Parametric Excitation Research Articles

Sliding bursting oscillations related to transcritical bifurcation delay in an excited vector field with frequency switching

The purpose of this paper is to report sliding bursting dynamics related to transcritical bifurcation delay, a common route to bursting dynamics. As an example, a simple nonlinear oscillator with a slow parametric excitation is considered, in which bursting oscillations resulted from transcritical bifurcation delay can be observed. Typically, such oscillations exhibit prolonged rest phases, characterized by the oscillations that moves along the unstable origin of the system. We show that interesting dynamical characteristics can be observed in the bursting oscillations if the excitation frequency switches between two different values. In particular, additional rest phases, i.e., the newly created non-zero sliding behaviors, characterized by that the trajectory slides along the frequency switching threshold for some time, can be exhibited in the presence of frequency switching. This forms the so-called sliding bursting oscillations. Then, we investigate the dynamical mechanisms of these oscillations and explore their transitions in relation to the variation of frequency switching threshold. As a result, several different patterns of sliding bursting oscillations are obtained. In particular, we find that sliding bursting oscillations may diverge to infinity for some threshold windows, and this can be understood by the analysis of attracting basins.

Principal-Internal Joint Resonance of an Axially Moving Beam with Elastic Constraints and Excited by Current-Carrying Wires

Principal-internal joint resonance of an axially moving beam with elastic constraints is investigated, where the beam is located in magnetic field excited by current-carrying wires. Based on the magnetoelasticity theory and Hamilton principle, the nonlinear magneto-elastic vibration equations are derived. The displacement function is obtained by the elastic constraint boundary condition, and then the equation is discretized into 2-DOF ordinary differential equations using the Galerkin integral method. The method of multiple scales is employed for obtaining the amplitude–frequency response equations with coupling of the first two vibration modes. Through examples, amplitudes varying with frequency tuning parameter, axial velocity, current intensity, and external excitation force are exhibited. Results indicate that as current intensity increases, electromagnetic damping increases and the amplitude decreases; As external excitation force increases and axial velocity decreases respectively, the amplitude increases and the system changes from single periodic motion to quasi-periodic motion and then to single periodic motion; The lower-order modes are always dominant when the principle-internal resonance occurs.

Analysis on Thermo-Electrical Principal Parametric Resonance of an Axially Moving Piezoelectric Thin Plate

In this paper, principal parametric resonance of an axially moving piezoelectric rectangular thin plate under thermal and electric field is investigated. Based on Kirchhoff–Love plate theory and Von Karman theory, the transverse vibration differential equation of a piezoelectric rectangular thin plate under thermal and electric field is derived by using Hamilton’s principle. The dimensionless vibration equation of piezoelectric rectangular thin plate with parametric excitations is discretized by Galerkin’s method. Then, the multiple scales method is applied to derive amplitude-frequency response equation and the stability conditions of the steady-state solution are obtained by Lyapunov stability theory. Numerical method is used to find the influences of specific parameters on the vibration performance and stability of the system. Based on the global bifurcation diagram and corresponding response diagram, the influences of bifurcation control parameters on the nonlinear dynamic characteristics of the system are discussed. Numerical results illustrate that the system amplitude frequency characteristic curve presents soft spring characteristics. There are periodic and chaotic motions with the increase of velocity and the central temperature difference, and the decrease of plate thickness and velocity will result in the decrease of chaotic threshold. The results also show that increase the velocity perturbation amplitude can prolong the chaotic motion.

Dynamic instability analysis of timoshenko FG sandwich nanobeams subjected to parametric excitation

According to the nonlocal theory, the dynamic instability and vibration of functionally graded (FG) porous sandwich nanobeams resting on a visco-elastic foundation under axial harmonic load are studied. In this paper the Timoshenko and nonlocal continuum theory are employed to take shear deformation, rotational bending and small-scale effects into account. The governing equations of motion are extracted using the nonlinear Von-Karman, and Hamilton approaches. Then, to turn the partial differential equations (PDEs) into ordinary differential equations (ODEs) in the case of equations of motion, the method of Galerkin is employed, followed by the use of the multiple time scale method to solve the resulting equations. According to the results of this study, it can be claimed that the porosity ratio is more effective than porosity distribution and nonlocal parameters on the amplitude response and dynamic instability regions. Moreover, to examine thermal increments, foundation characteristics, slenderness, and thickness ratios, the bifurcation diagrams are drawn and discussed. It is found that foundation and geometric characteristics are of the highest significance in the nonlinear response of the Timoshenko nanobeams. The main intention of this study is to present a holistic idea about the porous materials used in sandwich structures which can be used in many composite structures in aircraft and automobiles.

Orbits and chaos of a two‐fluid magnetized plasma oscillator subjected to parametric excitation with square delayed feedback

AbstractIn this manuscript, a two‐fluid magnetized plasma oscillator subjected to parametric excitation with square delayed feedback is studied both analytically and numerically. The Hamilton systems of triple‐well and narrow single‐well are discussed in detail. The scenarios of phase portraits and equilibria are given. Homoclinic and heteroclinic orbits are strictly derived. With the Melnikov method, the critical value of chaos arising from homoclinic or heteroclinic intersections is derived analytically. We have discovered some interesting dynamic phenomena, such as uncontrollable time delays with which chaos always occurs for this system. The influence of time‐delay on the chaotic property is also studied rigorously. On the basis of theoretical analysis, some numerical simulations including time histories, phase portraits, bifurcation diagrams, Poincaré sections, Lyapunov exponential spectrums and attractor basins are given. Numerical simulations are consistent with theoretical results.

Route to mixed-mode oscillations via step-shaped sharp transition of equilibria in a nonlinear gyroscope oscillator

Sharp transitions in relation to the variation of system parameters are frequently encountered in many multiple-timescale systems, and they have been found to be an important factor related to the generation of mixed-mode oscillations (MMOs). The present paper aims to report a novel type of sharp transition, referred to as step-shaped sharp transition, in a nonlinear gyroscope oscillator with multiple-frequency excitations, and investigate the resulting MMOs. We show that step-shaped sharp quantitative changes in relation to the variation of system parameters can be observed in the equilibrium branch, which yields the step-shaped sharp transition. In particular, with the increase of the frequency ratio between the parametric and external excitations, more step-shaped sharp transitions appear in the equilibrium branches, which evolve into the ones displaying different structures. Based on this, the rectangular-pulse-shaped explosion of equilibria is created. Furthermore, these sharp transitions can form active areas for the MMOs, leading to the alternations between large-amplitude and small-amplitude oscillations, and finally the route to MMOs is created. Our findings have significant implications for understanding the fast-slow dynamics of the nonlinear gyroscope oscillator, contributing to the exploration of new routes to MMOs. Thus, the results could provide theoretical support for the potential application of gyroscopes.

Nonlinear dynamics of a compact and multistable mechanical energy harvester

The use of smart materials as transducers in mechanical energy harvesting systems has gained significant attention in recent years. Despite the numerous proposed solutions in the literature, challenges still exist in terms of their implementation within limited spaces while maintaining optimal performance. This paper addresses these challenges through the concepts of compactness and space-efficient design, as well as the incorporation of nonlinear characteristics and additional degrees-of-freedom. A multistable dual beam nonlinear structure featuring two magnetic interactions and two piezoelectric transducers is presented. A reduced order model with 2-degrees-of-freedom is established based on the harvester structure in order to capture the essential qualitative characteristics of the system. Stability analysis demonstrates that the combination of two nonlinear magnetic interactions furnish unprecedented multistable characteristics to this type of harvester. A framework using a nonlinear dynamics perspective is established to analyze multistable systems based on energy harvesting purposes. Different dynamical and stability characteristics are determined by the differences in the system stiffness ratio. Parametric analyses are carried out classifying regions of high performance in the external excitation parameter space. These regions are associated with rich and complex dynamics. Finally, a comprehensive comparison is conducted between the proposed harvester and the classical bistable harvester, revealing improvements in performance across nearly all relevant conditions. These findings highlight the enhanced capabilities of the proposed harvester design, solidifying its potential of application in diverse energy harvesting scenarios.

Contactless deformation of fluid interfaces by acoustic radiation pressure

Reversible and programmable shaping of surfaces promises wide-ranging applications in tunable optics and acoustic metasurfaces. Based on acoustic radiation pressure, contactless and real-time deformation of fluid interface can be achieved. This paper presents an experimental and numerical study to characterize the spatiotemporal properties of the deformation induced by acoustic radiation pressure. Using localized ultrasonic excitation, we report the possibility of on-demand tailoring of the induced protrusion at water–air interface in space and time, depending on the shape of the input pressure field. The experimental method used to measure the deformation of the water surface in space and time shows close agreement with simulations. We demonstrate that acoustic radiation pressure allows shaping protrusion at fluid interfaces, which could be changed into a various set of spatiotemporal distributions, considering simple parameters of the ultrasonic excitation. This paves the way for novel approach to design programmable space and time-dependent gratings at fluid interfaces.

Performance analysis of nonlinear piezoelectric energy harvesting system under bidirectional excitations

In this paper, a cantilever beam piezoelectric energy harvester model of nonlinear partial differential equation based on Hamilton's Principle is established. A piezoelectric device using a bimorph cantilever beam with a fixed is subjected to horizontal and vertical excitation. Based on the Euler-Bernoulli thin beam model assumptions and inextensible deformation, the analysis further includes the effects of geometric nonlinearity and damping nonlinearity. The reduced-order nonlinear partial differential equations of motion with electro-mechanical coupling distributed parameter are derived by using Galerkin method. By using the method of multiple scales and solving the equations of motion, the energy harvester in its fundamental first-order resonance response is analyzed and the amplitudes of fundamental transverse deflection, output voltage and output power are determined. The major influence aspects of excitation amplitude, linear damping coefficient, nonlinear damping coefficient, impedance, nonlinear electro-mechanical coupling coefficient on transverse deflection, voltage and power are analyzed. The result shows that the linear damping coefficient and resistance affect the initial threshold of parametric excitation. The combination of parametric excitation and direct excitation gives full play to the advantages of parametric excitation and improve the energy conversion efficiency of the energy harvesting system.

Optimization method of electronic control parameters of antenna array for null controlling in specific regions and sidelobe suppression

ABSTRACT This paper presents a gradient-based optimisation method of antenna array for null controlling in specific regions and sidelobe suppression. The optimisation problem is formulated as optimising the electronic control parameters (excitation amplitude and phase) of the array to achieve that the maximum value of the peak sidelobe levels (PSLLs) is minimised and the depths of the nulls in specific regions are not greater than a threshold. The Kreisselmeier – Steinhauser (KS) function is used to describe the maximum value of the PSLLs, in this way, the optimisation problem becomes differentiable and can be solved efficiently by gradient-based algorithm. The sensitivities of the objective with respect to the design variables are analytically derived. Typical numerical examples and detailed evaluations are provided to validate the effectiveness of the proposed method. The results show that the null controlling in the predefined specific single, single-wide, dual, multiple, and annular regions is realised, and the PSLL suppression is performed comparing to the uniform planar arrays. In the 28 GHz base station transmitting antenna-array example, the proposed method effectively suppresses the PSLL and greatly saves the calculation time while maintaining the various specific null regions controlling.

Deciphering migraine pain mechanisms through electrophysiological insights of trigeminal ganglion neurons

Migraine is a complex neurological disorder that affects millions of people worldwide. Despite extensive research, the underlying mechanisms that drive migraine pain and related abnormal sensation symptoms, such as hyperalgesia, allodynia, hyperesthesia, and paresthesia, remain poorly understood. One of the proposed mechanisms is cortical spreading depression (CSD), which is believed to be involved in the regulation of trigeminovascular pathways by sensitizing the pain pathway. Another mechanism is serotonin depletion, which is implicated in many neurological disorders and has been shown to exacerbate CSD-evoked pain at the cortical level. However, the effects of CSD and serotonin depletion on trigeminal ganglion neurons, which play a critical role in pain signal transmission, have not been thoroughly studied. In this study, we aimed to investigate the association between CSD and serotonin depletion with peripheral sensitization processes in nociceptive small-to-medium (SM) and large (L) -sized trigeminal ganglion neurons at the electrophysiological level using rat models. We divided the rats into four groups: the control group, the CSD group, the serotonin depletion group, and the CSD/serotonin depletion group. We induced CSD by placing KCl on a burr hole and serotonin depletion by intraperitoneal injection of PCPA (para-chlorophenoxyacetic acid). We then isolated trigeminal ganglion neurons from all groups and classified them according to size. Using patch-clamp recording, we recorded the excitability parameters and action potential (AP) properties of the collected neurons. Our results showed that in SM-sized trigeminal ganglion neurons, the CSD-SM and CSD/serotonin depletion groups had a higher positive resting membrane potential (RMP) than the control-SM group (p = 0.001 and p = 0.002, respectively, post-hoc Tukey’s test). In addition, the gap between RMP and threshold in the CSD-SM group was significantly narrower than in the control-SM group (p = 0.043, post-hoc Tukey’s test). For L-sized neurons, we observed prolongation of the AP rising time, AP falling time, and AP duration in neurons affected by CSD (p < 0.05, pairwise comparison test). In conclusion, our study provides new insights into the underlying mechanisms of migraine pain and abnormal somatosensation. CSD and serotonin depletion promote the transmission of pain signals through the peripheral sensitization process of nociceptive small-to-medium-sized trigeminal ganglion neurons, as well as nociceptive and non-nociceptive large-sized trigeminal ganglion neurons.

Enhancing Electrical Generation Efficiency through Parametrical Excitation and Slapping Force in Nonlinear Elastic Beams for Vibration Energy Harvesting.

This study aims to enhance conventional vibration energy harvesting systems (VEHs) by repositioning the piezoelectric patch (PZT) in the middle of a fixed-fixed elastic steel sheet instead of the root, as is commonly the case. The system is subjected to an axial simple harmonic force at one end to induce transversal vibration and deformation. To further improve power conversion, a baffle is strategically installed at the point of maximum deflection, introducing a slapping force to augment electrical energy harvesting. Employing the theory of nonlinear beams, the equation of motion for this nonlinear elastic beam is derived, and the method of multiple scales (MOMS) is used to analyze the phenomenon of parametric excitation. This study demonstrates through experiments and theoretical analysis that the second mode yields better power generation benefits than the first mode. Additionally, the voltage generation benefits of the enhanced system with the added baffle (slapping force) surpass those of traditional VEH systems. Overall, the proposed model proves feasible and holds promising potential for efficient vibration energy harvesting applications in various industrial sectors.

Helicopter performance enhancement by alleviating retreating blade stall using active flow control

In this study, a model was created numerically to study the effect of active flow control on helicopter blade to improve the retreating blade stall. Active flow control is applied to helicopter blades to improve retreating blade stall along with the overall helicopter performance. The novel aspect of this study is using active control in a helicopter with a complex aerodynamic environment and using it in all significant flight modes. This has the advantage of practical application since active control can be used constantly without having to turn it off. The flow control is established by using blowing jets at the leading edge of the airfoil that is used at the tip part of the main rotor blade. 2D and 3D computational fluid dynamics (CFD) Turbulent-unsteady models are developed to investigate the effect of applying blowing jets on different helicopter modes of flight (hover and forward flight). Different excitation parameters and turbulence models are compared to get the maximum possible enhancement of the aerodynamic characteristic of the flow both in 2D and 3D. The results are validated against a NASA helicopter main rotor hub with known geometry and available performance parameters. Both models illustrated a good agreement with the published benchmark problem. The results revealed that the active control blowing jets can enhance the stall characteristics and aerodynamic performance of helicopter blades. The method delays the flow separation and increase the blade lift by about 10% in addition to a 40% increase in the lift to drag ratio. Thus, we can conclude that the present active control technique can enhance the helicopter in forward flight by delaying the retreating blade stall. This research offers insightful information on the usage of blowing jets for rotor flow control.

Excitability of somatosensory cortex is increased in ALS: A SEP recovery function study

ObjectiveNeuronal loss in the somatosensory, as well as the motor cortex in amyotrophic lateral sclerosis (ALS), indicative of a structural abnormality has been reported. Previously we have shown that afferent inhibition was impaired in ALS, suggestive of sensory involvement. In this study, we aimed to evaluate excitability changes in the somatosensory cortex of ALS patients. MethodsALS patients underwent a paired pulse somatosensory evoked potential (SEP) paradigm at various interstimulus intervals (ISI). The amplitude ratio obtained by dividing the amplitude of paired pulse SEP stimulation S2 (paired pulse stimulation) to S1 (the single pulse stimulation) was considered the somatosensory cortex excitability parameter. Findings were compared to the results obtained from healthy controls. Resting motor threshold (RMT) was also assessed in the ALS group. ResultsAn increased S2/S1 ratio was found in the ALS group in every ISI examined. Additionally, the reduced inhibition correlated negatively with forced vital capacity, Medical Research Council sum score, median nerve compound muscle action potential amplitude, while there was a positive association with Penn upper motor neuron score and sural nerve conduction velocity. No correlation existed with RMT. ConclusionsOur findings demonstrated increased somatosensory cortical excitability in ALS, which was associated with clinical parameters such as reduced pulmonary function and motor strength. SignificanceSomatosensory cortical excitability is impaired in ALS. Whether this is associated with increased motor cortical excitability requires further studies.

Chaotic dynamics of an extended Duffing-van der Pol system with a non-smooth perturbation and parametric excitation

Abstract Chaotic dynamics of a fifth-order extended Duffing-van der Pol system with a non-smooth periodic perturbation and parametric excitation are investigated both analytically and numerically in this paper. With the Fourier series, the system is expanded to the equivalent smooth system. The Melnikov perturbation method is used to derive the horseshoe chaos condition in the cases of homoclinic and heteroclinic intersections. The chaotic features for different system parameters are investigated in detail. The monotonic variation of the coefficients of parametric excitation and non-smooth periodic disturbance is found. With numerical methods, we validate the analytical results obtained by Melnikov’s method. The impact of initial conditions is carefully analyzed by basins of attraction and the effect of non-smooth periodic disturbance on the basin of attraction is also investigated. Besides, the effect of different parameters on the bifurcation pathway into chaotic attractors is examined.

Research on vibratory & oscillatory coexistence nonlinear dynamics based on drum-subgrade coupling model

In order to provide theoretical basis for subgrade continuous compaction monitoring technology and intelligent compaction technology, it is urgent to study the nonlinear coupling dynamics of drum and subgrade in the process of vibratory and oscillatory compaction. In this study, a nonlinear coupling dynamic model of 6-degree-of-freedom vibratory drum-subgrade is proposed, which considers the elastoplastic characteristics of the subgrade during compaction. According to the geometric and physical relationship between the drum and the subgrade in the contact area, the longitudinal dynamic contact force coefficient is derived, which establishes the coupling relationship between the drum-subgrade vertical vibration and longitudinal oscillation. Combined with the evolution law of material properties of subgrade in actual compaction operation, the nonlinear dynamic behavior of coupling system in the whole compaction period is analyzed. The results show that the chaotic compaction state in the vertical direction of the drum may occur during the full compaction cycle, which is related to the excitation parameters of the drum. Furthermore, the excitation parameters are more sensitive to the longitudinal one-cycle vibration response of the system than the vertical vibration response. Through the response characteristics of the drum and the subgrade and the bifurcation diagram of the drum, it is proved that the proposed model can effectively simulate the longitudinal-vertical nonlinear coupling characteristics of the drum and subgrade, and can provide a premise for theoretical exploration for the vibratory & oscillation compaction mode.

MATHEMATICAL MODELING OF DIRECT CURRENT MOTOR OPERATION WITH DIFFERENT EXCITATION TYPES FOR VIBRATIONAL MACHINES

This work is dedicated to the development and analysis of a mathematical model for a direct current motor with various types of excitation for vibrational machines. Vibrational machines play a crucial role in many industrial sectors, and their operational characteristics are determined by the efficiency and accuracy of motor performance. In this study, we investigate different types of excitation for direct current motors and develop corresponding mathematical models. Employing principles from control theory and quantitative electronics, we account for the influence of different excitation parameters on the motor's dynamic behavior. The obtained results could be valuable for the development of new hybrid excitation systems for vibrational machines, capable of operating in diverse modes depending on specific additional conditions. Additionally, the analysis and development of the mathematical model can serve as a foundation for further research in optimizing the operation of vibrational systems using direct current motors. Analyzing the results, we compare the efficiency of various excitation types and their impact on the operational characteristics of vibrational machines. Moreover, we explore possibilities for reducing power consumption and enhancing speed regulation accuracy. Special attention is devoted to analyzing system stability under different operating conditions and parameter variations. The findings of our research hold important practical applications in the design and improvement of vibrational machines for industrial, technical, and scientific purposes. They contribute to understanding the influence of different factors on the performance of direct current motors with various excitation types, which can aid engineers and designers in enhancing the efficiency and reliability of vibrational systems. In conclusion, this research is aimed at developing and analyzing a mathematical model for a direct current motor with various excitation types, considering their impact on the operational characteristics of vibrational machines. It makes a significant contribution to understanding and optimizing the processes of such systems, potentially exerting a substantial influence on the advancement of modern technology in the field of vibrational systems and their applications.

Investigation of the Motion Characteristics of Parts on a Platform Subjected to Planar Oscillations

Positioning applications are very important in a variety of industrial processes, including automatic assembly. This paper proposes a technique for positioning applications that involves employing a platform subjected to planar oscillations along circular, elliptical, and complex trajectories. Dynamic and mathematical models of the motion of a part on the platform were developed to investigate the motion characteristics of the part. The research showed that when the platform was excited in two perpendicular directions by sinusoidal waves, different trajectories of the part’s motion could be obtained by controlling excitation parameters such as the frequencies and amplitudes of the waves and the phase shift between the waves. Furthermore, by adjusting these parameters, the average displacement velocity of the part could be controlled. The results demonstrate that the part can be moved in any direction at a given velocity and can be subjected to complex dense positioning trajectories. Therefore, such a platform can be applied in feeding, positioning, and manipulation tasks.

Insight on uncertainty of geometrically nonlinear rotor with rub-impact under maneuvering motion

Maneuvering motion inevitably leads to parametric excitations and inertial forces, which greatly aggravates the whirling motion of rotor system and then induces rub-impact fault between rotor and stator. Under this circumstance, rotor dynamic analysis under maneuvering conditions is of considerable importance for safe and efficient functioning of rotating machinery. Furthermore, the uncertainties are inherently present in mechanical systems due to wear, properties variations and working condition evolutions. The main objective of this paper is to investigate the nonlinear characteristics and interval responses of deterministic and uncertain rotor systems under maneuvering motion. Due to whirling motion with large amplitude, the geometrical nonlinearity of shaft and rub-impact nonlinearity are considered in the rotor system. Then the equations of motion of deterministic rotor system with rub-impact under maneuvering motion are theoretically derived according to the Lagrange's equation. On this basis, the parametric uncertainties of disk eccentricity and flight maneuvers involved in the rotor system are described by the Chebyshev interval algorithm. After that the nonlinear dynamic characteristics of deterministic rotor system under maneuvering motion are numerically solved and analyzed in terms of bifurcation diagram, time histories, whirling orbit, Poincaré map and frequency spectrum. Additionally, the interval responses of vibration displacement and impact force at different rotational speeds are further examined.

Nonlinear parametric excitation and dynamic stability of auxetic honeycombs core with CNTRC face sheets sandwich plate

This study aims to analyze the Nonlinear vibration and instability of a sandwich plate with an Auxetic Honeycomb core and a Carbon Nanotube Reinforced Composite (CNTRC) face layer on a viscous elastic foundation under parametric excitation. In the analytical model, the Hamilton principle and nonlinear strain-displacement relations determined by Von Karman theory and the first shear deformation plate theory (FSDT) are used. The governing equations are solved using the Galerkin method, which involves expanding the displacement field based on orthogonal functions. Once the displacement field has been expanded, a multiple-scale method is used to solve the equation of motion. The results show that the bifurcation diagrams and stability of sandwich plates depend on several parameters, including the geometric dimension of the honeycomb core, the material properties of the CNTRC face layer, and the temperature increment. The results of this study will likely be helpful in optimizing the design of sandwich plates for engineering applications, including the aerospace and automotive industries, where sandwich structures are widely utilized because of their high strength-to-weight ratios and excellent energy absorption capabilities.