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Non-linear parametrically excited systems

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Abstract: Parametric amplification in cable-stayed bridges, free hanging marine flexible risers, ships, and planetary gear systems can be disastrous if not accounted for. However, parametric amplification is exploited in MEMS filters, low-noise signal amplifiers, and micro/macro vibration energy harvesters, where amplifying the system response is beneficial. Parametric amplification happens when system parameters vary with an independent variable (time). As an example, consider a person playing on a swing. To maximise their height, the person on the swing stands up at two extreme positions and squats down at the lowest position which changes the mass moment of inertia periodically. In this scenario, frequency of parametric change is twice of the frequency of the swing. This is the phenomenon of parametric resonance of a system under time-varying parametric excitation, which happens when the excitation frequency is equal to twice of the natural frequency of the system. Most parametrically excited systems introduced in literature neglect the effect of nonlinearity on parametric amplification. We modified the electromagnetic system introduced by Lord Rayleigh (1887) to investigate the effect of nonlinearity on parametrically excited systems. The experimental results validated the analytical results obtained from the averaging method. We found that hardening, and positive cubic parametric nonlinearities may be beneficial for designing vibration energy harvesters with a broad frequency bandwidth. We identified that negative cubic parametric nonlinearities, with careful selection of relative phase, reduced the response amplitude, which improves the design of mechanical vibration absorbers.

About the authour: Mrs. Bahareh Zaghari is PhD. student within the Faculty of Engineering and the Environment at the University of Southampton. Bahareh graduated with a Bachelor’s degree in Electronic Engineering. She got a Master’s degree in Advanced Mechanical Engineering at the University of Southampton in 2012. In 2013, she joined ISVR to work with Dr. Maryam Ghandchi Tehrani and Dr. Emiliano Rustighi on parametrically excited systems.

This talk is part of the Engineering Department Dynamics and Vibration Tea Time Talks series.

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