Effects of couple stresses on the in-plane vibration of micro-rotating disks

Abstract

Micro-rotating disks are extensively used in micro-electromechanical systems such as micro-gyroscopes and micro-rotors. Because of the sensitivity of these elements, enough knowledge about the mechanical behavior of these structures is an essential matter for designers and fabricators. The small-scale effects on the in-plane free vibration of such micro-disks present an important aspect of the mechanical behavior of these elements. The small-scale effects on the in-plane free vibration of these micro-disks are investigated in this study using the modified couple stress theory. By using the Hamilton principle, the partial differential equations governing the coupled radial and tangential motion of the disk particles with their corresponding boundary conditions are derived. Then, the solution for the boundary value problem is analytically presented. The effects of the angular speed of the micro-disks and the length scale parameter of the modified couple stress theory on the steady radial and tangential displacements, and on the natural frequencies are investigated. Those results are compared with the ones previously obtained from the classical continuum mechanics analysis.

Controlling of the melting through porous medium and magnetic field

“…The flow of the micro polar nanofluid was caused by a rotating disk in the existence of magnetic field explored by Ramzan et al 20 The nature of the oscillating magnetic field in the convective flow of a nanomaterial using a rotating stretchable disk was discussed by Hassan et al 21 Reducing the amount of melting and enhancing heat transfer rates with thicker melt layers by increasing the magnetic field parameter were proven in the latest efforts of Malepati. 22 The mechanical behavior of micro-rotating disk was presented in the recent work of Bagheri et al 23…”

“…The flow of the micro polar nanofluid was caused by a rotating disk in the existence of magnetic field explored by Ramzan et al 20 The nature of the oscillating magnetic field in the convective flow of a nanomaterial using a rotating stretchable disk was discussed by Hassan et al 21 Reducing the amount of melting and enhancing heat transfer rates with thicker melt layers by increasing the magnetic field parameter were proven in the latest efforts of Malepati. 22 The mechanical behavior of micro-rotating disk was presented in the recent work of Bagheri et al 23 The flow through magnetic hydrodynamic (MHD) is electrically conducting, which affects the behavior of flow, basically the apparent viscosity is developed in the fluid by implementation of MHD which realized reduction in the velocity of flow. There are many applications of MHD such as in the field of astrophysical phenomena, where the earth magnetic field protects us from radiations, MHD pumps, MHD generator and used in fluid mechanics and so on.…”