Abstract
A novel electric Gibbs function was proposed for the piezoelectric microbeams (PMBs) by employing a modified couple stress theory. Based on the new Gibbs function and the Euler-Bernoulli beam theory, the governing equations which incorporate the effects of couple stress, flexoelectricity, and piezoelectricity were derived for the mechanics of PMBs. The analysis of the effective bending rigidity shows the effects of size and flexoelectricity can greaten the stiffness of PMBs so that the natural frequency increases significantly compared with the Euler-Bernoulli beam, and then the mechanical and electrical properties of PMBs are enhanced compared to the classical beam. This study can guide the design of microscale piezoelectric/flexoelectric structures which may find potential applications in the microelectromechanical systems (MEMS).
Highlights
Piezoelectricity is a well-studied electromechanical coupling effect in which the mechanical strain leads to electric polarization in piezoelectric crystals, or vice versa
Ωf denotes the natural frequency of the present model; that is, both effects of piezoelectricity and flexoelectricity are taken into consideration
Based on the obtained model, the effects of piezoelectricity and flexoelectricity and the size effect were examined for the vibration behavior of piezoelectric microbeams (PMBs)
Summary
Piezoelectricity is a well-studied electromechanical coupling effect in which the mechanical strain leads to electric polarization in piezoelectric crystals, or vice versa. Due to the excellent electromechanical characteristics at microscale [1], piezoelectric based microstructures have found a wide range of applications in microtechnology, like microtransducers, microgenerators, microresonantors, and so forth [2, 3]. These above microstructures are quasi onedimensional structures which can be efficiently characterized by simple Euler-Bernoulli beam theory. Flexoelectricity [4,5,6,7] is, the coupling between the mechanical strain gradient and the electric polarization, and it is a universal electromechanical mechanism in all insulators including piezoelectric materials [8,9,10,11]. The flexoelectric structures are theoretically predicted to be more sensitive when scaled down to microdomains [16, 17], yet their work did not take the size effect at microscale into account
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