Dynamic stability/instability simulation of the rotary size-dependent functionally graded microsystem

In the current paper, vibrational and critical circular speed characteristics of a functionally graded (FG) rotary microdisk is examined considering a continuum nonlocal model called modified couple stress (MCS) model, for the first time in the literature. The generalized differential quadrature (GDQ) approach and variational method are used for deriving and solving the non-classical final relations. The FG size-dependent micro-sized disk's final relations and corresponding boundary conditions (BCs) are achieved on the basis of the higher-order shear deformation (HSD) model. Then, a parametric analysis has been conducted to analyze the influences of the length scale factor, circumferential, radius ratio and radial mode number, FG material's configuration, and BCs on the FG micro-scaled disk's frequency by taking into account the MCST. The outcomes reveal that, at the initial value of the FG index (beta), the negative impact from rotating speed on the dynamic stability of the system becomes bold. Furthermore, at the beta factor's lower amount and spinning velocity's higher amount, there is instability in the responses of the system. Additionally, it is indicated that the negative effect from radius ratio on the frequency responses of the rotary FG microdisk becomes considerable at the length scale factor's higher amount.

Automated summary

The paper examines the vibrational and critical circular speed characteristics of a functionally graded rotary microdisk using the modified couple stress model, for the first time in the literature. The study utilizes the GDQ approach and variational method to derive and solve non-classical relations, and conducts a parametric analysis to explore the influences of various factors on the frequency of the micro-scaled disk. The results reveal significant effects from the rotation speed, beta factor, and radius ratio on the dynamic stability and frequency responses of the rotary FG microdisk.