Vibration Analysis of Rotating Functionally Graded Piezoelectric Nanobeams Based on the Nonlocal Elasticity Theory

Purpose Rotating components such as rotating beams and plates are working in complex physical environments subjected to nonuniform distribution of their own materials, vibration caused by external excitation may result in work instability, structural fatigue and the like, so the dynamic analysis of rotating structures is of great significance. Methods Based on the nonlocal elasticity theory and Timoshenko beam model, the vibration of a rotating functionally graded piezoelectric nanobeam is investigated. First, the dynamic governing equations and corresponding boundary conditions are derived by the Hamiltonian principle. Then, the governing equations and boundary conditions are discretized by the differential quadrature method. Subsequently, the vibration characteristics of nanobeams are analyzed after detailed numerical calculations. Results The effects of various parameters including rotational velocity, nonlocal parameter, functional gradient index, length–height geometry ratio and external voltage on the vibration characteristics under different boundary conditions are examined. Finally, the numerical results show that these parameters have non-negligible effects on the natural frequencies and modal shapes. Conclusions The dynamics of rotating functionally graded nanobeams are affected by both external kinematic and voltage factors and inherent scale factor and their coupling effects. In particular, a nonlinear small-scale effect is observed for a rotating functionally graded piezoelectric nanobeam, which may be useful to the design and optimization of the nano-electro-mechanical system including the rotating structures.