Articles | Volume 5, issue 2
J. Sens. Sens. Syst., 5, 245–259, 2016
J. Sens. Sens. Syst., 5, 245–259, 2016

Regular research article 13 Jul 2016

Regular research article | 13 Jul 2016

Employing electro-mechanical analogies for co-resonantly coupled cantilever sensors

Julia Körner1, Christopher F. Reiche1, Bernd Büchner1,2, Thomas Mühl1, and Gerald Gerlach3 Julia Körner et al.
  • 1Leibniz Institute for Solid State and Materials Research IFW Dresden, Helmholtzstr. 20, 01069 Dresden, Germany
  • 2Institut für Festkörperphysik, Technische Universität Dresden, 01062 Dresden, Germany
  • 3Institut für Festkörperelektronik, Technische Universität Dresden, 01062 Dresden, Germany

Abstract. Understanding the behaviour of mechanical systems can be facilitated and improved by employing electro-mechanical analogies. These analogies enable the use of network analysis tools as well as purely analytical treatment of the mechanical system translated into an electric circuit. Recently, we developed a novel kind of sensor set-up based on two coupled cantilever beams with matched resonance frequencies (co-resonant coupling) and possible applications in magnetic force microscopy and cantilever magnetometry. In order to analyse the sensor's behaviour in detail, we describe it as an electric circuit model. Starting from a simplified coupled harmonic oscillator model with neglected damping, we gradually increase the complexity of the system by adding damping and interaction elements. For each stage, various features of the coupled system are discussed and compared to measured data obtained with a co-resonant sensor. Furthermore, we show that the circuit model can be used to derive sensor parameters which are essential for the evaluation of measured data. Finally, the much more complex circuit representation of a bending beam is discussed, revealing that the simplified circuit model of a coupled harmonic oscillator is a very good representation of the sensor system.

Short summary
The presented work gives insight into the behaviour of co-resonantly coupled oscillating cantilever beams by means of electro-mechanical analogies. An electric circuit model is analysed with various stages of complexity, and conclusions are drawn regarding the applicability of the co-resonant concept for sensors. Furthermore, this is validated by a comparison between the theoretical predictions and experimental data.