Coupled dynamics of a squeeze-film levitated mass and a vibrating piezoelectric disc: numerical analysis and experimental study

This work deals with the dynamics of a vibrating piezoelectric disc, which creates, under specific vibrating conditions, an air squeeze film that is able to levitate a freely suspended object.In such problems, the coupling effects between the various components affect the overall dynamical behaviour of the combined system. For complex systems, which combine elastic and electro-static effects together with compressible fluid effects, the coupled equations are often dealt with separately to avoid modelling and computational complexity. In this paper, the importance of handling such systems in a coupled manner is advocated by means of numerical and experimental examples. A coupled model is derived in this work making use of a concise numerical solver to allow for this investigation under several conditions. The piezoelectric part of the structure is modelled by finite elements while the squeeze film phenomenon is represented by means of finite-difference equations, to model a variant of the Reynolds equation. The numerical model was verified during each step in the development of the numerical algorithm and indeed showed good agreement with existing publications, but once the components were combined, it was found that several phenomena were misrepresented in the past due to the neglect of the coupling effects. Several physical insights are brought from the simulation and investigation of the numerical results. In the last part, the importance of coupled analysis is emphasized by introducing an experimental investigation of the dynamical behaviour while conducting a comparison with numerical simulation results. From this comparison, the limitations of state-of-the-art modelling procedures are clarified.