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Theoretical modelling of non-symmetric circular piezoelectric bimorphs

Michel Brissaud

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This paper deals with the theoretical modelling of non-symmetric and symmetric circular bimorphs. The model is restricted to the study of flexural vibration modes having radial symmetry (axisymmetry), as is often the case for piezoelectric devices such as MEMs. The calculation of the resonance frequencies and the displacement of the non-symmetric circular bimorph has been carried out and the influence of the elastic and geometric parameters of the cement layer has been introduced into the model. As is shown, the modelling of non-symmetric and symmetric circular bimorphs reduces to the determination of two global quantities: the global rigidity DG and the global Poisson ratio σG of the bimorph which is then equivalent to a homogenous element. Consequently, the results obtained with elastic and homogeneous circular plates can be applied to non-symmetric and symmetric bimorphs with the only condition of using the global DG and σG. The new modelling was applied to bimorph functioning either as an actuator or as a sensor and having a simply supported or clamped edge. The electromechanical coupling factor of flexure modes has been calculated and compared to the radial mode. Comparison between analytical models and simulations using the finite-element method is given and discussed.


PACS

85.50.-n Dielectric, ferroelectric, and piezoelectric devices

85.85.+j Micro- and nano-electromechanical systems (MEMS/NEMS) and devices

02.70.Dh Finite-element and Galerkin methods

Subjects

Computational physics

Electronics and devices

Nanoscale science and low-D systems

Dates

Issue 5 (May 2006)

Received 24 November 2005, in final form 27 February 2006

Published 24 March 2006



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