Investigation of free vibration of piezoelectric actuator reinforced with functionally graded Boron Nitride nanotube using timoshenko beam model and differential quadrature method

Abstract

The vibrational characteristics and natural frequencies of Boron Nitride Nanotube (BNNT)-reinforced piezoelectric beams, based on the Timoshenko model, have been studied for the first time in this paper. Four types of functionally graded (FG) distribution patterns of BNNT reinforcements were considered for the FG-BNNT-reinforced piezoelectric beam. It is assumed that the material properties of FG-BNNT-reinforced beams are estimated using the Representative Volume Element (RVE) micromechanical model. The FG-BNNT-reinforced piezoelectric beam with different Boundary Conditions (BCs) is exposed to electrical voltage. Coupled partial differential equations of the system have been derived with the aid of Hamilton's principle and then converted into corresponding dimensionless equations using dimensionless variables. The differential quadrature method (DQM) has been used to obtain the natural frequencies and shape modes. According to the convergence analysis, twelve grid points were enough to obtain an accurate result for the analysis. To confirm the accuracy and reliability of the present study, the obtained results were validated with frequencies from the literature. Also, the effects of BNNT volume fraction and its reinforcement pattern, as well as applied voltage, on dimensionless natural frequencies have been investigated for different BCs. The results show that applying electric loadings can be utilized as well as controlling parameters to modify the resonance frequency of the composite actuator. More specifically, it is shown that applying voltages to a FG-BNNT-reinforced piezoelectric beam changes the natural frequency for each reinforcement pattern, BCs, and mode numbers. Such ability could be employed when designing reinforced piezoelectric composites for vibrational applications.