Free Vibration Analysis of a Spinning Smart Piezoelectrically Actuated Heterogeneous Nanoscale Shell with Nonlocal Strain Gradient Theory

Abstract

In this paper, a numerical procedure is proposed for analyzing the effects of length scale parameter, external electric field, angular speed and nonlocal parameter on the free vibration of a functionally graded piezoelectric cylindrical nanoshell. Nonlocal strain gradient theory (NSGT) is employed to study Eringen’s size-dependent effect and the length scale parameter. This new proposed method can be considered as a combination of Eringen’s nonlocal model and classical strain gradient theory. The obtained results show that this model can be used reliably for small-scale systems. The effects of boundary conditions, applied voltage, nonlocal parameter, rotational speed and length scale parameter on natural frequencies are presented. Compared to other elasticity theories, NSGT achieves the highest natural frequency and critical rotational speed and also a wider stability region. Doubling and tripling the length scale increases the natural frequency by approximately 1.8 and 2.6 times, respectively; while doubling and tripling the nonlocal parameter value reduces the natural frequency by approximately 1.2 and 1.4 times, respectively. Therefore, the natural frequency is more sensitive to the length scale parameter than the nonlocal parameter. Finally, it was shown that the critical angular speed goes up by increasing the length scale parameter, applied voltage, or nonlocal parameter.