Parametric Excitation and Resonance
The following examples of dynamical systems which are subject to parametric excitation and parametric resonances are presented here in the context of SSM analysis
Extraction of Stability Diagrams
The following systems feature purely parametric excitation. For them the stability diagram and related forced response is computed
- Example of a prismatic beam discretized via a Galerkin Projection.
- The forced response for a Bernoulli Beam under parametric resonance.
- Stability of a Bernoulli Beam under parametric resonance.
Systems under parametric and external excitation
The following systems are subject to direct excitation in combination with resonant parametric driving.
- A Bernoulli Beam which exhibits an isolated response due to the presence of multiple resonances.
- Coupled Duffing Oscillators which exhibit an isola with a loop.
- A set of parametric amplifiers where the forced response bifurcates into a loop.
- Coupled self excited oscillators with cubic nonlinear damping and stiffness characteristics.
For more information refer to T. Thurnher, G. Haller & S. Jain, Nonautonomous Spectral Submanifolds for Model Reduction of Nonlinear Mechanical Systems under Parametric Resonance (2023). (submitted to Chaos)