The mathematical modeling of a rotating tapered Timoshenko beam with preset and pre-twist angles is constructed. The partial differential equations governing the six degrees, i.e., three displacements in the axial, fl...The mathematical modeling of a rotating tapered Timoshenko beam with preset and pre-twist angles is constructed. The partial differential equations governing the six degrees, i.e., three displacements in the axial, flapwise, and edgewise directions and three cross-sectional angles of torsion, flapwise bending, and edgewise bending, are obtained by the Euler angle descriptions. The power series method is then used to inves- tigate the natural frequencies and the corresponding complex mode functions. It is found that all the natural frequencies are increased by the centrifugal stiffening except the twist frequency, which is slightly decreased. The tapering ratio increases the first transverse, torsional, and axial frequencies, while decreases the second transverse frequency. Because of the pre-twist, all the directions are gyroscopically coupled with the phase differences among the six degrees.展开更多
For the system of the centre rigid_body mounted on an external cantilever beam, the equilibrium solution of the steadily rotating beam is stable if the effect of its shearing stress (i.e. the beam belongs to the Euler...For the system of the centre rigid_body mounted on an external cantilever beam, the equilibrium solution of the steadily rotating beam is stable if the effect of its shearing stress (i.e. the beam belongs to the Euler_Bernoulli type) is not considered. But for the deep beam, it is necessary to consider the effect of the shearing stress (i.e. the beam belongs to the Timoshenko type). In this case, the tension buckling of the equilibrium solution of the steadily rotating beam may occur. In the present work, using the general Hamilton Variation Principle, a nonlinear dynamic model of the rigid_flexible system with a centre rigid_body mounted on an external Timoshenko beam is established. The bifurcation regular of the steadily rotating Timoshenko beam is investigated by using numerical methods. Furthermore, the critical rotating velocity is also obtained.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.11672007,11402028,11322214,and 11290152)the Beijing Natural Science Foundation(No.3172003)the Key Laboratory of Vibration and Control of Aero-Propulsion System Ministry of Education,Northeastern University(No.VCAME201601)
文摘The mathematical modeling of a rotating tapered Timoshenko beam with preset and pre-twist angles is constructed. The partial differential equations governing the six degrees, i.e., three displacements in the axial, flapwise, and edgewise directions and three cross-sectional angles of torsion, flapwise bending, and edgewise bending, are obtained by the Euler angle descriptions. The power series method is then used to inves- tigate the natural frequencies and the corresponding complex mode functions. It is found that all the natural frequencies are increased by the centrifugal stiffening except the twist frequency, which is slightly decreased. The tapering ratio increases the first transverse, torsional, and axial frequencies, while decreases the second transverse frequency. Because of the pre-twist, all the directions are gyroscopically coupled with the phase differences among the six degrees.
文摘For the system of the centre rigid_body mounted on an external cantilever beam, the equilibrium solution of the steadily rotating beam is stable if the effect of its shearing stress (i.e. the beam belongs to the Euler_Bernoulli type) is not considered. But for the deep beam, it is necessary to consider the effect of the shearing stress (i.e. the beam belongs to the Timoshenko type). In this case, the tension buckling of the equilibrium solution of the steadily rotating beam may occur. In the present work, using the general Hamilton Variation Principle, a nonlinear dynamic model of the rigid_flexible system with a centre rigid_body mounted on an external Timoshenko beam is established. The bifurcation regular of the steadily rotating Timoshenko beam is investigated by using numerical methods. Furthermore, the critical rotating velocity is also obtained.
