Repository: DepositOnce – institutional repository for research data and publications of TU Berlin https://depositonce.tu-berlin.de
TY - THES
AU - Noll, Max-Uwe
PY - 2020
TI - On the modeling of a bistable beam with application to energy harvesting
T2 - Technische Universität Berlin
DO - 10.14279/depositonce-9761
UR - http://dx.doi.org/10.14279/depositonce-9761
PB - Technische Universität Berlin
M3 - Doctoral Thesis
CY - Berlin
LA - en
AB - The term energy harvesting refers to strategies to transform small amounts of ambient energy into a useful form. When the available energy is of a kinetic type, an energy harvester is often designed as a mechanical oscillator, made of a beam structure and attached piezoelectric patches to transform motion energy into electrical energy. One specific harvester has attracted a lot of attention, due to its potentially higher efficiency. It consists additionally of two permanent magnets near the free end of the beam. As a result, the system is nonlinear with two stable states for the deformed beam. When the piezoelectric part is neglected, the system is reduced to a bistable beam and its dynamics is most often described by the bistable Duffing equation with a cubic part in the restoring terms. This model has been extensively studied in literature. However, the assumptions which are necessary to reduce the reality of an experimental setup to this type of model, have so far not been studied as extensively. Hence, the validity of the theoretical predictions for an actual experimental setup is often doubtful.
This thesis is a step towards a more sophisticated modeling of such an experimental setup of a bistable beam. It is a cumulative dissertation based on three publications, each dealing with specific aspects of the model assumptions usually made in literature. In the first publication, the magnetoelastic force is of main interest. One of the article's goals is to present a method to determine the magnetic force numerically. The second publication investigates the shape of the deformed beam during forced vibrations. The third publication compares the experimental setup's stationary response to the predictions of a corresponding Duffing model. In conclusion, the predictions of a bistable Duffing model are, generally, in good agreement with the experimental results of the setup considered, and deviate only in some aspects, as this dissertation describes. This thesis constitutes a link between the modeling approach discussed in literature and a new modelling approach that will enable an optimization of the underlying energy harvesting system in future.
KW - bistability
KW - Duffing oscillator
KW - energy harvesting
KW - nonlinear dynamics
KW - Bistabilität
KW - Duffing-Oszillator
KW - nichtlineare Dynamik
ER -