Forced oscillations and stability analysis of a nonlinear micro-rotating shaft incorporating a non-classical theory

In this paper,the stability and bifurcation analysis of symmetrical and asymmetrical micro-rotating shafts are investigated when the rotational speed is in the vicinity of the critical speed.With the help of Hamilton's principle,nonlinear equations of motion are derived based on non-classical theories such as the strain gradient theory.In the dynamic modeling,the geometric nonlinearities due to strains,and strain gradients are considered.The bifurcations and steady state solution are compared between the classical theory and the non-classical theories.It is observed that using a non-classical theory has considerable effect in the steady-state response and bifurcations of the system.As a result,under the classical theory,the symmetrical shaft becomes completely stable in the least damping coefficient,while the asymmetrical shaft becomes completely stable in the highest damping coefficient.Under the modified strain gradient theory,the symmetrical shaft becomes completely stable in the least total eccentricity,and under the classical theory the asymmetrical shaft becomes completely stable in the highest total eccentricity.Also,it is shown that by increasing the ratio of the radius of gyration per length scale parameter,the results of the non-classical theory approach those of the classical theory.

Friction coefficient and error test via micro-rotation mechanics model

An air pressure-loading mode incorporated into the friction apparatus is firstly applied to coatings tribology involving large load, automation, stepless and continuous loading processes. A novel measurement principle is proposed and a micro-rotation mechanics model was developed for high precision measurement of friction coefficient. By properly designing and locating two sensors real-time monitoring the normal and friction forces, the troublesome influences in friction measurement is considerably relieved which come from surface characteristics of coatings of the samples in traditional friction test processes. By calculation and analysis, the max rotation angle 0max = 0.0018°is gained, which indicates that the measurement error of the apparatus is greatly reduced. The whole system error is about 1.15% given by finite element method and indication error of the least square fitting of measurements.

On Propagation of Rayleigh Type Surface Wave in a Micropolar Piezoelectric Medium

In the present paper, the governing equations of a linear transversely isotropic micropolar piezoelectric medium are specialized for x-z plane after using symmetry relations in constitutive coefficients. These equations are solved for the general surface wave solutions in the medium. Following radiation conditions in the half-space, the particular solutions are obtained, which satisfy the appropriate boundary conditions at the stress-free surface of the half-space. A secular equation for Rayleigh type surface wave is obtained. An iteration method is applied to compute the non-dimensional wave speed of the Rayleigh surface wave for specific material parameters. The effects of piezoelectricity, non-dimensional frequency and non-dimensional material constant, charge free surface and electrically shorted surface are shown graphically on the wave speed of Rayleigh wave.