In this paper, a modified averaging scheme is presented for a class of time-delayed vibration systems with slow variables. The new scheme is a combination of the averaging techniques proposed by Hale and by Lehman and...In this paper, a modified averaging scheme is presented for a class of time-delayed vibration systems with slow variables. The new scheme is a combination of the averaging techniques proposed by Hale and by Lehman and Weibel, respectively. The averaged equation obtained from the modified scheme is simple enough but it retains the required information for the local nonlinear dynamics around an equilibrium. As an application of the present method, the delay value for which a secondary Hopf bifurcation occurs is successfully located for a delayed van der Pol oscillator.展开更多
Based on the Hamilton principle and the moderate deflection beam theory, discretizing the helicopter blade into a number of beam elements with 15 degrees of freedora, and using a quasi-steady aero-model, a nonlinear c...Based on the Hamilton principle and the moderate deflection beam theory, discretizing the helicopter blade into a number of beam elements with 15 degrees of freedora, and using a quasi-steady aero-model, a nonlinear coupled rotor/fuselage equation is established. A periodic solution of blades and fuselage is obtained through aeroelastic coupled trim using the temporal finite element method （TEM）. The Peters dynamic inflow model is used for vehicle stability. A program for computation is developed, which produces the blade responses, hub loads, and rotor pitch controls. The correlation between the analytical results and related literature is good. The converged solution simultaneously satisfies the blade and the vehicle equilibrium equations.展开更多
On the basis of analysis of the fluid drag acting on a suspended cable subjected to transverse fluid excitation, an expression is established for the fluid forces applied on the cable. By using a coordinate transform,...On the basis of analysis of the fluid drag acting on a suspended cable subjected to transverse fluid excitation, an expression is established for the fluid forces applied on the cable. By using a coordinate transform, the equations of motion of the cable are simplified into those in terms of the stretch and rotation coordinates. In the case of small ratio of sag-to-span, a study is made on the fluid-induced vibration behavior of the cable, including the critical fluid flow speed, the stability of equilibrium position, as well as the influences of gravitational parameter on the cable dynamics.展开更多
By means of the frozen time approach and the Kronecker product, two criteria of asymptotic stability are derived for the linear, time variant dynamic systems with either short time delays or with weak feedback involvi...By means of the frozen time approach and the Kronecker product, two criteria of asymptotic stability are derived for the linear, time variant dynamic systems with either short time delays or with weak feedback involving arbitrary time delays, respectively. It is found that the asymptotic stability of these retarded dynamic systems is governed by the maximal and minimal singular values of the coefficient matrices and their time derivatives. (Author abstract) 10 Refs.展开更多
The phenomenon of stochastic resonance is investigated in an asymmetric bistable system with coloured noises. The approximate Fokker Planck equation is derived based on the Novikov theorem and the Fox approach. By app...The phenomenon of stochastic resonance is investigated in an asymmetric bistable system with coloured noises. The approximate Fokker Planck equation is derived based on the Novikov theorem and the Fox approach. By applying the two-state theory, the expression of the signal-to-noise ratio is obtained in the adiabatic limit. The effects of the noise parameters on signal-to-ratio are discussed. It is found that the stochastic resonance phenomena appear in most cases and disappear in some special cases.展开更多
In this paper, we propose an impact finite element （FE） model for an airbag landing buf- fer system. First, an impact FE model has been formulated for a typical airbag landing buffer system. We use the independence ...In this paper, we propose an impact finite element （FE） model for an airbag landing buf- fer system. First, an impact FE model has been formulated for a typical airbag landing buffer system. We use the independence of the structure FE model from the full impact FE model to develop a hierarchical updating scheme for the recovery module FE model and the airbag system FE model. Second, we define impact responses at key points to compare the computational and experimental results to resolve the inconsistency between the experimental data sampling frequency and experi- mental triggering. To determine the typical characteristics of the impact dynamics response of the airbag landing buffer system, we present the impact response confidence factors （IRCFs） to evalu- ate how consistent the computational and experiment results are. An error function is defined between the experimental and computational results at key points of the impact response （KPIR） to serve as a modified objective function. A radial basis function （RBF） is introduced to construct updating variables for a surrogate model for updating the objective function, thereby converting the FE model updating problem to a soluble optimization problem. Finally, the developed method has been validated using an experimental and computational study on the impact dynamics of a classic airbag landing buffer system.展开更多
The dynamics of a mechanical system in the Lagrange space yields a set of differential equations of the second order and involves much less variables and constraints than that described in the state space. This paper ...The dynamics of a mechanical system in the Lagrange space yields a set of differential equations of the second order and involves much less variables and constraints than that described in the state space. This paper presents a so-called Legendre pseudo-spectral (PS) approach for directly estimating the costates of the Bolza problem of optimal control of a set of dynamic equations of the second order. Under a set of closure conditions, it is proved that the Karush-Kuhn-Tucker (KKT) multipliers satisfy the same conditions as those determined by collocating the costate equations of the second order. Hence, the KKT multipliers can be used to estimate the costates of the Bolza problem via a simple linear map- ping. The proposed approach can be used to check the optimality of the direct solution for a trajectory optimization problem involving the dynamic equations of the second order and to remove any conver- sion of the dynamic system from the second order to the first order. The new approach is demonstrated via two classical benchmark problems.展开更多
基金FANEDD of China (200430)the National Natural Science Foundation of China (10372116,10532050)
文摘In this paper, a modified averaging scheme is presented for a class of time-delayed vibration systems with slow variables. The new scheme is a combination of the averaging techniques proposed by Hale and by Lehman and Weibel, respectively. The averaged equation obtained from the modified scheme is simple enough but it retains the required information for the local nonlinear dynamics around an equilibrium. As an application of the present method, the delay value for which a secondary Hopf bifurcation occurs is successfully located for a delayed van der Pol oscillator.
基金Project supported by the National Natural Science Foundation of China (No. 10872089)
文摘Based on the Hamilton principle and the moderate deflection beam theory, discretizing the helicopter blade into a number of beam elements with 15 degrees of freedora, and using a quasi-steady aero-model, a nonlinear coupled rotor/fuselage equation is established. A periodic solution of blades and fuselage is obtained through aeroelastic coupled trim using the temporal finite element method （TEM）. The Peters dynamic inflow model is used for vehicle stability. A program for computation is developed, which produces the blade responses, hub loads, and rotor pitch controls. The correlation between the analytical results and related literature is good. The converged solution simultaneously satisfies the blade and the vehicle equilibrium equations.
文摘On the basis of analysis of the fluid drag acting on a suspended cable subjected to transverse fluid excitation, an expression is established for the fluid forces applied on the cable. By using a coordinate transform, the equations of motion of the cable are simplified into those in terms of the stretch and rotation coordinates. In the case of small ratio of sag-to-span, a study is made on the fluid-induced vibration behavior of the cable, including the critical fluid flow speed, the stability of equilibrium position, as well as the influences of gravitational parameter on the cable dynamics.
基金The project supported by the National Natural Science Foundation of China under the Grant of 59625511
文摘By means of the frozen time approach and the Kronecker product, two criteria of asymptotic stability are derived for the linear, time variant dynamic systems with either short time delays or with weak feedback involving arbitrary time delays, respectively. It is found that the asymptotic stability of these retarded dynamic systems is governed by the maximal and minimal singular values of the coefficient matrices and their time derivatives. (Author abstract) 10 Refs.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10672074)
文摘The phenomenon of stochastic resonance is investigated in an asymmetric bistable system with coloured noises. The approximate Fokker Planck equation is derived based on the Novikov theorem and the Fox approach. By applying the two-state theory, the expression of the signal-to-noise ratio is obtained in the adiabatic limit. The effects of the noise parameters on signal-to-ratio are discussed. It is found that the stochastic resonance phenomena appear in most cases and disappear in some special cases.
基金co-supported by the National Natural Science Foundation of China(No.11472132)the Fundamental Research Funds for Central Universities in China(No.NS2014002)+1 种基金the Research Fund of State Key Laboratory of Mechanics and Control of Mechanical Structures(Nanjing University of Aeronautics and Astronautics)(No.0113Y01)the Priority Academic Program Development(PAPD)of Jiangsu Higher Education Institutions in China
文摘In this paper, we propose an impact finite element （FE） model for an airbag landing buf- fer system. First, an impact FE model has been formulated for a typical airbag landing buffer system. We use the independence of the structure FE model from the full impact FE model to develop a hierarchical updating scheme for the recovery module FE model and the airbag system FE model. Second, we define impact responses at key points to compare the computational and experimental results to resolve the inconsistency between the experimental data sampling frequency and experi- mental triggering. To determine the typical characteristics of the impact dynamics response of the airbag landing buffer system, we present the impact response confidence factors （IRCFs） to evalu- ate how consistent the computational and experiment results are. An error function is defined between the experimental and computational results at key points of the impact response （KPIR） to serve as a modified objective function. A radial basis function （RBF） is introduced to construct updating variables for a surrogate model for updating the objective function, thereby converting the FE model updating problem to a soluble optimization problem. Finally, the developed method has been validated using an experimental and computational study on the impact dynamics of a classic airbag landing buffer system.
基金Supported by the National Natural Science Foundation of China (Grant Nos. 10372039, 10672073)the Innovation Fund for Graduate Students of NUAA (Grant No. 4003-019016)
文摘The dynamics of a mechanical system in the Lagrange space yields a set of differential equations of the second order and involves much less variables and constraints than that described in the state space. This paper presents a so-called Legendre pseudo-spectral (PS) approach for directly estimating the costates of the Bolza problem of optimal control of a set of dynamic equations of the second order. Under a set of closure conditions, it is proved that the Karush-Kuhn-Tucker (KKT) multipliers satisfy the same conditions as those determined by collocating the costate equations of the second order. Hence, the KKT multipliers can be used to estimate the costates of the Bolza problem via a simple linear map- ping. The proposed approach can be used to check the optimality of the direct solution for a trajectory optimization problem involving the dynamic equations of the second order and to remove any conver- sion of the dynamic system from the second order to the first order. The new approach is demonstrated via two classical benchmark problems.
