Influence of various temperature distributions on critical speed and vibrational characteristics of rotating cylindrical microshells with modified lengthscale parameter

Abstract

In this article, the influences of various temperature distributions on the vibration analysis of temperature-dependent rotating cylindrical functionally graded (FG) microshells are investigated using the modified couple stress theory (MCST) in a thermal environment. MCST is applied to this model which is practical in the design and analysis of micro actuators and micro sensors. The modeled cylindrical FG microshell, its equations of motion and boundary conditions are derived by Hamilton’s principle and the first-order shear deformation theory (FSDT). For the first time, in the present study, the functionally graded lengthscale parameter changing along the thickness has been considered in temperature-dependent rotating cylindrical FG microshells. The accuracy of the presented model is verified with previous studies and also with those obtained by the Navier analytical method. The novelty of the current study is the consideration of rotation, various temperature distributions and size effect as well as satisfying various boundary conditions implemented on the proposed model using MCST. The generalized differential quadrature method (GDQM) is applied to discretize the equations of motion. In this study the simply supported conditions have been applied to edges $\theta = 0,2\pi$ and various boundary conditions have been studied in $x=0,L$ . Finally, the effects of various geometrical and material parameters on natural frequencies are studied.