Large amplitude vibration of carbon nanotube reinforced functionally graded composite beams with piezoelectric layers

Large amplitude free vibration of functionally graded carbon nanotube reinforced composite (CNTRC) beams with surface-bonded piezoelectric layers subjected to a temperature change and an applied voltage is studied in this paper. The governing equations of the piezoelectric CNTRC beam are derived based on Euler–Bernoulli beam theory, von Kármán geometric nonlinearity and the physical neutral surface concept. Both uniformly distribution (UD) and functionally graded (FG) distribution patterns of the single-walled carbon nanotube (SWCNT) reinforcements are considered. It is assumed that the material properties of the FG-CNTRC beam vary in the thickness direction, and that the SWCNTs are aligned and straight. Galerkin procedure is used to obtain the second order nonlinear ordinary equation in time with cubic nonlinear term. Multiple times scales method is then employed to determine the nonlinear free vibration characteristics of the beam clamped at both ends. The effects of the applied voltage, temperature change, beam geometry, the volume fraction and distribution pattern of the SWCNTs on the linear and nonlinear frequencies of the piezoelectric CNTRC beams are investigated through a comprehensive parametric study.