Due to the advanced mechanical properties, such as high strength and stiffness and light weight, carbon nanotube-reinforced composites (CNTRCs) have received considerable attention from research and engineering communities (Thostenson et al. 2001, Esawi & Farag 2007). One of the latest developments in CNTRCs is functionally graded carbon nanotubereinforced composites (FG-CNTRCs) in which carbon nanotube (CNT) reinforcements are distributed nonuniformly in the matrix to further improve the mechanical properties of CNTRCs (Shen 2009, Wu et al. 2016). Smart composite structures, in which the piezoelectric materials are utilized as actuators or sensors, are practically very important for the mechanical behaviour control and structural health monitoring (Trollope & Burnham 2013, Zhang et al. 2016). Nonetheless, only a few researches on FGCNTRC beams equipped with piezoelectric layers are available in the literature. Among those, Rafiee and his co-authors analyzed the large amplitude vibration (Rafiee et al. 2013a) and thermal bifurcation buckling (Rafiee et al. 2013b) of piezoelectric FG-CNTRC beams under a thermo-electric loading. Yang et al. (2015) investigated the dynamic buckling

free vibration. The influences of slenderness ratio and boundary conditions are discussed as well.