Energy Conservative Limit Cycle Oscillations

Energy Conservative Limit Cycle Oscillations

This paper shows how globally attractive limit cycle oscillations can be induced in a system with a nonlinear feedback element. Based on the same principle as the Van der Pol oscillator, the feedback behaves as a negative damping for low velocities but as an ordinary damper for high velocities. This nonlinear damper can be physically implemented with a continuous variable transmission and a spr...

Limit Cycle Oscillations of a Complete Aircraft

This paper presents results for the aeroelastic stability and LCO behavior for a complete aircraft. Comparison are presented between the results predicted by a cantilevered wing model, an untrimmed aircraft model (no gravity or drag) and a trimmed aircraft model. It is seen that the stability behavior is predicted accurately only if the correct trim loads are applied to the wing. The LCO behavi...

Sensitivity analysis of limit cycle oscillations

Many unsteady problems equilibrate to periodic behavior. For these problems the sensitivity of periodic outputs to system parameters are often desired, and must be estimated from a finite time or frequency domain calculation. Sensitivities computed in the time domain over a finite time span can take excessive time to converge, or fail altogether to converge to the periodic value. We derive a th...

Numerical Investigation of Self-sustained Limit-cycle Oscillations in a Flapping-foil Energy Harvester

Least Squares Shadowing sensitivity analysis of chaotic limit cycle oscillations

The adjoint method, among other sensitivity analysis methods, can fail in chaotic dynamical systems. The result from these methods can be too large, often by orders of magnitude, when the result is the derivative of a long time averaged quantity. This failure is known to be caused by ill-conditioned initial value problems. This paper overcomes this failure by replacing the initial value problem...