Higher-order shear and normal deformation theory is used in this paper to account thickness stretching effect for free vibration analysis of the cylindrical micro/nano shell subjected to an applied voltage and uniform...Higher-order shear and normal deformation theory is used in this paper to account thickness stretching effect for free vibration analysis of the cylindrical micro/nano shell subjected to an applied voltage and uniform temperature rising.Size dependency is included in governing equations based on the modified couple stress theory.Hamilton’s principle is used to derive governing equations of the cylindrical micro/nano shell.Solution procedure is developed using Navier technique for simply-supported boundary conditions.The numerical results are presented to investigate the effect of significant parameters such as some dimensionless geometric parameters,material properties,applied voltages and temperature rising on the free vibration responses.展开更多
Composite hollow shafts are used in power transmission applications due to their high specific stiffness and high specific strength.The dynamic characteristics of these shafts are important for transmission applicatio...Composite hollow shafts are used in power transmission applications due to their high specific stiffness and high specific strength.The dynamic characteristics of these shafts are important for transmission applications.Dynamic modelling of these shafts is generally carried out using Equivalent Modulus Beam Theory(EMBT)and Layerwise Beam Theory(LBT)formulations.The EMBT formulation is modified by considering stacking sequence,shear normal coupling,bending twisting coupling and bending stretching coupling.It is observed that modified EMBT formulation is underestimating the shafts stiffness at lower length/mean diameter(l/dm)ratios.In the present work,a new formulation is developed by adding shear deformation along the thickness direction to the existing modified EMBT formulation.The variation of shear deformation along the thickness direction is found using different shear deformation theories,i.e.,first-order shear deformation theory(FSDBT),parabolic shear deformation theory(PSDBT),trigonometric shear deformation theory(TSDBT),and hyperbolic shear deformation theory(HSDBT).The analysis is performed at l/d_(m) ratios of 5,10,15,20,25,30,35,and 40 for carbon/epoxy composites,E-glass/epoxy composites,and boron/epoxy composite shafts.The results show that new formulation has improved the bending natural frequency of the composite shafts for l/d_(m)<15 in comparison with modified EMBT.The effect of new formulation is more significant for the second and third bending modes of natural frequencies.展开更多
Shock wave is emitted into the plate and sphere when a sphere hypervelocity impacts onto a thin plate.The fragmentation and phase change of the material caused by the propagation and unloading of shock wave could resu...Shock wave is emitted into the plate and sphere when a sphere hypervelocity impacts onto a thin plate.The fragmentation and phase change of the material caused by the propagation and unloading of shock wave could result in the formation of debris cloud eventually.Propagation models are deduced based on one-dimensional shock wave theory and the geometry of sphere,which uses elliptic equations(corresponding to ellipsoid equations in physical space)to describe the propagation of shock wave and the rarefaction wave.The“Effective thickness”is defined as the critical plate thickness that ensures the rarefaction wave overtake the shock wave at the back of the sphere.The“Effective thickness”is directly related to the form of the debris cloud.The relation of the“Effective thickness”and the“Optimum thickness”is also discussed.The impacts of Al spheres onto Al plates are simulated within SPH to verify the propagation models and associated theories.The results show that the wave fronts predicted by the propagation models are closer to the simulation result at higher impact velocity.The curvatures of the wave fronts decrease with the increase of impact velocities.The predicted“Effective thickness”is consistent with the simulation results.The analysis about the shock wave propagation and unloading in this paper can provide a new sight and inspiration for the quantitative study of hypervelocity impact and space debris protection.展开更多
基金The authors would like to thank the Iranian Nanotechnology Development Committee for their financial support.
文摘Higher-order shear and normal deformation theory is used in this paper to account thickness stretching effect for free vibration analysis of the cylindrical micro/nano shell subjected to an applied voltage and uniform temperature rising.Size dependency is included in governing equations based on the modified couple stress theory.Hamilton’s principle is used to derive governing equations of the cylindrical micro/nano shell.Solution procedure is developed using Navier technique for simply-supported boundary conditions.The numerical results are presented to investigate the effect of significant parameters such as some dimensionless geometric parameters,material properties,applied voltages and temperature rising on the free vibration responses.
文摘Composite hollow shafts are used in power transmission applications due to their high specific stiffness and high specific strength.The dynamic characteristics of these shafts are important for transmission applications.Dynamic modelling of these shafts is generally carried out using Equivalent Modulus Beam Theory(EMBT)and Layerwise Beam Theory(LBT)formulations.The EMBT formulation is modified by considering stacking sequence,shear normal coupling,bending twisting coupling and bending stretching coupling.It is observed that modified EMBT formulation is underestimating the shafts stiffness at lower length/mean diameter(l/dm)ratios.In the present work,a new formulation is developed by adding shear deformation along the thickness direction to the existing modified EMBT formulation.The variation of shear deformation along the thickness direction is found using different shear deformation theories,i.e.,first-order shear deformation theory(FSDBT),parabolic shear deformation theory(PSDBT),trigonometric shear deformation theory(TSDBT),and hyperbolic shear deformation theory(HSDBT).The analysis is performed at l/d_(m) ratios of 5,10,15,20,25,30,35,and 40 for carbon/epoxy composites,E-glass/epoxy composites,and boron/epoxy composite shafts.The results show that new formulation has improved the bending natural frequency of the composite shafts for l/d_(m)<15 in comparison with modified EMBT.The effect of new formulation is more significant for the second and third bending modes of natural frequencies.
基金supported by the National Natural Science Foundation of China(11627901,11872118).
文摘Shock wave is emitted into the plate and sphere when a sphere hypervelocity impacts onto a thin plate.The fragmentation and phase change of the material caused by the propagation and unloading of shock wave could result in the formation of debris cloud eventually.Propagation models are deduced based on one-dimensional shock wave theory and the geometry of sphere,which uses elliptic equations(corresponding to ellipsoid equations in physical space)to describe the propagation of shock wave and the rarefaction wave.The“Effective thickness”is defined as the critical plate thickness that ensures the rarefaction wave overtake the shock wave at the back of the sphere.The“Effective thickness”is directly related to the form of the debris cloud.The relation of the“Effective thickness”and the“Optimum thickness”is also discussed.The impacts of Al spheres onto Al plates are simulated within SPH to verify the propagation models and associated theories.The results show that the wave fronts predicted by the propagation models are closer to the simulation result at higher impact velocity.The curvatures of the wave fronts decrease with the increase of impact velocities.The predicted“Effective thickness”is consistent with the simulation results.The analysis about the shock wave propagation and unloading in this paper can provide a new sight and inspiration for the quantitative study of hypervelocity impact and space debris protection.
