In this paper, the modified iteration method is successfully extended to investigate the nonlinear free vibration of corrugated circular plates with full corrugations. The analytical relation for the amplitude-frequen...In this paper, the modified iteration method is successfully extended to investigate the nonlinear free vibration of corrugated circular plates with full corrugations. The analytical relation for the amplitude-frequency response of corrugated circular plates is obtained and discussions on the influences of geometrical parameters on vibration behaviours of corrugated circular plates are made. The present results are practically important in the design of elastic elements in precision instruments.展开更多
On the basis of paper [1], assuming the logarithm of thickness at arbitrary point on a U-shaped bellows meridian is linear with the logarithm of distance between that point and axis of symmetry, perturbation solutions...On the basis of paper [1], assuming the logarithm of thickness at arbitrary point on a U-shaped bellows meridian is linear with the logarithm of distance between that point and axis of symmetry, perturbation solutions of the corresponding problems of large axisymmetrical deflection are given. The effects of thickness distribution variation, which result from technology factors, on stiffness of bellows are discussed.展开更多
We consider the existence and asymptotic behavior of singularly perturbed boundary value problem;εX″= b（X,t）X′,t ∈（0, 1）（1）X（0） =α, X（1） =β, （2）where, ε】0, is a sufficiently small parameter, b（X,t...We consider the existence and asymptotic behavior of singularly perturbed boundary value problem;εX″= b（X,t）X′,t ∈（0, 1）（1）X（0） =α, X（1） =β, （2）where, ε】0, is a sufficiently small parameter, b（X,t） is continuous in R×[0,1 ],α,βare prescribedboundary condition, and there is a function X<sub>0</sub>（t） satisfying the implicit equation b[X<sub>0</sub>（t）,t] 0t∈[0,1 ].Boundary value problem in this case is rarely studied by other mathematician, the auther has ever dis-cussed the autonomous equation corresponding the boundary value problem （1）,（2）. Generally speaking,the solution of the corresponding problem has boundary layer at each end of the time interval [0 ,1] , itsinner solution is commposed by one or several constant function, these constant is the zero point of the au-展开更多
This paper investigates the linear stability behaviour of plane Poiseuille flow under unsteady distortion by multiscale perturbation method and discusses further the problem proposed by paper [1]. The results show tha...This paper investigates the linear stability behaviour of plane Poiseuille flow under unsteady distortion by multiscale perturbation method and discusses further the problem proposed by paper [1]. The results show that in the initial period of disturbance development, the distortion profiles presented by paper [1] will make the disturbances grow up, thus augmenting the possibility of instability.展开更多
This paper proposes a new method to improve the stability condition of difference scheme of a parabolic equation. Necessary and sufficient conditions of the stability of this new method are given and proved. Some nume...This paper proposes a new method to improve the stability condition of difference scheme of a parabolic equation. Necessary and sufficient conditions of the stability of this new method are given and proved. Some numerical examples show that this method has some calculation advantages.展开更多
This paper discusses the nonlinear stability behaviour of distorted plane Couette flow to 2-dimensional disturbances, and compares it with that of distorted plane Poiseuille flow. The results show that plane Couette f...This paper discusses the nonlinear stability behaviour of distorted plane Couette flow to 2-dimensional disturbances, and compares it with that of distorted plane Poiseuille flow. The results show that plane Couette flow is more unstable than plane Poiseuille flow to finite-amplitude disturbances.展开更多
The author presents a theory, including the complete analysis and incomplete analysis,of perturbational finite element analysis for the solution of nonlinear buckling critical loadsof structures.
文摘In this paper, the modified iteration method is successfully extended to investigate the nonlinear free vibration of corrugated circular plates with full corrugations. The analytical relation for the amplitude-frequency response of corrugated circular plates is obtained and discussions on the influences of geometrical parameters on vibration behaviours of corrugated circular plates are made. The present results are practically important in the design of elastic elements in precision instruments.
文摘On the basis of paper [1], assuming the logarithm of thickness at arbitrary point on a U-shaped bellows meridian is linear with the logarithm of distance between that point and axis of symmetry, perturbation solutions of the corresponding problems of large axisymmetrical deflection are given. The effects of thickness distribution variation, which result from technology factors, on stiffness of bellows are discussed.
文摘We consider the existence and asymptotic behavior of singularly perturbed boundary value problem;εX″= b（X,t）X′,t ∈（0, 1）（1）X（0） =α, X（1） =β, （2）where, ε】0, is a sufficiently small parameter, b（X,t） is continuous in R×[0,1 ],α,βare prescribedboundary condition, and there is a function X<sub>0</sub>（t） satisfying the implicit equation b[X<sub>0</sub>（t）,t] 0t∈[0,1 ].Boundary value problem in this case is rarely studied by other mathematician, the auther has ever dis-cussed the autonomous equation corresponding the boundary value problem （1）,（2）. Generally speaking,the solution of the corresponding problem has boundary layer at each end of the time interval [0 ,1] , itsinner solution is commposed by one or several constant function, these constant is the zero point of the au-
基金This work is supported by National Science Foundationthe Science Foundation of Shanghai University of Technology
文摘This paper investigates the linear stability behaviour of plane Poiseuille flow under unsteady distortion by multiscale perturbation method and discusses further the problem proposed by paper [1]. The results show that in the initial period of disturbance development, the distortion profiles presented by paper [1] will make the disturbances grow up, thus augmenting the possibility of instability.
文摘This paper proposes a new method to improve the stability condition of difference scheme of a parabolic equation. Necessary and sufficient conditions of the stability of this new method are given and proved. Some numerical examples show that this method has some calculation advantages.
文摘This paper discusses the nonlinear stability behaviour of distorted plane Couette flow to 2-dimensional disturbances, and compares it with that of distorted plane Poiseuille flow. The results show that plane Couette flow is more unstable than plane Poiseuille flow to finite-amplitude disturbances.
文摘The author presents a theory, including the complete analysis and incomplete analysis,of perturbational finite element analysis for the solution of nonlinear buckling critical loadsof structures.
