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
A viscoelastic beam in a two-dimensional space is considered with nonlinear tension. A boundary feedback is applied at the right boundary of the beam to suppress the undesirable vibration. The well-posedness of the pr...A viscoelastic beam in a two-dimensional space is considered with nonlinear tension. A boundary feedback is applied at the right boundary of the beam to suppress the undesirable vibration. The well-posedness of the problem is established. With the multiplier method, a uniform decay result is proven.展开更多
A bending beam,subjected to state of plane stress,was chosen to investigate.The determination of the neutral surface of the structure was made,and the calculating formulas of neutral axis,normal stress,shear stress a...A bending beam,subjected to state of plane stress,was chosen to investigate.The determination of the neutral surface of the structure was made,and the calculating formulas of neutral axis,normal stress,shear stress and displacement were derived.It is concluded that, for the elastic bending beam with different tension-compression modulus in the condition of complex stress, the position of the neutral axis is not related with the shear stress, and the analytical solution can be derived by normal stress used as a criterion, improving the multiple cyclic method which determines the position of neutral point by the principal stress. Meanwhile, a comparison is made between the results of the analytical solution and those calculated from the classic mechanics theory, assuming the tension modulus is equal to the compression modulus, and those from the finite element method (FEM) numerical solution. The comparison shows that the analytical solution considers well the effects caused by the condition of different tension and compression modulus. Finally, a calculation correction of the structure with different modulus is proposed to optimize the structure.展开更多
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.
文摘A viscoelastic beam in a two-dimensional space is considered with nonlinear tension. A boundary feedback is applied at the right boundary of the beam to suppress the undesirable vibration. The well-posedness of the problem is established. With the multiplier method, a uniform decay result is proven.
文摘A bending beam,subjected to state of plane stress,was chosen to investigate.The determination of the neutral surface of the structure was made,and the calculating formulas of neutral axis,normal stress,shear stress and displacement were derived.It is concluded that, for the elastic bending beam with different tension-compression modulus in the condition of complex stress, the position of the neutral axis is not related with the shear stress, and the analytical solution can be derived by normal stress used as a criterion, improving the multiple cyclic method which determines the position of neutral point by the principal stress. Meanwhile, a comparison is made between the results of the analytical solution and those calculated from the classic mechanics theory, assuming the tension modulus is equal to the compression modulus, and those from the finite element method (FEM) numerical solution. The comparison shows that the analytical solution considers well the effects caused by the condition of different tension and compression modulus. Finally, a calculation correction of the structure with different modulus is proposed to optimize the structure.
