In this paper, a new equivalent nonlinearization method is developed and used in analysing the response of nonlinear systems to Gaussian while noise excitation. Its basic idea and calculation method are expounded. Wit...In this paper, a new equivalent nonlinearization method is developed and used in analysing the response of nonlinear systems to Gaussian while noise excitation. Its basic idea and calculation method are expounded. With the help of the presented method, several kinds of usual nonlinear random vibration systems are analyzed. The numerical results show that the mean square responses of the proposed approach are much closer to the exact solutions or Monte Carlo solutions, than that obtained from equivalent linearization method.展开更多
The mathematical model of single degree of freedom(DOF)nonlinear autonomous bearing system under constant flow supporting model is deduced.The single DOF nonlinear autonomous bearing system is transformed with the met...The mathematical model of single degree of freedom(DOF)nonlinear autonomous bearing system under constant flow supporting model is deduced.The single DOF nonlinear autonomous bearing system is transformed with the method of linear and nonlinear treatment,the mathematical expression and parameters sensitivity of relative error of stiffness and damping are presented.Finally,the main factors of magnetic-liquid double suspension bearing(MLDSB)are analyzed,and the influence on bearing performance indicators of single DOF nonlinear autonomous bearing system of main factors is revealed.The results show that linear stiffness/damping is the first part of equivalent stiffness/damping,and the second and third parts are high order minor term of Tayor series transform.The film thickness,the magnetic-liquid proportionality coefficient,the mass of rotor are the major influence factor of the bearing performance.The research can provide the theoretical reference for the design and nonlinear analysis of MLDSB.展开更多
We studied the response of fractional-order van de Pol oscillator to Gaussian white noise excitation in this letter. An equivalent integral-order nonlinear stochastic system is obtained to replace the given system bas...We studied the response of fractional-order van de Pol oscillator to Gaussian white noise excitation in this letter. An equivalent integral-order nonlinear stochastic system is obtained to replace the given system based on the principle of minimum mean-square error. Through stochastic averaging, an averaged Ito equation is deduced. We obtained the Fokker–Planck–Kolmogorov equation connected to the averaged Ito equation and solved it to yield the approximate stationary response of the system. The analytical solution is confirmed by using Monte Carlo simulation.展开更多
This paper investigates the stability analysis and H_∞ control for a class of nonlinear timedelay systems,and proposes a number of new results.Firstly,an equivalent form is given for this class of systems by means of...This paper investigates the stability analysis and H_∞ control for a class of nonlinear timedelay systems,and proposes a number of new results.Firstly,an equivalent form is given for this class of systems by means of coordinate transformation and orthogonal decomposition of vector fields.Then,based on the equivalent form,some delay-dependent results are derived for the stability analysis of the systems by constructing a novel Lyapunov functional.Thirdly,the authors use the equivalent form and the obtained stability results to investigate the H_∞ control problem for a class of nonhnear time-delay control systems,and present a control design procedure.Finally,an illustrative example is given to show the effectiveness of the results obtained in this paper.It is shown that the main results of this paper are easier to check than some existing ones,and have less conservatism.展开更多
文摘In this paper, a new equivalent nonlinearization method is developed and used in analysing the response of nonlinear systems to Gaussian while noise excitation. Its basic idea and calculation method are expounded. With the help of the presented method, several kinds of usual nonlinear random vibration systems are analyzed. The numerical results show that the mean square responses of the proposed approach are much closer to the exact solutions or Monte Carlo solutions, than that obtained from equivalent linearization method.
基金the National Natural Science Foundation of China(No.51705445)General Project of Natural Science Foundation of Hebei Province(No.E2016203324)Youth Fund Project of Scientific Research Project of Hebei University(No.QN202013).
文摘The mathematical model of single degree of freedom(DOF)nonlinear autonomous bearing system under constant flow supporting model is deduced.The single DOF nonlinear autonomous bearing system is transformed with the method of linear and nonlinear treatment,the mathematical expression and parameters sensitivity of relative error of stiffness and damping are presented.Finally,the main factors of magnetic-liquid double suspension bearing(MLDSB)are analyzed,and the influence on bearing performance indicators of single DOF nonlinear autonomous bearing system of main factors is revealed.The results show that linear stiffness/damping is the first part of equivalent stiffness/damping,and the second and third parts are high order minor term of Tayor series transform.The film thickness,the magnetic-liquid proportionality coefficient,the mass of rotor are the major influence factor of the bearing performance.The research can provide the theoretical reference for the design and nonlinear analysis of MLDSB.
基金supported by the National Natural Science Foundation of China(10932009,11072212,11272279,and 11002059)the Specialized Research Fund for the Doctoral Program of Higher Education(20103501120003)the Fundamental Research Funds for Huaqiao University(JB-SJ1010)
文摘We studied the response of fractional-order van de Pol oscillator to Gaussian white noise excitation in this letter. An equivalent integral-order nonlinear stochastic system is obtained to replace the given system based on the principle of minimum mean-square error. Through stochastic averaging, an averaged Ito equation is deduced. We obtained the Fokker–Planck–Kolmogorov equation connected to the averaged Ito equation and solved it to yield the approximate stationary response of the system. The analytical solution is confirmed by using Monte Carlo simulation.
基金supported by the National Natural Science Foundation of China under Grant Nos.G60774009,61074068,61034007,61374065,and 61304033the Research Fund for the Doctoral Program of Chinese Higher Education under Grant No.200804220028+1 种基金the Natural Science Foundation of Shandong Province under Grant Nos.ZR2013ZEM006,ZR2011EL021,BS2011ZZ012,2013ZRB01873Colleges and Universities in Shandong Province Science and Technology Project under Grant Nos.J13LN37 and J12LN29
文摘This paper investigates the stability analysis and H_∞ control for a class of nonlinear timedelay systems,and proposes a number of new results.Firstly,an equivalent form is given for this class of systems by means of coordinate transformation and orthogonal decomposition of vector fields.Then,based on the equivalent form,some delay-dependent results are derived for the stability analysis of the systems by constructing a novel Lyapunov functional.Thirdly,the authors use the equivalent form and the obtained stability results to investigate the H_∞ control problem for a class of nonhnear time-delay control systems,and present a control design procedure.Finally,an illustrative example is given to show the effectiveness of the results obtained in this paper.It is shown that the main results of this paper are easier to check than some existing ones,and have less conservatism.
