Abstract
In bending of a purely elastic beam or plate, it is well established that the cross-sectional shape changes character with decreasing bending radius-of-curvature and that the transition can be characterized by the Searle parameter. In a piezoelectric structure, the cross-sectional deformation is affected by the opposite anticlastic and electromechanical bending curvatures. The behavior is consequently more complicated and it is an open question how the cross-sectional shape develops with increasing bending. In this paper, analytical solutions are used to study the cross-sectional deformation of piezoelectric cantilever-actuators taking both anticlastic and electromechanical bending effects into account. We consider unimorph and bimorph actuators. In the case of electrical actuation, as for the purely mechanical case, we find that the Searle parameter is an important parameter characterizing the shape of the cross-section. A load scaling rule gives a criterion for fixed cross-section-deflection for different actuator widths. Using this scaling rule, the Searle parameter is kept unchanged. The analytical results are verified by non-linear finite element analysis using electric potential and mechanical moment as applied loads.
Highlights
Anticlastic deformation is the phenomenon that for a beam or plate, curvature along the width direction is induced by bending along the length direction due to the existence of Poisson’s ratio [1]
In bending of a purely elastic beam or plate, it is well established that the cross-sectional shape changes character with decreasing bending radius-of-curvature and that the transition can be characterized by the Searle parameter
Analytical solutions are used to study the cross-sectional deformation of piezoelectric cantilever-actuators taking both anticlastic and electromechanical bending effects into account
Summary
Anticlastic deformation is the phenomenon that for a beam or plate, curvature along the width direction is induced by bending along the length direction due to the existence of Poisson’s ratio [1]. The transition from narrow to wide orthotropic non-piezoelectric beam was studied by Swanson [6] using the linear plate equations, where the effect of width/length ratio on the cross-section deformation was investigated. The deformation was affected by the width/length ratio because of the boundary conditions at the ends of the structure This is to be expected from SaintVenant’s principle [25] and is a different effect from the anticlastic deformation studied by Ashwell [3] which is a nonlinear effect of a beam in pure bending. The effects on the cross-section deformation are studied and verified by finite element (FE) analysis To this end we compare to the cross section in the middle of a long structure to secure that the result is not affected by the boundary conditions. While the shape of the cross-section depends on the combination of mechanical loading and electrical actuation we show that it is possible to find a scaling relation between the two which keeps the shape of the cross-section fixed when the width is varied at constant Searl parameter
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