Nonlinear Dynamic Characteristics Research Articles

Dynamics of bistable composite plates

Nonlinear asymmetric bi-stable composite laminates, characterized by multistable nature and rich dynamics, have seen increased application potential recently. This has necessitated a detailed dynamical analysis of bistable laminates. In this manuscript, the nonlinear behaviour of asymmetric [0n/90n] bistable laminates with free–free boundary conditions is investigated through simulations and experimental observations. A refined 17 degrees of freedom (dofs) analytical model is developed, fusing Raleigh–Ritz with Hamilton’s principle to obtain the governing nonlinear equations of motion. A nonlinear finite element (FE) model is also developed using ABAQUS®. Experiments are conducted by clamping the midpoint of the plate with a shaker and then exciting it. The composite laminate shows many intricate dynamics, such as sub-harmonic and super-harmonic oscillations, intra-well oscillation (periodic and chaotic), and inter-well snap-through (periodic and chaotic snap-through) prominently. The primary focus of this paper is to highlight the potential of bistable laminates by elucidating the existence of large-amplitude vibrations over a broad frequency range under different input and system parameters. Further, it has been observed that attached mass plays a significant role in modifying the response bandwidth for cross-well oscillation for a given excitation frequency and amplitude. Hence fine-tuning of masses can excite different nonlinear dynamic characteristics of the laminate, making it applicable in different engineering fields.

Nonlinear dynamic wave characteristics of optical soliton solutions in ion-acoustic wave

Traveling wave solutions are utilized to depict reaction-diffusion and analyze electrical signal transmission and propagation in space-time nonlinear fractional order partial differential equations like the space-time fractional Telegraph and Kolmogorov-Petrovsky Piskunov equations, and that are used in physical science to model combustion, biological research to model nerve impulse propagation, chemical dynamics to model concentration in order wave propagation, and plasma to model the progression of a set of duffing oscillators. In this study, the new generalized (G′/G)−expansion technique was employed to construct some novel and more universal closed-form traveling wave solutions in the sense of conformable derivatives which explain the above-stated phenomena properly. By utilizing complex fractional transformation, the ordinary differential equations are generated from fractional order differential equations. The recommended technique allowed us to produce some dynamical wave patterns of kink, single soliton, compacton, periodic shape, multiple periodic waves, anti-kink, and other structures are developed, which are shown using 3D plots and contour plots to illustrate the physical layout clearly. The traveling waveform responses can be defined in terms of functions based on trigonometry, hyperbolic operations, and rational functions and that are quick, flexible, and simple to reproduce. Furthermore, the obtained closed-form solutions for nonlinear fractional evolution equations make stability analysis and accuracy comparison amongst numerical solvers easier, which asserts that the new generalized (G′/G)−expansion technique is one of the most proficient and effective approaches.

Analysis of Non-Linear Dynamic Characteristics of Fuzzy-Based SRM Drive for Electric Vehicle Applications

Analysis of Non-Linear Dynamic Characteristics of Fuzzy-Based SRM Drive for Electric Vehicle Applications

Nonlinear dynamic characteristics of the multistable wake-galloping energy harvester

Nonlinear dynamic characteristics of the multistable wake-galloping energy harvester

A Concise 4D Conservative Chaotic System with Wide Parameter Range, Offset Boosting Behavior and High Initial Sensitivity

In this paper, we present a concise four-dimensional (4D) conservative chaotic system with a wide parameter range. Since there are no terms higher than first order, the circuit does not contain multipliers, resulting in a simple circuit implementation. The nonlinear dynamic characteristics, such as phase diagrams, equilibrium points, divergence, Poincaré cross-sections, Lyapunov exponents, bifurcation diagrams, and Lyapunov dimension, are analyzed in detail, which illustrates the conservativity. Besides, the system exhibits different offset boosting behaviors. Through offset boosting, the system can propagate along a line, convert signal polarity, control variable amplitude, generate coexisting attractors, and even induce changes in its state. Specially, we realize the transition from a single-vortex attractor to a multivortex one by some changes in the initial values. Furthermore, the Pearson correlation coefficient is used to demonstrate the higher initial value sensitivity of the system. Finally, the system is implemented through Multisim simulation and analog circuit separately, and their consistency validates the system effectively.

High‐Dissolution Mechanism of Ti–48Al–2Cr–2Nb Alloy in Electrochemical Machining from a Nonlinear Dynamic Perspective

High‐rate dissolution process of Ti–48Al–2Cr–2Nb alloy in electrochemical machining exhibits strong nonlinear dynamic characteristics, but the quantitative relationship between these nonlinear characteristics and surface topography, as well as the electro‐dissolution mechanism, is unknown. Therefore, the fractal and recursive features of dissolution behavior and quantitative characterization of the dissolved surface topography were investigated. Additionally, an electro‐dissolution mechanism model in electrochemical machining process was presented. Applying a higher potential of 11 V can enhance the stability of the electrochemical system, resulting in a smoother and uniform surface. The saturation correlation dimension, surface roughness, and integral area of lacunarity initially decrease before increasing with higher electrolytic pressure, while laminarity and determinism show an initial increase followed by a decrease. These five characteristic parameters reach their optimal values at an electrolyte pressure of 0.4 MPa, indicating that achieving a stable and deterministic electrochemical system is crucial for obtaining a uniform smooth surface. These nonlinear dynamic characteristic parameters can be considered as in‐situ monitoring parameters for surface quality in ECM. The anodic dissolution process comprises three stages: initial passive film dissolution and breakdown, rapid dissolving with surface coarsening, and stable dissolving with polishing.

Nonlinear dynamic characteristics of mechatronics integrated planetary gears considering wear and temperature effects

The electromechanical planetary gear system has high work efficiency and long service life, but factors such as heat, wear, and electrical signals can affect the transmission performance of electromechanical planetary gears. This article comprehensively considers factors such as temperature, tooth surface wear, lubrication, current and voltage, damping ratio, etc. Based on the principle of thermal deformation, Archard wear model, and equivalent circuit principle, a dynamic model of electromechanical planetary gears is established. The existing literature has not comprehensively analyzed the effects of temperature, wear, and electrical signal changes on the nonlinear characteristics of electromechanical planetary gear systems. The results show that when the motor current is between 7 A and 18 A and the voltage is lower than the rated voltage, the system is in a stable state; as the temperature rises, the system tends to stabilize; the gear wear exceeds 30 μm, and the bifurcation characteristics of the system are more pronounced.

Offset-Free Koopman Model Predictive Control of Thermal Comfort Regulation for a Variable Refrigerant Flow-Dedicated Outdoor Air System-Combined System

Abstract Variable refrigerant flow (VRF) system has been an appealing solution of air conditioning for residential and commercial buildings, due to its flexibility and cost effectiveness, while lack of ventilation capability is a major drawback. Incorporation of dedicated outdoor air system (DOAS) is a typical practice. However, good coordination between DOAS and VRF is critical for achieving desired thermal comfort is challenging due to the possible complexity of mixed sensible and latent heat exchanges. In this paper, to handle the nonlinear dynamic characteristics of VRF-DOAS system, we propose an offset-free Koopman model predictive control (MPC) strategy for thermal comfort regulation, in which the MPC design is computationally more efficient due to the convex problem formulation and the use of reduced-order Koopman models, and the offset-free MPC structure enhances the robustness to model uncertainties and unmeasured disturbances. A control-oriented model is obtained by hybridizing the first-principle and data-driven modeling approach. The proposed controls strategy is evaluated with a Modelica simulation model of a VRF-DOAS system. A Dymola-Python cosimulation platform is developed via the functional mockup interface (FMI), for which the MPC algorithms are implemented in Python. Simulation results show significantly better performance of the offset-free Koopman MPC in thermal comfort regulation.

Blast resistance performance and failure modes of prestressed thin-walled aqueducts subjected to underwater contact explosion

To solve the problem of regional water resource shortage, water diversion projects have been built around the world. As an essential lifeline project, the prestressed aqueduct is commonly used in cross-regional water transfer and diversion projects. However, the prestressed aqueduct is inclined to damage and collapse under explosion loading due to its thin structure. The main purpose of this paper is to investigate the nonlinear dynamic performance and failure modes of the large prestressed U-shaped thin shell aqueduct to underwater contact explosion. The prestress application approach is validated by theoretical calculations. The reliability of the analysis method of underwater contact explosion for reinforced concrete structures is verified by the underwater contact explosion test. Damage cracking process and nonlinear dynamic response characteristics of prestressed aqueducts to the underwater contact explosion with different explosive weights are performed. Blast resistance performances of prestressed aqueducts are discussed in terms of the crack length, residual displacement, and prestressing force loss. The influence of prestress level on the damage modes of the prestressed aqueduct under the blast loading is discussed. The results indicate that thin-walled U-shaped structures are extremely vulnerable to localized damage from underwater contact explosions. The blast-resistance performance of the U-shaped thin shell aqueduct can be significantly improved by applying prestress.

Effect of Interstage Torsional Damping on Nonlinear Dynamic Characteristics of Two-Stage Planetary Gear System

Abstract This paper explores the influence of interstage torsional damping on the nonlinear dynamics of a two-stage planetary gear transmission system. A comprehensive nonlinear dynamic model is developed, incorporating interstage torsional damping, stiffness, time-varying meshing parameters, damping, and tooth side clearance. The nonlinear equations are derived and solved using the fourth-order Runge–Kutta method. The investigation reveals that the changes in torsional damping between stages significantly affect the nonlinear dynamic characteristics of the system, especially under load fluctuations. Bifurcation characteristics are analyzed using phase diagrams, Poincaré diagrams, time history diagrams, and frequency–domain spectrograms. The simulation results demonstrate that heightened torsional damping between stages distinctly affects the motion states across excitation frequencies. Notably, it mitigates the unstable motion state caused by high-frequency excitation when tooth side clearance is minimal.

Nonlinear dynamic modeling and analysis of the fluid-transporting cracked pipe using the hybrid semi-analytical and finite element method

The fatigue cracks may develop in the pipe systems due to long-term cyclic loading, which may cause catastrophic accidents. The finite element method (FEM) is usually adopted to simulate the stress singularity and breathing effect, resulting in expensive computational costs. Therefore, in this paper, an efficient hybrid semi-analytical and finite element (SA-FE) method is proposed to study the nonlinear dynamic characteristics of the fluid-transporting cracked pipe (FTCP) considering the breathing effect. Furthermore, the crack sensitivity parameters are obtained through bending-bending and bending-axial vibration analysis. For the SA-FE method, the semi-analytical method (SAM) and FEM are separately used to construct the dynamic models of the non-cracked and cracked regions, and the connection at the interface is performed by constraint equations. Subsequently, the validity of the modeling method is substantiated through both FEM and experimental tests. Finally, the effects of crack and fluid parameters on the dynamic characteristics of the FTCP are analyzed. The results indicate that changes in crack positions may trigger different-order mode switching, and continuous switching may occur between higher-order modes. In addition, the bending-bending and bending-axial coupling responses can effectively detect crack failures of the FTCP with varying levels of damage. The proposed model can offer valuable insights for fault diagnosis and health monitoring of FTCP.

On the aeroelastic bifurcation of a flexible panel subjected to cavity pressure and inviscid oblique shock

The aeroelasticity of a panel in the presence of a shock is a fundamental issue of great significance in the development of hypersonic vehicles. In practical engineering, cavity pressure emerges as a crucial factor that influences the nonlinear dynamical characteristics of the panel. This study focuses on the aeroelastic bifurcation of a flexible panel subjected to both cavity pressure and oblique shock. To this end, a computational method is devised, coupling a high-fidelity reduced-order model for unsteady aerodynamic loads with nonlinear structural equations. The solution is meticulously tracked by continuous calculations. The obtained results indicate that cavity pressure plays a pivotal role in determining the bifurcation and stability characteristics of the system. First, the system exhibits hysteresis behaviour in response to the ascending and descending dynamic pressures. The evolution of hysteresis behaviour originates from the phenomenon of cusp catastrophe. Second, variations in cavity pressure induce three types of bifurcation phenomena, exhibiting characteristics akin to supercritical Hopf bifurcation, subcritical Hopf bifurcation and saddle-node bifurcation of cycles. The system's response at the critical points of these bifurcations manifests as long-period asymptotic flutter or explosive flutter. Lastly, the evolution of the dynamical system among these three types of bifurcations is an important factor contributing to the discrepancies observed in certain research results. This study enhances the understanding of the nonlinear dynamical behaviour of panel aeroelasticity in complex practical environments and provides new explanations for the discrepancies observed in certain research results.

Nonlinear dynamics analysis of electromechanical planetary gear systems with temperature effects considered

PurposeThe electromechanical planetary transmission system has the advantages of high transmission power and fast running speed, which is one of the important development directions in the future. However, during the operation of the electromechanical planetary transmission system, friction and other factors will lead to an increase in gear temperature and thermal deformation, which will affect the transmission performance of the system, and it is of great significance to study the influence of the temperature effect on the nonlinear dynamics of the electromechanical planetary system.Design/methodology/approachThe effects of temperature change, motor speed, time-varying meshing stiffness, meshing damping ratio and error amplitude on the nonlinear dynamic characteristics of electromechanical planetary systems are studied by using bifurcation diagrams, time-domain diagrams, phase diagrams, Poincaré cross-sectional diagrams, spectra, etc.FindingsThe results show that when the temperature rise is less than 70 °C, the system will exhibit chaotic motion. When the motor speed is greater than 900r/min, the system enters a chaotic state. The changes in time-varying meshing stiffness, meshing damping ratio, and error amplitude will also make the system exhibit abundant bifurcation characteristics.Originality/valueBased on the principle of thermal deformation, taking into account the temperature effect and nonlinear parameters, including time-varying meshing stiffness and tooth side clearance as well as comprehensive errors, a dynamic model of the electromechanical planetary gear system was established.

Experimental Research on Dynamic Characteristics of a Multi-Disc Rotor System Supported by Aerostatic Bearings

Gas bearings have the advantages of small friction loss, wide applicable speed range, no pollution, etc., and have important application prospects in micro and small high-speed rotating machinery. However, due to its compressibility and low viscosity, its dynamic stability in high-speed rotating machinery is the key to constraining its development. The experimental study of shaft system dynamics is the main means to explore the mechanism of rotor behavior. On the test platform of dynamic characteristics of multi-disc rotor system supported by aerostatic bearings, experimental research on the nonlinear dynamic characteristics of a rotor system was carried out, and nonlinear vibration test and analysis methods, such as axial orbits, bifurcation diagrams, and spectral characteristics, were adopted, and vibration phenomena, including the critical rotational speed accumulating energy and low-frequency accumulating energy, were presented and the vibration characteristics of bearing fracture faults were presented. The bearing supply pressure and rubber damping pad were introduced as a method to suppress the low-frequency vibration of the aerostatic bearing rotor system, and its vibration-reduction effect was verified by experiments. The above results can provide technical support for vibration control and fault diagnosis of rotor systems supported by aerostatic bearings.

Nonlinear dynamic separation characteristics of friction pair and experimental analysis

This paper aims to reduce friction pair erosion of the clutch in the case of continuous shift; the dynamic separation process of the friction pair is investigated. The temperature of the friction pair, friction torque, and separation speed in the separation process are taken as the research objects, and the dynamics simulation model and finite element thermal coupling simulation model of the clutch separation process are established. The nonlinear dynamic separation characteristics of the friction pair are investigated by comparing and analyzing the effects of control parameters such as rotational speed difference, damping ratio, and lubricant viscosity on the friction torque, friction pair separation speed, separation gap, and contact stress during the separation process. The gap recovery coefficient is proposed as a response indicator for observing the separation process in response to the inability to observe the nonlinear dynamic motion of the friction pair during the separation process and to measure the end time of the separation. Finally, the clutch was subjected to a separation test. The results show that the proposed gap recovery coefficient accurately describes the separation process. The simulation model can simulate the clutch's separation and predict the trend of separation parameters.

On the nonlinear dynamic characteristics of forced acoustic oscillations in a heat-driven thermoacoustic engine

On the nonlinear dynamic characteristics of forced acoustic oscillations in a heat-driven thermoacoustic engine

Three soliton interactions and the implementation of their all optical switching function

Abstract As a key component in all optical networks, all optical switches play a role in constructing all optical switching. Due to the absence of photoelectric conversion, all optical networks can overcome the constraints of electronic bottlenecks, thereby improving communication speed and expanding their communication bandwidth. This paper is based on the interactions among three optical solitons to study all optical switches. By analytically solving the coupled nonlinear Schrödinger equation, the three soliton solution of the equation is obtained. We discuss the nonlinear dynamic characteristics of various optical solitons under different initial conditions. Meanwhile, we analyze the influence of relevant physical parameters on the realization of all optical switching function during the process of three soliton interactions. The relevant conclusions will be beneficial for expanding network bandwidth and reducing power consumption to meet the growing demand for bandwidth and traffic.

Dynamics of neuronal firing modulated by high-frequency electrical pulse stimulations at axons in rat hippocampus

Objective. The development of electrical pulse stimulations in brain, including deep brain stimulation, is promising for treating various brain diseases. However, the mechanisms of brain stimulations are not yet fully understood. Previous studies have shown that the commonly used high-frequency stimulation (HFS) can increase the firing of neurons and modulate the pattern of neuronal firing. Because the generation of neuronal firing in brain is a nonlinear process, investigating the characteristics of nonlinear dynamics induced by HFS could be helpful to reveal more mechanisms of brain stimulations. The aim of present study is to investigate the fractal properties in the neuronal firing generated by HFS. Approach. HFS pulse sequences with a constant frequency 100 Hz were applied in the afferent fiber tracts of rat hippocampal CA1 region. Unit spikes of both the pyramidal cells and the interneurons in the downstream area of stimulations were recorded. Two fractal indexes—the Fano factor and Hurst exponent were calculated to evaluate the changes of long-range temporal correlations (LRTCs), a typical characteristic of fractal process, in spike sequences of neuronal firing. Main results. Neuronal firing at both baseline and during HFS exhibited LRTCs over multiple time scales. In addition, the LRTCs significantly increased during HFS, which was confirmed by simulation data of both randomly shuffled sequences and surrogate sequences. Conclusion. The purely periodic stimulation of HFS pulses, a non-fractal process without LRTCs, can increase rather than decrease the LRTCs in neuronal firing. Significance. The finding provides new nonlinear mechanisms of brain stimulation and suggests that LRTCs could be a new biomarker to evaluate the nonlinear effects of HFS.

Motion Learning and Generalization of Musculoskeletal Robot Using Gain Primitives

Organisms have an innate ability to rapidly produce diverse and flexible movement. Biological motor systems are composed of highly redundant muscle actuators and have strongly nonlinear dynamic characteristics. How organisms cope with such complex system is still an open question. Motor primitive theory proposed by neuroscientists has provided a convincing explanation for this extraordinary ability and have supported by several biological evidence. In this paper, based on the gain primitive model of cortical network proposed by neuroscientists, new algorithms for learning and combining gain primitives were designed to control musculoskeletal and robotic system with highly redundant actuators. It can realize dimensionality reduction of controll from the number of actuators to the number of primitives. A parameter adaptation algorithm inspired by monoamines modulation mechanism was applied to improve the learning efficiency of gain primitive. Learned motion experiences and primitives were introduced to effectively generate new movements. Validation experiments were carried out on a musculoskeletal model with 9 muscles and an articulated robot Baxter with redundant actuators. The experimental results demonstrated that the recurrent neural network modulated by gain primitives can generate high-dimensional control signals and realize efficient motion generalization for practical systems. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper applied a biologically plausible control method with gain primitive to practical systems with highly redundant actuators. To reduce the cumulative error occurring in learning gain primitive for control networks with high dimensional output, a bioinspired Hebbian learning rule was applied to train a recurrent neural network for optimizing the gain primitive. During the training process, systematic entropy was introduced as an index to adaptively adjust learning parameters, so as to reduce the exploration cost and improve the learning stability of the system. To realize easy implementation and generalization, prior motion experiences were introduced into the initialization of the optimization algorithm, and motion generalization was realized by using the particle swarm optimization algorithm. The algorithms designed in this paper are applicable to complex systems with highly redundant actuators such as humanoid robots.

Effect of Turbulent Wind Conditions on the Dynamic Characteristics of a Herringbone Planetary Gear System of a Wind Turbine

Due to complex environmental factors, the gear transmission systems of wind turbines are continuously affected by large torque load excitation with periodic and random properties. This paper shares the load-sharing and dynamic characteristics of a herringbone planetary gear system applied in a wind turbine. The gear dynamic model is established using a typical lumped parameter method, in which the nonlinear transmission errors of the gear pairs and left and right-side coupling stiffness of the herringbone gears are included. With the help of the blade element momentum theory, the precise calculation of the hub load of the wind turbine, which is the external excitation of the gear system, is implemented, in which the wind shear, tower shadow, turbulent effect, and tip loss correction are taken into consideration. The nonlinear dynamic characteristics of the system are obtained using the Runge-Kutta method and then discussed. The results show that the turbulent effect plays a major role in the impact on the load-sharing characteristics, and a reasonable set of the support stiffness of rotational components can improve the load-sharing characteristics of the system. The purpose of this research is to provide some useful references in numerical modelling and methods for designers and researchers of wind turbine transmission systems.