On the Optimal Time-averaged Power Yielding from a Damped Harmonic Oscillator with Variable Damping
S.B. de Jong (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Wim T.van van Horssen – Mentor (TU Delft - Mathematical Physics)
Henk Schuttelaars – Graduation committee member (TU Delft - Mathematical Physics)
NV Budko – Graduation committee member (TU Delft - Numerical Analysis)
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Abstract
Energy can be harvested from vibrations by using a damped harmonic oscillator with base excitation, providing a sustainable way of yielding energy. By solving the equations of motion for this oscillator and studying the steady state solution, an expression for the time-averaged power is obtained. Different damping values of the oscillator influence how much power is yielded. In this thesis, it is analytically shown that a constant damping value equal to $c_{v} = \frac{\sqrt{c_{m}^{2}\psi^{2}f_{s}^{2}+(f_{s}^{2}-1)^{2}}}{\psi f_{s}}$ yields the most time-averaged power for the case where there is no switch in damping value and when there is a singular arbitrary switch in damping value. It is numerically shown that this damping value also yields the most time-averaged power for multiple switches in the damping value.