**Hong-Xia Jing 1, Xiao-Ting He 1,2,\*, Da-Wei Du 1, Dan-Dan Peng <sup>1</sup> and Jun-Yi Sun 1,2**


Received: 23 July 2020; Accepted: 10 August 2020; Published: 11 August 2020

**Abstract:** Piezoelectric materials have been found to have many electromechanical applications in intelligent devices, generally in the form of the flexible cantilever element; thus, the analysis to the corresponding cantilever is of importance, especially when advanced mechanical properties of piezoelectric materials should be taken into account. In this study, the vibration problem of a piezoelectric cantilever beam with bimodular functionally-graded properties is solved via analytical and numerical methods. First, based on the equivalent modulus of elasticity, the analytical solution for vibration of the cantilever beam is easily derived. By the simplified mechanical model based on subarea in tension and compression, as well as on the layer-wise theory, the bimodular functionally-graded materials are numerically simulated; thus, the numerical solution of the problem studied is obtained. The comparison between the theoretical solution and numerical study is carried out, showing that the result is reliable. This study shows that the bimodular functionally-graded properties may change, to some extent, the dynamic response of the piezoelectric cantilever beam; however, the influence could be relatively small and unobvious.

**Keywords:** piezoelectric effect; bimodular model; functionally-graded materials; cantilever; vibration
