A three-dimensional(3D)thermomechanical vibration model is developed for rotating pre-twisted functionally graded(FG)microbeams according to the refined shear deformation theory(RSDT)and the modified couple stress the...A three-dimensional(3D)thermomechanical vibration model is developed for rotating pre-twisted functionally graded(FG)microbeams according to the refined shear deformation theory(RSDT)and the modified couple stress theory(MCST).The material properties are assumed to follow a power-law distribution along the chordwise direction.The model introduces one axial stretching variable and four transverse deflection variables including two pure bending components and two pure shear ones.The complex modal analysis and assumed mode methods are used to solve the governing equations of motion under different boundary conditions(BCs).Several examples are presented to verify the effectiveness of the developed model.By coupling the slenderness ratio,gradient index,rotation speed,and size effect with the pre-twisted angle,the effects of these factors on the thermomechanical vibration of the microbeam with different BCs are investigated.It is found that with the increase in the pre-twisted angle,the critical slenderness ratio and gradient index corresponding to the thermal instability of the microbeam increase,while the critical material length scale parameter(MLSP)and rotation speed decrease.The sensitivity of the fundamental frequency to temperature increases with the increasing slenderness ratio and gradient index,and decreases with the other increasing parameters.Moreover,the size effect can suppress the dynamic stiffening effect and enhance the Coriolis effect.Finally,the mode transition is quantitatively demonstrated by a modal assurance criterion(MAC).展开更多
Modeling of pre-twisted composite rotor blades is very complicated not only because of the geometric non-linearity, but also because of the cross-sectional warping and the transverse shear deformation caused by the an...Modeling of pre-twisted composite rotor blades is very complicated not only because of the geometric non-linearity, but also because of the cross-sectional warping and the transverse shear deformation caused by the anisotropic material properties. In this paper, the geometrically exact nonlinear modeling of a generalized Timoshenko beam with arbitrary cross-sectional shape,generally anisotropic material behavior and large deflections has been presented based on Hodges＇ method. The concept of decomposition of rotation tensor was used to express the strain in the beam. The variational asymptotic method was used to determine the arbitrary warping of the beam cross section. The generalized Timoshenko strain energy was derived from the equilibrium equations and the second-order asymptotically correct strain energy. The geometrically exact nonlinear equations of motion were established by Hamilton＇s principle. The established modeling was used for the static and dynamic analysis of pre-twisted composite rotor blades, and the analytical results were validated based on experimental data. The influences of the transverse shear deformation on the pre-twisted composite rotor blade were investigated. The results indicate that the influences of the transverse shear deformation on the static deformation and the natural frequencies of the pre-twisted composite rotor blade are related to the length to chord ratio of the blade.展开更多
基金the National Natural Science Foundation of China(Nos.11602204 and 12102373)the Fundamental Research Funds for the Central Universities of China(Nos.2682022ZTPY081 and 2682022CX056)the Natural Science Foundation of Sichuan Province of China(Nos.2023NSFSC0849,2023NSFSC1300,2022NSFSC1938,and 2022NSFSC2003)。
文摘A three-dimensional(3D)thermomechanical vibration model is developed for rotating pre-twisted functionally graded(FG)microbeams according to the refined shear deformation theory(RSDT)and the modified couple stress theory(MCST).The material properties are assumed to follow a power-law distribution along the chordwise direction.The model introduces one axial stretching variable and four transverse deflection variables including two pure bending components and two pure shear ones.The complex modal analysis and assumed mode methods are used to solve the governing equations of motion under different boundary conditions(BCs).Several examples are presented to verify the effectiveness of the developed model.By coupling the slenderness ratio,gradient index,rotation speed,and size effect with the pre-twisted angle,the effects of these factors on the thermomechanical vibration of the microbeam with different BCs are investigated.It is found that with the increase in the pre-twisted angle,the critical slenderness ratio and gradient index corresponding to the thermal instability of the microbeam increase,while the critical material length scale parameter(MLSP)and rotation speed decrease.The sensitivity of the fundamental frequency to temperature increases with the increasing slenderness ratio and gradient index,and decreases with the other increasing parameters.Moreover,the size effect can suppress the dynamic stiffening effect and enhance the Coriolis effect.Finally,the mode transition is quantitatively demonstrated by a modal assurance criterion(MAC).
基金supported by the National Natural Science Foundation of China (No. 11572150)
文摘Modeling of pre-twisted composite rotor blades is very complicated not only because of the geometric non-linearity, but also because of the cross-sectional warping and the transverse shear deformation caused by the anisotropic material properties. In this paper, the geometrically exact nonlinear modeling of a generalized Timoshenko beam with arbitrary cross-sectional shape,generally anisotropic material behavior and large deflections has been presented based on Hodges＇ method. The concept of decomposition of rotation tensor was used to express the strain in the beam. The variational asymptotic method was used to determine the arbitrary warping of the beam cross section. The generalized Timoshenko strain energy was derived from the equilibrium equations and the second-order asymptotically correct strain energy. The geometrically exact nonlinear equations of motion were established by Hamilton＇s principle. The established modeling was used for the static and dynamic analysis of pre-twisted composite rotor blades, and the analytical results were validated based on experimental data. The influences of the transverse shear deformation on the pre-twisted composite rotor blade were investigated. The results indicate that the influences of the transverse shear deformation on the static deformation and the natural frequencies of the pre-twisted composite rotor blade are related to the length to chord ratio of the blade.
