. I have considered the Newton Raphson method and I have used 'fzero' and 'fsolve' in Matlab which have not allowed me to generate plots even remotely similar to the system results in question due to the highly nonlinear nature of the system. I am asking this board for good methods with which to solve this system and produce the frequency response plots.
Hopefully the question is clear enough and thanks for any responses/help.
Regards, James