The linear and nonlinear torsional free vibration analyses of functionMly graded micro/nuno-tubes （FGMTs） are analytically investigated based on the couple stress theory. The employed non-classical continuum theory ...The linear and nonlinear torsional free vibration analyses of functionMly graded micro/nuno-tubes （FGMTs） are analytically investigated based on the couple stress theory. The employed non-classical continuum theory contains one material length scale parameter, which can capture the small scale effect. The FGMT model accounts for the through-radius power-law variation of a two-constituent material. Hamilton＇s principle is used to develop the non-classical nonlinear governing equation. To study the effect of the boundary conditions, two types of end conditions, i.e., fixed-fixed and fixed-free, are considered. The derived boundary value governing equation is of the fourthorder, and is solved by the homotopy analysis method （HAM）. This method is based on the Taylor series with an embedded parameter and is capable of providing very good approximations by means of only a few terms, if the initial guess and the auxiliary linear operator are properly selected. The analytical expressions are developed for the linear and nonlinear natural frequencies, which can be conveniently used to investigate the effects of the dimensionless length scale parameter, the material gradient index, and the vibration amplitude on the natural frequencies of FGMTs.展开更多
Gas flows through micro shock tubes are widely used in many engineering applications such as micro engines, particle delivery devices etc. Recently, few studies have been carried out to explore the shock wave excursio...Gas flows through micro shock tubes are widely used in many engineering applications such as micro engines, particle delivery devices etc. Recently, few studies have been carried out to explore the shock wave excursions through micro shock tubes at very low Reynolds number and at rarefied gas condition. But these studies assumed centered shock and expansion waves, which are generally produced by instantaneous diaphragm rupture process. But in real scenario, the diaphragm ruptures with a finite rupture time and this phenomenon will significantly alter the shock wave propagation characteristics. In the present research, numerical simulations have been carried out on a two dimensional micro shock tube model to simulate the effect of finite diaphragm rupture process on the wave characteristics. The rarefaction effect was simulated using Maxwell’s slip wall equations. The results show that shock wave attenuates rapidly in micro shock tubes compared to conventional macro shock tubes. Finite diaphragm rupture causes the formation of non-centered shock wave at some distance ahead of the diaphragm. The shock propagation distance is also drastically reduced by the rupture effects.展开更多
文摘The linear and nonlinear torsional free vibration analyses of functionMly graded micro/nuno-tubes （FGMTs） are analytically investigated based on the couple stress theory. The employed non-classical continuum theory contains one material length scale parameter, which can capture the small scale effect. The FGMT model accounts for the through-radius power-law variation of a two-constituent material. Hamilton＇s principle is used to develop the non-classical nonlinear governing equation. To study the effect of the boundary conditions, two types of end conditions, i.e., fixed-fixed and fixed-free, are considered. The derived boundary value governing equation is of the fourthorder, and is solved by the homotopy analysis method （HAM）. This method is based on the Taylor series with an embedded parameter and is capable of providing very good approximations by means of only a few terms, if the initial guess and the auxiliary linear operator are properly selected. The analytical expressions are developed for the linear and nonlinear natural frequencies, which can be conveniently used to investigate the effects of the dimensionless length scale parameter, the material gradient index, and the vibration amplitude on the natural frequencies of FGMTs.
文摘Gas flows through micro shock tubes are widely used in many engineering applications such as micro engines, particle delivery devices etc. Recently, few studies have been carried out to explore the shock wave excursions through micro shock tubes at very low Reynolds number and at rarefied gas condition. But these studies assumed centered shock and expansion waves, which are generally produced by instantaneous diaphragm rupture process. But in real scenario, the diaphragm ruptures with a finite rupture time and this phenomenon will significantly alter the shock wave propagation characteristics. In the present research, numerical simulations have been carried out on a two dimensional micro shock tube model to simulate the effect of finite diaphragm rupture process on the wave characteristics. The rarefaction effect was simulated using Maxwell’s slip wall equations. The results show that shock wave attenuates rapidly in micro shock tubes compared to conventional macro shock tubes. Finite diaphragm rupture causes the formation of non-centered shock wave at some distance ahead of the diaphragm. The shock propagation distance is also drastically reduced by the rupture effects.
