Subjects -> AERONAUTICS AND SPACE FLIGHT (Total: 124 journals)
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 Nonlinear DynamicsJournal Prestige (SJR): 1.468 Citation Impact (citeScore): 4Number of Followers: 22      Hybrid journal (It can contain Open Access articles) ISSN (Print) 1573-269X - ISSN (Online) 0924-090X Published by Springer-Verlag  [2467 journals]
• Exact solutions to the fractional complex Ginzburg–Landau equation with
time-dependent coefficients under quadratic–cubic and power law
nonlinearities

Abstract: Abstract In this paper, the fractional complex Ginzburg–Landau equation with time-dependent coefficients, which is used to depict diverse physical phenomena like superfluidity, superconductivity, Bose–Einstein condensation, second-order phase transitions, strings and liquid crystals, is investigated by three different methods under the circumstance of taking two forms of nonlinearity into account. A number of exact solutions are derived and fallen into different categories for the sake of discussing the dynamic behaviors of this equation further. More narrowly, we acquire the solitary, soliton and elliptic wave solutions through the unified method as well as the trigonometric, hyperbolic trigonometric and rational solutions through the improved F-expansion method in the sense of quadratic–cubic nonlinearity. And as another achievement, we obtain the bright, dark, combined bright–dark, singular soliton, mixed singular soliton and singular periodic wave solutions by employing the extended Sinh-Gordon equation expansion method under power law nonlinearity. Moreover, we draw the 2D, 3D and contour images for some of these solutions with fit choices of parameters to realize the propagations of waves more visually and deeply, thereby uncovering more physical phenomena in connection with the governing model.
PubDate: 2023-03-01

• A generalized (2+1)-dimensional Hirota bilinear equation: integrability,
solitons and invariant solutions

Abstract: Abstract In this paper, we consider an extended form of generalized $$(2+1)$$ -dimensional Hirota bilinear equation which demonstrates nonlinear wave phenomena in shallow water, oceanography and nonlinear optics. We have successfully studied the integrability characteristic of the nonlinear equation in different aspects. We have applied the Painlevè analysis technique on the equation and found that it is not completely integrable in Painlevè sense. The concept of Bell polynomial form is introduced and the Hirota bilinear form, Bäcklund transformations are obtained. By means of Cole-Hopf transformation, we have derived the Lax pairs by direct linearization of coupled system of binary Bell polynomials. We have also derived infinite conservation laws from two field condition of the generalized $$(2+1)$$ -dimensional Hirota bilinear equation. We have exploited the expressions of one-soliton, two-soliton and three-soliton solutions directly from Hirota bilinear form and demonstrated them pictorially. Further, Lie symmetry approach is applied to analyze the Lie symmetries and vector fields of the considered problem. The symmetry reductions were then obtained using similarity variables and some closed-form solutions such as parabolic wave solutions and kink wave solutions are secured.
PubDate: 2023-03-01

• Command filtered dual backstepping variable structure robust switching
control of uncertain nonlinear system

Abstract: Abstract This paper presents the design and stability analysis of a dual backstepping variable structure robust controller based on command filter for a class of nonlinear system with bounded uncertain structure. First, a normal backstepping recursive design procedure is divided into two distinguished sub-backstepping recursive sequences according to different control objectives or tasks. Then, a set of the switching logic is introduced from the variable structure switching scheme to connect different sub-backstepping controllers. The switching logic function divides the whole process into saturation switching phase and linear transient phase. Meanwhile, command filters are employed to suppress the redouble explosion of the derivation terms from sequences. This mechanism is proposed to make up the shortcoming of chatting in variable structure switching and give more flexibility in designing feedback control law to protect the beneficial nonlinear characteristics. Furthermore, compared with the existing traditional single backstepping method, the developed method not only guarantees the uniform ultimately bounded of all the closed-loop system with uncertainty, but also improves the tracking performance. The steady output tracking error can be made arbitrarily small by choosing control parameters appropriately. Finally, the effectiveness and advantages of this mechanism are illustrated by a practical example.
PubDate: 2023-03-01

• New solitary wave solutions of a generalized BBM equation with distributed
delays

Abstract: Abstract Solitary wave solutions for a generalized Benjamin–Bona–Mahony equation with distributed delay and dissipative perturbation are considered in this paper. The corresponding traveling wave equation is transformed into a four-dimensional dynamical system, which is regarded as a singularly perturbed system for small time delay. The four-dimensional dynamical system is reduced to a near-Hamiltonian planar system via geometric singular perturbation method. The existence of solitary wave solutions with a single crest or trough is established by proving the persistence of homoclinic orbits of the near-Hamiltonian system. More importantly, a new type of solitary wave solution with coexisting crest and trough, which corresponds to a large concave homoclinic orbit, is observed theoretically by using Melnikov’s method. The selection principle for wave speed of the solitary wave is presented which can be utilized directly to determine the limit wave speed. Numerical simulations are in complete agreement with the theoretical predictions.
PubDate: 2023-03-01

• A model of binaural auditory nerve oscillator network for bearing fault
diagnosis by integrating two-channel vibration signals

Abstract: Abstract Rolling bearing plays an important role in rotary machines. In rotating machine fault diagnosis, two-channel signals that are recorded from bearing provide sufficient information. It is meaningful to integrate two-channel signals for improving the comprehensiveness and accuracy of status information extracted from the signals. Human auditory nerve system can integrate the binaural information through the mechanism of neurons oscillation and delivery of oscillation. In view of the aspects mentioned above, to simulate the operating mechanism of human binaural auditory system, a double-layer auditory nerve oscillator network (DLNON) model, whose inputs are two-channel vibration signals, is proposed for features extraction and faults diagnosis. By this model, independent component analysis (ICA) is used at the first place to reduce the correlation and increase the independence between the signals; then, outputs of ICA are processed by short-time Fourier transform (STFT) and spectral envelop to reduce the complexity of frequency structure and highlight the formant informant of signal. After that, two results of time–frequency envelop are processed, respectively, by the first-layer oscillator network to obtain synchronous oscillatory period function (SOPF). Finally, information of two SOPFs and two time–frequency envelops is integrated by the second-layer oscillator network, so as to simulate auditory masking effect. The synchronous oscillatory feature function (SOFF) reflected the feature of two-channel signals is obtained by calculating the oscillatory result (SOPF) of the second oscillator network. The performance of DLNON model is evaluated by experiments. The results show that this model can effectively extract fault features, and distinguish fault types, fault severity ratings.
PubDate: 2023-03-01

• Efficient and integration stable nonlinear model predictive controller for
autonomous vehicles based on the stabilized explicit integration method

Abstract: Abstract There has been a growing interest in nonlinear model predictive control (NMPC) for the motion control of autonomous driving. However, it is odd that integration stability has not been considered enough when developing these applications for autonomous driving, which results in inefficient performance of NMPC-based motion controllers. The stabilized explicit Runge–Kutta (RK) integration method is adopted in this paper to solve the integration stability problem in motion control of autonomous vehicles (AVs). In comparison with other explicit integration methods, this method provides a wider stable region and is more efficient than implicit integration methods. This integration method is integrated into the framework of offset free nonlinear model predictive control (OF-NMPC) solver based on gradient-based MPC (GRAMPC) by us. As a result, the problem of computational stability at low speeds of motion control can be resolved. And, a larger integration step size can be adopted, NMPC becomes more computationally efficient. The results of simulation and real vehicle experiment show that the problem of low-speed integration stability when using nonlinear dynamic model as a prediction model is successfully solved. At the same time, since the offset free NMPC is adopted, the longitudinal and lateral steady-state errors are eliminated.
PubDate: 2023-03-01

• Stochastic investigation of the input uncertainty effects on the dynamic
responses of constrained pipelines conveying fluids

Abstract: Abstract The dynamic response of a cantilevered pipe conveying fluid is investigated when several input parameters of the system are introduced to uncertainty. After the nonlinear equations of motions are derived, five input parameters are subject to a $$\pm \,5\%$$ uncertainty with a uniform distribution. First, a parametric study is performed by varying each parameter individually. Then, the Pearson correlation coefficients are calculated and discussed before a full Monte Carlo simulation is performed, and the histograms of results are investigated. It is evident that the outer diameter of the pipe has the largest effect on the maximum displacement of the pipe in the post-flutter regime. Chaotic behavior is exhibited when motion-limiting constraints are present in the system, so the system is tested with motion-limiting constraints as well. Monte Carlo simulation is performed, and bivariate diagrams are plotted to investigate how uncertainty affects the maximum displacement and periodicity of the oscillations together. Again, the outer diameter of the pipe is seen to be the most sensitive parameter to uncertainty when motion-limiting constraints are present. However, the parameters besides the outer diameter exhibit more sensitivity at high flow speeds. The results indicate that it is necessary to control the uncertainty introduced in the outer diameter to achieve expected dynamical responses at low flow speeds, but the uncertainty in all parameters must be controlled at higher flow speeds when motion-limiting constraints are present to achieve the expected behavior and chaotic responses.
PubDate: 2023-03-01

• Dynamical analysis of a fractional discrete-time vocal system

Abstract: Abstract The study in this article aims at investigating the chaotic behavior of the 2-D vocal dynamical system using commensurate and incommensurate fractional order Caputo difference operator. Dynamics of the discrete fractional order 2-D vocal dynamical system is analysed with bifurcation, Lyapunov exponents and coexisting attractors. Stability analysis for both commensurate and incommensurate order of the model is performed at unique fixed point supported with numerical calculation and simulations. The importance of constructing real-life models with incommensurate order models is illustrated by means of bifurcation diagrams and phase plane diagrams. The article focuses on analysis of change in the behaviour of the system dynamics under the influence of fractional order of the system, thereby showcasing the advantages of employing discrete fractional operators towards modelling. Article also portrays the transition that occurs on the vibration of the tissues in vocal fold in comparison with obtained theoretical mathematical and numerical results.
PubDate: 2023-03-01

• Nonlinear torsional vibration analysis of shearer semi-direct drive
cutting transmission system subjected to multi-frequency load excitation

Abstract: Abstract The cutting transmission system is always subjected to multi-frequency load excitation due to the complicated working conditions of shearer. Under this condition, the multi-frequency load excitation not only affects the torsional vibration response of the transmission system, but also induces various resonance cases. Thus, the oversimplification of excitation may lead to large errors in the dynamic response of the transmission system and further result in the inaccuracy of the torsional vibration analysis. According to the Lagrange principle, a simplified two-inertia electromechanical coupling torsional vibration model for the rotor system is established considering the electromagnetic excitation as well as the multi-frequency load excitation. Then, the resonance response of the rotor system is solved by the multiple scales method, and a parametric study is conducted to reveal the effects of electromagnetic excitation and load excitation on the amplitude–frequency response, respectively. In addition, other possible resonance cases (combination resonance and combination subharmonic resonance) are also discussed in this research. Finally, by utilizing the Runge–Kutta method, the numerical simulation is carried out to verify the validity of the analytical solutions and the reliability of the proposed dynamic model. The results indicate that the presence of the multi-frequency load excitation introduces the interaction between various harmonic excitations, which significantly change the vibration behaviors of shearer semi-direct drive cutting transmission system.
PubDate: 2023-03-01

• Bifurcation behaviors and bursting regimes of a piezoelectric buckled beam
harvester under fast–slow excitation

Abstract: Abstract In this manuscript, considering a piezoelectric buckled beam system under fast–slow excitation, the energy harvesting with bursting regimes is discussed analytically and numerically. For the fast sub-system, the averaging process with the generalized harmonic balancing method shows that pitchfork bifurcations will result in small amplitude buckled configurations and large-amplitude configuration centering around the trivial branch. Meanwhile, folds of cycle initiate additional coexisting branches. The structures of the numerical bifurcation diagram are consistent with the analytical results. Moreover, when the amplitude of the fast excitation is relatively large, long-term chaotic transients can be observed. Considering two cases of low-frequency excitation, i.e., the quasi-static one and non-static one, the corresponding bursting patterns are discussed. For the quasi-static case, the fast–slow analysis shows that the fractal basin of the fast sub-system evokes the snap-through transition of the fast–slow flow. Particularly, when the fast sub-system possesses strong transients, the fast–slow flow presents distinct long-term snap-through behaviors. While for the non-static case, the motions of the fast–slow flow are totally dominated by the transient effects. Analysis about the averaged output power shows that introducing the low-frequency excitation to the buckled beam harvester can help broadening the output bandwidth. Moreover, when the transient effects of the fast sub-system are relatively weak, the non-static slow excitation always provides better output performance. However, if the fast sub-system possesses strong transients, there exists a band within which the quasi-static slow excitation provides higher output power.
PubDate: 2023-03-01

• A hybrid averaging and harmonic balance method for weakly nonlinear
asymmetric resonators

Abstract: Abstract Models for nonlinear vibrations commonly employ polynomial terms that arise from series expansions about an equilibrium point. The analysis of symmetric systems with cubic stiffness terms is very common, and the inclusion of asymmetric quadratic terms is known to modify the effective cubic nonlinearity in weakly nonlinear systems. When using low (second, in this case)-order perturbation methods, the net effect in these cases is found to be a monotonic dependence of the free vibration frequency on the amplitude squared, with a single term that depends on the coefficients of the quadratic and cubic terms. However, in many applications, such a monotonic dependence is not observed, necessitating the use of techniques for strongly nonlinear systems, or the inclusion of higher-order terms and perturbation methods in weakly nonlinear formulations. In either case, the analysis involves very tedious and/or numerical approaches for determining the system response. In the present work, we propose a method that is a hybrid of the methods of averaging and harmonic balance, which provides, with relatively straightforward calculations, good approximations for the free and forced vibration response of weakly nonlinear asymmetric systems. For free vibration, it captures the correct amplitude–frequency dependence, including cases of non-monoticity. The method can also be used to determine the steady-state response of damped, harmonically driven vibrations, including information about stability. The method is described, and general results are obtained for an asymmetric system with up to quintic nonlinear terms. The results are applied to a numerical example and validated using simulations. This approach will be useful for analyzing a variety of system models with polynomial nonlinearities.
PubDate: 2023-03-01

• Robust $$H_{\infty }$$ impulsive control for time-varying delays
descriptor jump systems based on impulse instants correlative L–K
functional

Abstract: Abstract This paper deals with the problem of robust $$H_{\infty }$$ impulsive control for time-varying delays descriptor Markovian jump systems based on impulse instants correlative Lyapunov–Krasovskii functional. By exploiting singular value decomposition technique and matrix transformation method, a desired impulsive feedback controller is designed, which not only ensures the stochastic admissibility of time-varying delays descriptor jump system, but also meets the $$H_{\infty }$$ performance index. An improved impulse instants correlative Lyapunov–Krasovskii functional is utilized to obtain novel conditions of stochastic admissibility and realize impulsive feedback controller design, which are derived from a set of linear matrix inequalities. Finally, the validity of the results is illustrated by a numerical example and a reservoir fish culture model.
PubDate: 2023-03-01

• A novel linear uncertainty propagation method for nonlinear dynamics with
interval process

Abstract: Abstract Interval process is a preferable model for time-varying uncertainty propagation of dynamic systems when only the range of uncertainties can be obtained. However, for nonlinear systems, except for Monte Carlo (MC) simulation, there are still few efficient uncertainty propagation methods under the interval process model. This paper develops a non-intrusive and semi-analytical uncertainty propagation method, named the “convex model linearization method (CMLM),” by constructing a linearization formulation of a nonlinear system in a non-probabilistic sense. First, the criterion to evaluate the difference between the original system and the linearization formulation is derived, represented by the discrepancy of middle point, radius and correlations of response. By minimizing these three parameters, the coefficients of linear equations will be optimized to obtain the linearization formulation of the original system. Then, analytical equations are built to calculate uncertainty response under the interval process, without time-consuming analysis of the original system. To further improve the efficiency of the linearization process, Chebyshev polynomial is introduced to approximate the nonlinear dynamic analysis. Two numerical examples of duffing oscillators and vehicle rides are set to test the proposed CMLM. Compared to the MC method, with comparable uncertainty response precision, the CMLM just needs 1–10% times of dynamic analyses of the nonlinear system. Furthermore, a practical launch vehicle ascent trajectory problem with black-box dynamics is solved by, respectively, the CMLM and MC method. The results verify the capacity of the CMLM to deal with black-box problems and show that the CMLM performs better in terms of accuracy, efficiency and robustness.
PubDate: 2023-03-01

• The bounded sets, Hamilton energy, and competitive modes for the chaotic
plasma system

Abstract: Abstract This paper estimates a new ultimate bound set (UBS) for the chaotic system caused by the interaction of the whistler and ion-acoustic waves with the plasma oscillation. The intrinsic Hamilton energy is estimated by using the Helmholtz theorem, and this kind of energy function is the most suitable Lyapunov function to discern its dynamic stability. It is found that the Hamilton energy is relative to the firing states of the dynamical system. In a stable state, the energy is also a constant, while a chaotic state is resulting from an oscillation in the energy. We use the Lagrange coefficient method to solve an optimization problem analytically so that we can find an accurate UBS for the plasma chaotic system. Further, we present the competitive modes (CMs) for the plasma system to investigate its different dynamical behaviors for different parameters. Simulation results for CMs confirm the theories presented about the Hamilton energy function and UBS.
PubDate: 2023-03-01

• Analysis of dynamic properties of carbon emission–carbon absorption
model with time delay based on China

Abstract: Abstract Since the proposal of China’s double carbon goal, it has attracted wide attention from all walks of life. In order to study the impact of energy, economy and the time it takes for carbon dioxide released into the atmosphere to be completely absorbed on China’s future carbon emission and carbon absorption trend, and to provide estimates and suggestions for China’s carbon neutrality in future, we establish a carbon emission–carbon absorption model with time delay. First, we calculate the equilibrium of the model and analyze the stability of the equilibrium and then further analyze the existence of the Hopf bifurcation of the equilibrium, the Hopf bifurcation normal form of the model is derived by using the multiple time scales method, and the Hopf bifurcation direction and the stability of the bifurcation periodic solution are determined. Finally, we fit and analyze the official data, give the actual model parameters and use MATLAB to carry out numerical simulations to verify the correctness of the theoretical analysis. We find that numerically periodic solutions exist in a wide range around time delay. According to our model, the final results show that China will reach the carbon peak in 2027, but according to the current development model and carbon absorption level of China, carbon neutrality cannot be achieved before 2060. In this regard, we put forward relevant policies and suggestions to accelerate the realization of carbon neutrality.
PubDate: 2023-03-01

• Dynamics and manipulation of Airy beam in fractional system with
diffraction modulation and PT-symmetric potential

Abstract: Abstract We investigate the dynamics and manipulation of finite energy Airy (FEA) beam in fractional system with diffraction modulation and PT-symmetric potential. In the absence of PT-symmetric potential, we first present the approximate analytical solution of chirp-free FEA beam. Based on the analytical solution, we investigate analytically and numerically the split and collision of chirp-free FEA beam under diffraction modulation, and discuss the possibility of inverse design of diffraction modulation according to the predefined trajectory. Furthermore, through coherent combining technique, we derive the analytical solution of chirped FEA beam, and investigate analytically and numerically the asymmetric evolutions of chirped FEA beam in real space and spectral space, and discuss qualitatively the relation between the asymmetry and the chirp parameter. In the presence of PT-symmetric potential, we derive a general eigenvalue equation dependent on diffraction modulation and present the band structure modulated by varying fractional diffraction. Based on the band structure modulated by varying fractional diffraction, we study numerically the asymmetric conical evolution of chirp-free FEA beam under diffraction modulation, which demonstrates that the propagation channels of FEA beam can be jointly manipulated by diffraction modulation and PT-symmetric potential. For chirped FEA beam, the competition effect between the chirp and the PT-symmetric potential on the beam dynamics is explored in detail.
PubDate: 2023-03-01

• Autapse-induced logical resonance in the FitzHugh–Nagumo neuron

Abstract: Abstract It was demonstrated that the chaos-driven FitzHugh–Nagumo (FHN) neuron can be considered as a logic system to implement the reliable logical operations through the mechanism of logical resonance. Autapse (meaning the self-synapse) widely exists in various kinds of neurons, and it significantly affects the neuronal dynamics and functionalities. However, the effects of autapse on logical resonance have not been reported yet. Here, we explore the effects of autapse on the reliability of AND & NAND logical operations based on the autaptic FHN neuron model with time-varying coupling intensity. The numerical results demonstrate that there are the optimal ranges of parameters (including autaptic time delay, amplitude, frequency and phase fluctuation of autaptic coupling intensity) at which the reliability of logical operations can be maximized. Namely, autapse-induced logical resonance can be realized in the autaptic FHN neuron model. More interestingly, multiple logical resonances can be obtained by regulating autaptic time delay, phase fluctuation of autaptic coupling intensity, as well as frequency ratio between and autaptic coupling intensity and external periodic driving force. Finally, an intuitive interpretation for autapse-induced logical resonance is given based on the motion of the particle in the potential landscape.
PubDate: 2023-03-01

• Novel bright-dark mixed $$\textit{N}$$ -soliton for the ( $$3+1$$
)-component Mel’nikov system and its multi-component generalization

Abstract: Abstract Based on the KP-hierarchy reductionmethod, we construct the novel bright-dark mixed N-soliton for the ( $$3+1$$ )-component Mel’nikov system including 3-component short waves (SWs) and one-component long wave (LW) for all possible combinations of nonlinearity coefficients. It is verified that dark or bright solitons can exist in the SW components, but only bright solitons appear in the LW component. According to different combinations of solitons in three different SW components, the bright-dark mixed N-soliton for the ( $$3+1$$ )-component Mel’nikov system is mainly discussed into two types that two-bright-one-dark and one-bright-two-dark solitons. Finally, the ( $$3+1$$ )-component Mel’nikov system can be directly extended to ( $$M+1$$ )-component ( $$M\ge 3$$ ) case comprised of M-component SWs and one-component LW, and the bright-dark mixed N-soliton for the multi-component generalization is also given in Gram determinant form.
PubDate: 2023-03-01

• Dynamic modelling and analysis of cracked gear system with tip relief
based on proposed variable-angle deformation energy integration method

Abstract: Abstract Due to ignoring the effects of the change of the tooth attachment position caused by the cracks, traditional time vary mesh stiffness (TVMS) calculation models and dynamic simulations for cracked gears will lose their precision in the body crack case. To address this shortcoming, a new analytical TVMS calculation model of cracked gear considering tip relief (TR) is developed based on a proposed variable-angle deformation energy integration method. On this basis, a dynamic model of the gear system for the analysis of fault vibration characteristics is established. The effectiveness and accuracy of the proposed TVMS calculation model are verified by the finite element method. A comprehensive investigation is finally carried out to reveal the effects of the parameters of TR, load and crack on the TVMS and dynamic characteristics of the cracked gears. The study results indicate that the proposed models can meet the accurate TVMS calculation and dynamic simulation for both the tooth- and body-cracked gears, and the influences of the tooth attachment position change caused by the crack cannot be ignored. This study could provide a systematic methodology and meaningful reference for the dynamic modelling, simulation and fault diagnosis of gear systems with crack failures.
PubDate: 2023-03-01

• New criteria for asymptotic stability of a class of nonlinear real-order
time-delay systems

Abstract: Abstract This paper investigates the asymptotic stability of a new class of nonlinear time-varying real-order systems that involve multiple delays. First, we introduce a comparison principle and a new lemma that give an estimation for the bounds between the solutions to any two relative systems. Then, by using the inequalities and comparison methodology, we develop some new mathematical results for the asymptotic stability analysis of the zero solution to such a class of systems. We establish new fractional-order-dependent and delay-dependent, and fractional-order-dependent and delay-independent conditions for the analysis of such a class of systems. At the end, we present three examples and demonstrate that some established criteria are very effective for the analysis and control of such systems.
PubDate: 2023-03-01

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