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| 1 | Stochastic averaging technique for SDOF strongly nonlinear systems with delayed feedback fractional-order PD controller显示文摘A stochastic averaging technique is proposed to study the randomly excited single-degree-of-freedom(SDOF) strongly nonlinear systems with delayed feedback fractional-order proportional-derivative(PD) controller. The delayed feedback fractional-order PD control force is approximated by an equivalent non-delay feedback control force combining with a quasi-linear elastic force and a quasi-linear damping force. The averaged It? stochastic differential equation for amplitude of the equivalent nonlinear system is derived by the generalized harmonic functions. The analytical stationary probability density function(PDF) is obtained with solving the reduced Fokker-Planck-Kolmogorov(FPK) equation. Two examples of van der Pol oscillator and RayleighDuffing oscillator are studied to illustrate the application and effectiveness of the proposed method. Numerical results display that the proposed method can yield to the high precision, and the time delay could ruin the control effectiveness, but also even amplifies the response of the system more than that of uncontrolled system. Furthermore, the study finds that the parameters of fractional-order α and time delay may cause the stochastic P-bifurcation. It is indicated that the delayed feedback fractional-order PD controller can offer a potentially effective tool for anti-control of stochastic | CHEN LinCong LIANG Xiao ZHU WeiQiu ZHAO YaoBing | 2019 | Science China(Technological Sciences)2019，62，2： | 5 |
| 2 | Stochastic response of fractional-order van der Pol oscillator显示文摘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. | Lincong Chen Weiqiu Zhu | 2014 | Theoretical & Applied Mechanics Letters2014，4，1： | 4 |
| 3 | Optimization for vibro-impact nonlinear energy sink under randomexcitation显示文摘As a promising vibration control device, the vibro-impact nonlinear energy sink (VI-NES) gathered extensively attention in recent years. However, general optimization procedures have not been available forthe design of VI-NES subjected to random excitations. To this end, this paper constitutes a research effortto address this gap. Specifically, the approximate analytical solution of the system stochastic responseis obtained in conjunction with non-smooth conversion and stochastic averaging methodology. Takingadvantages of this approximate solution, the variance of the system is defined and easily minimized tocalculate the optimal parameters for VI-NES. In addition, the results computed by this way fairly correlatewith direct numeric simulations. | Jiamin Qian Lincong Chen | 2022 | Theoretical & Applied Mechanics Letters2022，12，5： | 1 |
| 4 | STOCHASTIC OPTIMAL VIBRATION CONTROL OF PARTIALLY OBSERVABLE NONLINEAR QUASI HAMILTONIAN SYSTEMS WITH ACTUATOR SATURATION显示文摘An optimal vibration control strategy for partially observable nonlinear quasi Hamiltonian systems with actuator saturation is proposed. First,a controlled partially observable non-linear system is converted into a completely observable linear control system of finite dimension based on the theorem due to Charalambous and Elliott. Then the partially averaged It stochastic differential equations and dynamical programming equation associated with the completely observable linear system are derived by using the stochastic averaging method and stochastic dynamical programming principle,respectively. The optimal control law is obtained from solving the final dynamical programming equation. The results show that the proposed control strategy has high control effectiveness and control effciency. | Ronghua Huan Lincong Chen Weiliang Jin Weiqiu Zhu | 2009 | Acta Mechanica Solida Sinica2009，22，2： | 1 |
| 5 | Asymptotic stability with probability one of MDOF nonlinear oscillators with fractional derivative damping显示文摘In this paper,the asymptotic stability with probability one of multi-degree-of-freedom(MDOF)nonlinear oscillators with fractional derivative damping parametrically excited by Gaussian white noises is investigated.A stochastic averaging method and the Khasminskii’s procedure are employed to evaluate the largest Lyapunov exponent,whose sign determines the stability of the system.As an example,two coupled nonlinear oscillators with fractional derivative damping is worked out to demonstrate the proposed procedure and to examine the effect of fractional order on the stochastic stability of system.In particular,the case of factional order more than 1 is studied for the first time. | CHEN LinCong LI HaiFeng LI ZhongShen ZHU WeiQiu | 2013 | Science China(Physics,Mechanics & Astronomy)2013，56，11： | 1 |
| 6 | Synergistic lubricating effect of graphene/ionic liquid composite material used as an additive显示文摘We prepared a graphene/ionic liquid(G/IL)composite material by the hybridization of G and an IL for use as a lubricating oil additive.The friction coefficient and wear volume of a base oil containing 0.04 wt%of the G/IL composite was reduced by 45%and 90%,respectively.Furthermore,the base oil containing the G/IL composite exhibited better lubricating properties than the base oil containing G,IL,or a mixture of IL and G at the same mass fraction.A synergistic lubrication mechanism was also revealed.The G/IL composite was adsorbed and deposited on the wear surface,forming a more ordered protective film and a unique tribochemical reaction film during rubbing.Therefore,the G/IL composite exhibited the synergistic lubricating effects of G and IL,which significantly improved the lubricating performance of the base oil.This study also suggested a way to limit the out-of-plane puckering of G at the macroscale. | Lincong LIU Ming ZHOU Youtang MO Pengpeng BAI Qilin WEI Long JIN Shengli YOU Mingyue WANG Liangchuan LI Xin CHEN Xiao LI Yu TIAN | 2021 | Friction2021，9，6： | 1 |
| 7 | First passage failure of SDOF nonlinear oscillator with lightly fractional derivative damping under real noise excitations显示文摘 | CHEN Lincong ZHU Weiqiu | | 0，，2： | 1 |
| 8 | First passage failure of quasi non-integrable generalized Hamiltonian systems显示文摘 | CHEN Lincong ZHU Weiqiu | | 0，，8： | 1 |
| 9 | Solving the transient response of the randomly excited dry friction system via piecewise RBF neural networks显示文摘Over the years,practical importance and interesting dynamical features have caused a growing interest in dry friction systems.Nevertheless,an effective approach to capture the non-smooth transition behavior of such systems is still lacking.Accordingly,we propose a piecewise radial basis function neural network(RBFNN)strategy to solve the transient response of the randomly excited dry friction system.Within the established framework,the transient probability density function of the dry friction system is expressed in a piecewise form.Each segment of the solution is expressed by the sum of a series of Gaussian activation functions with time-dependent weights.These time dependent weights are solved by minimizing the loss function,which involves the residual of the Fokker-Planck-Kolmogorov equations and constraint conditions.To avoid the singularity of the initial condition being a Dirac delta function,a short-time Gaussian approximation strategy is presented to solve the initiating time-dependent weights.Based on some numerical results,the proposed scheme effectively performs.Moreover,a comparison with other existing methods reveals that the proposed scheme can completely capture the nonlinear characteristic of the dry friction system stochastic response more closely.Noteworthy,we can easily extend the proposed method to other types of non-smooth systems with piecewise response characteristics.Moreover,the semi-analytical solution provides a valuable reference for system optimization. | QIAN JiaMin CHEN LinCong SUN JianQiao | 2023 | Science China(Technological Sciences)2023，66，5： | 0 |
| 10 | A highly-efficient method for stationary response of multi-degree-of-freedom nonlinear stochastic systems显示文摘Analytical and numerical studies of multi-degree-of-freedom(MDOF) nonlinear stochastic or deterministic dynamic systems have long been a technical challenge.This paper presents a highly-efficient method for determining the stationary probability density functions(PDFs) of MDOF nonlinear systems subjected to both additive and multiplicative Gaussian white noises. The proposed method takes advantages of the sufficient conditions of the reduced Fokker-Planck-Kolmogorov(FPK) equation when constructing the trial solution. The assumed solution consists of the analytically constructed trial solutions satisfying the sufficient conditions and an exponential polynomial of the state variables, and delivers a high accuracy of the solution because the analytically constructed trial solutions capture the main characteristics of the nonlinear system. We also make use of the concept from the data-science and propose a symbolic integration over a hypercube to replace the numerical integrations in a higher-dimensional space, which has been regarded as the insurmountable difficulty in the classical method of weighted residuals or stochastic averaging for high-dimensional dynamic systems. Three illustrative examples of MDOF nonlinear systems are analyzed in detail. The accuracy of the numerical results is validated by comparison with the Monte Carlo simulation(MCS) or the available exact solution. Furthermore, we also show the substantial gain in the computational efficiency of the proposed method compared with the MCS. | Lincong CHEN J.Q.SUN | 2020 | Applied Mathematics and Mechanics(English Edition)2020，41，6： | 0 |
| 11 | Novel method for random vibration analysis of single-degree-of-freedom vibroimpact systems with bilateral barriers显示文摘The vibroimpact systems with bilateral barriers are often encountered in practice.However,the dynamics of the vibroimpact system with bilateral barriers is full of challenges.Few closed-form solutions were obtained.In this paper,we propose a novel method for random vibration analysis of single-degree-of-freedom(SDOF)vibroim-pact systems with bilateral barriers under Gaussian white noise excitations.A periodic approximate transformation is employed to convert the equations of the motion to a con-tinuous form.The probabilistic description of the system is subsequently defined through the corresponding Fokker-Planck-Kolmogorov(FPK)equation.The closed-form station-ary probability density function(PDF)of the response is obtained by solving the reduced FPK equation and using the proposed iterative method of weighted residue together with the concepts of the circulatory probability flow and the potential probability flow.Finally,the versatility of the proposed approach is demonstrated by its application to two typical examples.Note that the solution obtained by using the proposed method can be used as the benchmark to examine the accuracy of approximate solutions obtained by other methods. | Lincong CHEN Haisheng ZHU J.Q.SUN | 2019 | Applied Mathematics and Mechanics(English Edition)2019，40，12： | 0 |
| 12 | Random vibration of hysteretic systems under Poisson white noise excitations显示文摘Hysteresis widely exists in civil structures,and dissipates the mechanical energy of systems.Research on the random vibration of hysteretic systems,however,is still insufficient,particularly when the excitation is non-Gaussian.In this paper,the radial basis function(RBF)neural network(RBF-NN)method is adopted as a numerical method to investigate the random vibration of the Bouc-Wen hysteretic system under the Poisson white noise excitations.The solution to the reduced generalized Fokker-PlanckKolmogorov(GFPK)equation is expressed in terms of the RBF-NNs with the Gaussian activation functions,whose weights are determined by minimizing the loss function of the reduced GFPK equation residual and constraint associated with the normalization condition.A steel fiber reinforced ceramsite concrete(SFRCC)column loaded by the Poisson white noise is studied as an example to illustrate the solution process.The effects of several important parameters of both the system and the excitation on the stochastic response are evaluated,and the obtained results are compared with those obtained by the Monte Carlo simulations(MCSs).The numerical results show that the RBF-NN method can accurately predict the stationary response with a considerable high computational efficiency. | Lincong CHEN Zi YUAN Jiamin QIAN J.Q.SUN | 2023 | Applied Mathematics and Mechanics(English Edition)2023，44，2： | 0 |
| 13 | Stochastic stability of the harmonically and randomly excited Duffing oscillator with damping modeled by a fractional derivative显示文摘The stochastic stability of the harmonically and randomly excited Duffing oscillator with damping modeled by a fractional derivative of Caputo's definition is analyzed.First,the system state is approximately described by It equations through the stochastic averaging method based on the generalized harmonic function.Then,the associated expression for the largest Lyapunov exponent of the linearized averaged It is derived,and the necessary and sufficient condition for the asymptotic stability with probability one of the trivial solution of the original system is obtained approximately by letting the largest Lyapunov exponent be negative.The effects of fractional orders and random excitation intensities on the asymptotic stability with probability one determined by the largest Lyapunov exponent are shown graphically. | CHEN LinCong LOU Qun LI ZhongShen ZHU WeiQiu | 2012 | Science China(Physics,Mechanics & Astronomy)2012，55，12： | 0 |
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