Linear Vibration Analysis of Rotating Piezoelectric Nano-Reddy-Beams Based on Nonlocal Strain Gradient Theory

This paper investigates the vibration behaviors of a rotating functionally graded piezoelectric nanobeam based on the nonlocal strain gradient theory and Reddy beam model. Firstly, the differential equations of motion are obtained by the energy variation. The numerical method is used to transform derived partial differential equations into algebraic equations. Subsequently, the natural frequencies values are obtained of the nanobeam by solving the eigenvalues of the matrix. The influence of rotational velocity, nonlocal parameter, the strain gradient parameter and voltage on the natural frequencies are analyzed. Finally, the results show that the effects of nonlocal parameters on the vibtation frequencies of nanobeams is related to the ratio of the nonlocal parameter and the strain gradient parameter. This further illustrates the rationality of using two small scale parameters to study nanomachenics. Additionally, the changes in value of rotational velocity and voltage will change the natural frequencies. The research results of this paper may play an important guiding significance for the design of micro-nano rotating machinery and related mechanical research.