Nonlinear dynamics of flexible tethered satellite system subject to space environment

The paper studies the nonlinear dynamics of a flexible tethered satellite system subject to space environments, such as the J2 perturbation, the air drag force, the solar pressure, the heating effect, and the orbital eccentricity. The flexible tether is modeled as a series of lumped masses and viscoelastic dampers so that a finite multi- degree-of-freedom nonlinear system is obtained. The stability of equilibrium positions of the nonlinear system is then analyzed via a simplified two-degree-freedom model in an orbital reference frame. In-plane motions of the tethered satellite system are studied numerically, taking the space environments into account. A large number of numerical simulations show that the flexible tethered satellite system displays nonlinear dynamic characteristics, such as bifurcations, quasi-periodic oscillations, and chaotic motions.

Nonlinear Characteristic Analysis of Gas-Interconnected Quasi-Zero Stiffness Pneumatic Suspension System:A Theoretical and Experimental Study

Because of significantly changed load and complex and variable driving road conditions of commercial vehicles,pneumatic suspension with lower natural frequencies is widely used in commercial vehicle suspension system.How ever,traditional pneumatic suspension system is hardly to respond the greatly changed load of commercial vehicles To address this issue,a new Gas-Interconnected Quasi-Zero Stiffness Pneumatic Suspension(GIQZSPS)is presented in this paper to improve the vibration isolation performance of commercial vehicle suspension systems under frequent load changes.This new structure adds negative stiffness air chambers on traditional pneumatic suspension to reduce the natural frequency of the suspension.It can adapt to different loads and road conditions by adjusting the solenoid valves between the negative stiffness air chambers.Firstly,a nonlinear mechanical model including the dimensionless stiffness characteristic and interconnected pipeline model is derived for GIQZSPS system.By the nonlinear mechanical model of GIQZSPS system,the force transmissibility rate is chosen as the evaluation index to analyze characteristics.Furthermore,a testing bench simulating 1/4 GIQZSPS system is designed,and the testing analysis of the model validation and isolating performance is carried out.The results show that compared to traditional pneumatic suspension,the GIQZSPS designed in the article has a lower natural frequency.And the system can achieve better vibration isolation performance under different load states by switching the solenoid valves between air chambers.

Nonlinear dynamics of a circular curved cantilevered pipe conveying pulsating fluid based on the geometrically exact model

Due to the novel applications of flexible pipes conveying fluid in the field of soft robotics and biomedicine,the investigations on the mechanical responses of the pipes have attracted considerable attention.The fluid-structure interaction(FSI)between the pipe with a curved shape and the time-varying internal fluid flow brings a great challenge to the revelation of the dynamical behaviors of flexible pipes,especially when the pipe is highly flexible and usually undergoes large deformations.In this work,the geometrically exact model(GEM)for a curved cantilevered pipe conveying pulsating fluid is developed based on the extended Hamilton's principle.The stability of the curved pipe with three different subtended angles is examined with the consideration of steady fluid flow.Specific attention is concentrated on the large-deformation resonance of circular pipes conveying pulsating fluid,which is often encountered in practical engineering.By constructing bifurcation diagrams,oscillating shapes,phase portraits,time traces,and Poincarémaps,the dynamic responses of the curved pipe under various system parameters are revealed.The mean flow velocity of the pulsating fluid is chosen to be either subcritical or supercritical.The numerical results show that the curved pipe conveying pulsating fluid can exhibit rich dynamical behaviors,including periodic and quasi-periodic motions.It is also found that the preferred instability type of a cantilevered curved pipe conveying steady fluid is mainly in the flutter of the second mode.For a moderate value of the mass ratio,however,a third-mode flutter may occur,which is quite different from that of a straight pipe system.

Target layer state estimation in multi-layer complex dynamical networks considering nonlinear node dynamics

In many engineering networks, only a part of target state variables are required to be estimated.On the other hand,multi-layer complex network exists widely in practical situations.In this paper, the state estimation of target state variables in multi-layer complex dynamical networks with nonlinear node dynamics is studied.A suitable functional state observer is constructed with the limited measurement.The parameters of the designed functional observer are obtained from the algebraic method and the stability of the functional observer is proven by the Lyapunov theorem.Some necessary conditions that need to be satisfied for the design of the functional state observer are obtained.Different from previous studies, in the multi-layer complex dynamical network with nonlinear node dynamics, the proposed method can estimate the state of target variables on some layers directly instead of estimating all the individual states.Thus, it can greatly reduce the placement of observers and computational cost.Numerical simulations with the three-layer complex dynamical network composed of three-dimensional nonlinear dynamical nodes are developed to verify the effectiveness of the method.

Dynamics and response reshaping of nonlinear predator-prey system undergoing random abrupt disturbances

An actual ecological predator-prey system often undergoes random environmental mutations owing to the impact of natural disasters and man-made destruction, which may destroy the balance between the species. In this paper,the stochastic dynamics of the nonlinear predator-prey system considering random environmental mutations is investigated, and a feedback control strategy is proposed to reshape the response of the predator-prey system against random abrupt environmental mutations. A delayed Markov jump system(MJS) is established to model such a predator-prey system. A novel first integral is constructed which leads to better approximation solutions of the ecosystem. Then, by applying the stochastic averaging method based on this novel first integral, the stochastic response of the predator-prey system is investigated, and an analytical feedback control is designed to reshape the response of the ecosystem from the disturbed state back to the undisturbed one.Numerical simulations finally illustrate the accuracy and effectiveness of the proposed procedure.

Finite Deformation, Finite Strain Nonlinear Dynamics and Dynamic Bifurcation in TVE Solids with Rheology

This paper presents a mathematical model consisting of conservation and balance laws (CBL) of classical continuum mechanics (CCM) and ordered rate constitutive theories in Lagrangian description derived using entropy inequality and the representation theorem for thermoviscoelastic solids (TVES) with rheology. The CBL and the constitutive theories take into account finite deformation and finite strain deformation physics and are based on contravariant deviatoric second Piola-Kirchhoff stress tensor and its work conjugate covariant Green’s strain tensor and their material derivatives of up to order m and n respectively. All published works on nonlinear dynamics of TVES with rheology are mostly based on phenomenological mathematical models. In rare instances, some aspects of CBL are used but are incorrectly altered to obtain mass, stiffness and damping matrices using space-time decoupled approaches. In the work presented in this paper, we show that this is not possible using CBL of CCM for TVES with rheology. Thus, the mathematical models used currently in the published works are not the correct description of the physics of nonlinear dynamics of TVES with rheology. The mathematical model used in the present work is strictly based on the CBL of CCM and is thermodynamically and mathematically consistent and the space-time coupled finite element methodology used in this work is unconditionally stable and provides solutions with desired accuracy and is ideally suited for nonlinear dynamics of TVES with memory. The work in this paper is the first presentation of a mathematical model strictly based on CBL of CCM and the solution of the mathematical model is obtained using unconditionally stable space-time coupled computational methodology that provides control over the errors in the evolution. Both space-time coupled and space-time decoupled finite element formulations are considered for obtaining solutions of the IVPs described by the mathematical model and are presented in the paper. Factors or the physics influencing dynamic response and dynamic bifurcation for TVES with rheology are identified and are also demonstrated through model problem studies. A simple model problem consisting of a rod (1D) of TVES material with memory fixed at one end and subjected to harmonic excitation at the other end is considered to study nonlinear dynamics of TVES with rheology, frequency response as well as dynamic bifurcation phenomenon.

Nonlinear fast–slow dynamics of a coupled fractional order hydropower generation system

Internal effects of the dynamic behaviors and nonlinear characteristics of a coupled fractional order hydropower generation system(HGS) are analyzed. A mathematical model of hydro-turbine governing system(HTGS) with rigid water hammer and hydro-turbine generator unit(HTGU) with fractional order damping forces are proposed. Based on Lagrange equations, a coupled fractional order HGS is established. Considering the dynamic transfer coefficient eis variational during the operation, introduced e as a periodic excitation into the HGS. The internal relationship of the dynamic behaviors between HTGS and HTGU is analyzed under different parameter values and fractional order. The results show obvious fast–slow dynamic behaviors in the HGS, causing corresponding vibration of the system, and some remarkable evolution phenomena take place with the changing of the periodic excitation parameter values.

New Systems Solution for Resolving Nonlinear Dynamics Based on Systems Thinking

This study describes a new solution for resolving nonlinear dynamics. Surprisingly, it has been resolved and completed by non-physicists on behalf of physicists in 2021. It is a revolutionary solution like the Copernican Theory, which is perfectly different from the existing chaos theory. In the past, nonlinear dynamics has been analyzed using logical solutions, such as chaos theory, based on logical thinking. However, it is not perfect systematic solution, hence;the new solution has been analyzed and resolved by systematic analytical tool in other sciences. Then, the result is more perfect and precise than the old chaos theory. Regrettably, most physicists do not welcome this advancement, because they have primitive solutions such as chaos theory. If the new solution is true, it is very disadvantageous to them like Galileo’s heliocentric theory. Therefore, they do not welcome it and deny and reject it. Hence, they wish it to fail;moreover, they want to remain in safe zone. Unfortunately, they became outsiders because they have no ability to review new solutions. Unfortunately, we have no obligation to follow physicists. If so, non-physicists, bypassing physicists, must study independently nonlinear dynamics based on systems thinking, and have to share the findings other scientists. It means that the new solution would be replaced the chaos theory in traditional physics;moreover, it would be resolved many unsolved nonlinear dynamics in the future.

Investigation on nonlinear rolling dynamics of amphibious vehicle under wind and wave load

Nonlinear amphibious vehicle rolling under regular waves and wind load is analyzed by a single degree of freedom system.Considering nonlinear damping and restoring moments,a nonlinear rolling dynamical equation of amphibious vehicle is established.The Hamiltonian function of the nonlinear rolling dynamical equation of amphibious vehicle indicate when subjected to joint action of periodic wave excitation and crosswind,the nonlinear rolling system degenerates into being asymmetric.The threshold value of excited moment of wave and wind is analyzed by the Melnikov method.Finally,the nonlinear rolling motion response and phase portrait were simulated by four order Runge-Kutta method at different excited moment parameters.

Nonlinear dynamics of axially moving viscoelastic Timoshenko beam under parametric and external excitations

This investigation focuses on the nonlinear dynamic behaviors in the trans- verse vibration of an axiMly accelerating viscoelastic Timoshenko beam with the external harmonic excitation. The parametric excitation is caused by the harmonic fluctuations of the axial moving speed. An integro-partial-differential equation governing the transverse vibration of the Timoshenko beam is established. Many factors are considered, such as viscoelasticity, the finite axial support rigidity, and the longitudinally varying tension due to the axial acceleration. With the Galerkin truncation method, a set of nonlinear ordinary differential equations are derived by discretizing the governing equation. Based on the numerical solutions, the bifurcation diagrams are presented to study the effect of the external transverse excitation. Moreover, the frequencies of the two excitations are assumed to be multiple. Further, five different tools, including the time history, the Poincaré map, and the sensitivity to initial conditions, are used to identify the motion form of the nonlinear vibration. Numerical results also show the characteristics of the quasiperiodic motion of the translating Timoshenko beam under an incommensurable re- lationship between the dual-frequency excitations.

NONLINEAR DYNAMIC CHARACTERISTICS OF HYDRODYNAMIC JOURNAL BEARING-FLEXIBLE ROTOR SYSTEM

The nonlinear dynamic behaviors of flexible rotor system with hydrodynamicbearing supports are analyzed. The shaft is modeled by using the finite element method that takesthe effect of inertia and shear into consideration. According to the nonlinearity of thehydrodynamic journal bearing-flexible rotor system, a modified modal synthesis technique withfree-interface is represented to reduce degrees-of-freedom of model of the flexible rotor system.According to physical character of oil film, variational constrain approach is introduced tocontinuously revise the variational form of Reynolds equation at every step of dynamic integrationand iteration. Fluid lubrication problem with Reynolds boundary is solved by the isoparametricfinite element method without the increasing of computing efforts. Nonlinear oil film forces andtheir Jacobians are simultaneously calculated and their compatible accuracy is obtained. Theperiodic motions are obtained by using the Poincare -Newton-Floquet (PNF) method. A method,combining the predictor-corrector mechanism to the PNF method, is presented to calculate thebifurcation point of periodic motions to be subject to change of system parameters. The localstability and bifurcation behaviors of periodic motions are obtained by Floquet theory. The chaoticmotions of the bearing-rotor system are investigated by power spectrum. The numerical examples showthat the scheme of this study saves computing efforts but also is of good precision.

CONTROLLING EROSION OF SAFE BASIN IN NONLINEAR PARAMETRICALLY EXCITED SYSTEMS

This paper considers the dynamical behavior of a Duffing-Mathieu type system with a cubic single-well potential during the principal parametric resonance. Both the cases of constant and time-dependent excitation amplitude are used to observe the variation of the extent and the rate of the erosion in safe basins. It is evident that the appearance of fractal basin boundaries heralds the onset of the losing of structural integrity. The minimum value of control parameter to prevent the basin from erosion is given along with the excitation amplitude varying. The results show the time-dependence of excitation amplitude can be used to control the extent and the rate of the erosion and delay the first occurrence of heteroclinic tangency.

Nonlinear Dynamics and Stability of Neural Networks with Delay-Time

In this paper we study the dynamic properties and stabilities of neural networks with delay-time (which includes the time-varying case) by differential inequalities and Lyapunov function approaches. The criteria of connective stability, robust stability, Lyapunov stability, asymptotic atability, exponential stability and Lagrange stability of neural networks with delay-time are established, and the results obtained are very useful for the design, implementation and application of adaptive learning neural networks.

Particle filter for nonlinear systems with multi-sensor asynchronous random delays

This paper is concerned with the recursive filtering problem for a class of discrete-time nonlinear stochastic systems in the presence of multi-sensor measurement delay. The delay occurs in a multi-step and asynchronous manner, and the delay probability of each sensor is assumed to be known or unknown. Firstly, a new model is constructed to describe the measurement process, based on which a new particle filter is developed with the ability to fuse multi-sensor information in the case of known delay probability.In addition, an online delay probability estimation module is introduced in the particle filtering framework, which leads to another new filter that can be implemented without the prior knowledge of delay probability. More importantly, since there is no complex iterative operation, the resulting filter can be implemented recursively and is suitable for many real-time applications. Simulation results show the effectiveness of the proposed filters.

Analysis and Application of Multiple-Precision Computation and Round-off Error for Nonlinear Dynamical Systems

This research reveals the dependency of floating point computation in nonlinear dynamical systems on machine precision and step-size by applying a multiple-precision approach in the Lorenz nonlinear equations. The paper also demoastrates the procedures for obtaining a real numerical solution in the Lorenz system with long-time integration and a new multiple-precision-based approach used to identify the maximum effective computation time （MECT） and optimal step-size （OS）. In addition, the authors introduce how to analyze round-off error in a long-time integration in some typical cases of nonlinear systems and present its approximate estimate expression.

Evaluation on Stability of Stope Structure Based on Nonlinear Dynamics of Coupling Artificial Neural Network

The nonlinear dynamical behaviors of artificial neural network (ANN) and their application to science and engineering were summarized. The mechanism of two kinds of dynamical processes, i.e. weight dynamics and activation dynamics in neural networks, and the stability of computing in structural analysis and design were stated briefly. It was successfully applied to nonlinear neural network to evaluate the stability of underground stope structure in a gold mine. With the application of BP network, it is proven that the neuro-com- puting is a practical and advanced tool for solving large-scale underground rock engineering problems.

NONLINEAR DYNAMICS OF LATERAL MICRO-RESONATOR INCLUDING VISCOUS AIR DAMPING

The nonlinear dynamics of the lateral micro-resonator including the air damping effect is researched. The air damping force is varied periodically during the resonator oscillating, and the air damp coefficient can not be fixed as a constant. Therefore the linear dynamic analysis which used the constant air damping coefficient can not describe the actual dynamic characteristics of the mi-cro-resonator. The nonlinear dynamic model including the air damping force is established. On the base of Navier-Stokes equation and nonlinear dynamical equation, a coupled fluid-solid numerical simulation method is developed and demonstrates that damping force is a vital factor in micro-comb structures. Compared with existing experimental result, the nonlinear numerical value has quite good agreement with it. The differences of the amplitudes （peak） between the experimental data and the results by the linear model and the nonlinear model are 74.5% and 6% respectively. Nonlinear nu-merical value is more exact than linear value and the method can be applied in other mi-cro-electro-mechanical systeme （MEMS） structures to simulate the dynamic performance.

Low-speed instability analysis for hydraulic motor based on nonlinear dynamics

A nonlinear dynamics model and a mathematical expression were set up to investigatethe mechanism and conditions of vibration creep acceleration.The model showsthat hydraulic spring and nonlinear friction are major factors that can affect low-speed instability.The mathematic model was established to obtain the change rule of speed andinstantaneous acceleration of the hydraulic motor.Then, Matlab was used to simulate theeffect of nonlinear friction force and hydraulic motor parameters such as coefficient of leakand compression ratio, etc., under low speed.Finally, some measures were proposed toimprove the low-speed stability of the hydraulic motor.

Analysis of nonlinear dynamic character in the surrounding rock system for deep buried underground engineering

Combining the field monitoring results of a deep-buried tunnel in Chongqing,the dynamic characteristics of the surrounding rock system under high in situ stress wasanalyzed by phase space reconstruction, calculating correlation dimension, Kolmogoroventropy and largest Lyapunov exponents.Both the Kolmogorov entropy and largestLyapunov exponents show that the surrounding rock system is a chaotic one.Based onthis, a local model was applied to predict surrounding rock displacement, and a nonlineardynamic model was derived to forecast the interaction of the surrounding rock and supportstructure.The local method was found to have an extremely small total error.Also, thenonlinear dynamic model forecasting curves agree with the monitoring ones very well.It isproved that the nonlinear dynamic characteristic study is very important in analyzing rockstability and predicting the evolution of rock systems.

A Fuzzy-Neural Network Control of Nonlinear Dynamic Systems

In this paper, an adaptive dynamic control scheme based on a fuzzy neural network is presented, that presents utilizes both feed-forward and feedback controller elements. The former of the two elements comprises a neural network with both identification and control role, and the latter is a fuzzy neural algorithm, which is introduced to provide additional control enhancement. The feedforward controller provides only coarse control, whereas the feedback controller can generate on-line conditional proposition rule automatically to improve the overall control action. These properties make the design very versatile and applicable to a range of industrial applications.