Axial Free Vibration of Rotating FG Piezoelectric Nano-rods Accounting for Nonlocal and Strain Gradient Effects

Purpose To reveal the dynamic behaviors and electromechanical coupling characteristics of rotating nonuniform nanocomponents in nanoelectromechanical system, we investigate the axial-free vibration of a rotating functionally graded (FG) piezoelectric nano-rod with continuous variations in material physical properties along the thickness direction. Methods Based on the nonlocal strain gradient theory, the governing equations of motion and boundary conditions of freely vibrating FG piezoelectric nano-rods with rotation are derived via Hamilton principle, where the material inhomogeneity of rod nanostructures, and the nonlocal and strain gradient effects at a nanoscale are considered. The partial differential equations are discretized into a set of algebraic equations by the differential quadrature method (DQM), and then natural frequencies of axial vibration are determined by solving eigenvalue equations. Results and Conclusion Some numerical examples are carried out according to the size and parameters of existing myosin molecular motors. Effects of the material gradient index, nonlocal parameter, strain gradient characteristic parameter, rotational speed and external electrostatic voltage on the vibration behaviors are demonstrated and analyzed. A mutual restriction between the nonlocal parameter and strain gradient characteristic parameter is implied. The positive voltage and negative voltage are equivalent to axial tension and axial compression, respectively. The present research and corresponding numerical results are expected to be used as reference for the design and optimization of emerging micro/nano-rotating machinery.