Several models within the framework of continuum mechanics have been proposed over years to solve free vibration problem micro beams. Foremost amongst these are those based on non-local elasticity, classical couple stress, gradient elasticity and modified stress theories. Many retain basic features Bernoulli–Euler or Timoshenko–Ehrenfest theories, but they introduce one more material scale leng...

In this paper, the flow of couple stress fluid is investigated in a helical screw rheometer (HSR). By unwrapping the channel, lands, and the outside rotating barrel, the geometry of HSR is approximated as a shallow infinite channel. Both oneand two-dimensional analysis of the problem is presented using rectangular coordinates. In either case an exact solution of the flow problem is presented an...

this paper describes the effects of induced magnetic field and partial slip on the peristaltic flow of a couple stress fluids in an asymmetric channel. the two dimensional equation of couple stress fluid are simplified by making the assumptions of long wave length and low reynolds number. the exact solutions of reduced momentum equation and magnetic force function have been computed in wave fra...

A (linear) nonsingular solution for the edge dislocation in the translational gauge theory of defects is presented. The stress function method is used and a modified stress function is obtained. All field quantities are globally defined and the solution agrees with the classical solution for the edge dislocation in the far field. The components of the stress, strain, distortion and displacement...

This is a review paper containing the governing equations and analytical solutions of classical shear deformation theories functionally graded straight beams. The classical, first-order, third-order account for through-thickness variation two-constituent material, modified couple stress (i.e., strain gradient), von Kármán nonlinearity. Analytical bending linear theories, some which are not read...

In this study, the vibration behavior of functional graded (FG) circular and annular nanoplate embedded in Visco-Pasternak foundation and coupled with temperature change is studied. It is assumed that a uniform radial magnetic field acts on the top surface of the plate and the magnetic permeability coefficient of the plate along its thickness are assumed to vary according to the volume distribu...

ABSTRACT The method described in Part 1 of this paper was applied to about 30 earthquakes in various parts of the world. The modified single couple hypothesis proposed in Part 1 appears to explain the observations generally better than the double couple hypothesis. Surprisingly consistent pictures of tectonics were obtained in the Mediterranean region and in Japan on the basis of the modified s...