Jumping Phenomena Research Articles

Frequency Splitting and Transmission Characteristics of MCR-WPT System Considering Non-Linearities of Compensation Capacitors

The frequency splitting phenomenon and transmission characteristics have been research hotspots in the field of magnetically coupled resonance wireless power transfer (MCR-WPT). In this paper, non-linear dynamics theory was innovatively introduced into the research, and non-linear coupled transmission dynamics modelling of the MCR-WPT system was established considering the non-linearities of the compensation capacitor. The mechanism of the frequency splitting phenomenon of the MCR-WPT system was revealed through systematic mathematical analyses based on the modelling. The analysis results showed that the system usually has dual natural frequencies which are low resonance frequency and high resonance frequency. Based on non-linear dynamics theory, the transmission characteristics of the system with different non-linear parameters were discussed comprehensively in relation to the modelling. The results of the numerical simulations and theoretical analyses showed that non-linear parameters can cause the jumping phenomena with the output responses, and the output responses in the vicinities of the lower resonance frequencies were extremely sensitive to changes in the coupling coefficient. According to analyses of the linear and non-linear systems, the energy transmissions performed in the vicinity of the high resonance frequency had a wider working frequency band and a better transmission stability under non-linear conditions.

Vibration analysis of a free moving thin plate with fully covered active constrained layer damping treatment

A comprehensive dynamic model for a free moving thin plate with fully covered active constrained layer damping (ACLD) treatment is developed. The discrete equations of motion of the moving ACLD plate are derived by using Ritz method and Lagrange’s equations. Free vibration analysis of the composite plate undergoing large rotational or translational motions are performed by solving the complex modal eigenvalue problem of the system in open-loop and closed-loop cases. Interesting frequency curve veering, mode shape switching as well as damping ratio jumping phenomena are observed and discussed for the plate rotating around two different axes. It is demonstrated that the flexible plate undergoing rigid motions can not only generate dynamic stiffening effect but also dynamic softening effect. Effects of parameters such as angular velocity, acceleration, and control gain on the modal and damping characteristics of the ACLD plate are also investigated.

Jump phenomena in vortex-induced vibrations of a circular cylinder at a low Reynolds number

The cross flow-induced vibrations of a circular cylinder at the Reynolds number of 150 are numerically investigated in a systematic manner in terms of a wide range of reduced velocity. The effect of the mass ratio on the cylinder behavior is studied, with three mass ratios, namely, 2, 10, and 50, being considered particularly in detail. The mass ratio is defined as the mass of the cylinder to the mass of the fluid it displaces. A sudden decrease in the vibration amplitude takes place at a certain value of the reduced velocity, accompanied by an abrupt increase in the lift coefficient and the vortex shedding frequency. The vortex shedding frequency at the upper end of the lock-in region is about 0.14 for all the mass ratios, which may mark the lower limit of the vortex shedding frequency at this Reynolds number. The jump phenomena may be ascribed to this limitation. Moreover, the vortex shedding frequency in the non-lock-in region varies slightly with the reduced velocity but is not approaching the Strouhal number for the stationary cylinder at the same Reynolds number. In fact, the frequency rises with the increasing mass ratio and reaches about 0.2 as the mass ratio is larger than 10. Besides, the vortex shedding mode does not remain “2S” for the mass ratio larger than 14 when the reduced velocity is increased to get into the non-lock-in region since the vortex shedding frequency is separate from the cylinder oscillation frequency.

Two-To-One Internal Resonance of Super-Critically Axially Moving Beams

Internal resonance is a common phenomenon in super-critically axially moving beams. It can lead to an energy exchange among associated modes and produce a large-amplitude response. However, the effect of the internal resonance on the dynamics of system is not clear. Therefore, in the present paper, we investigated the nonlinear dynamics of a super-critically axially moving beam with two-to-one internal resonance. By applying a proper transporting speed, the two-to-one internal resonance condition of the system is established. The method of multiple scales is employed to solve the governing equation so as to obtain the nonlinear response of the system. To analyze the effect of the quadratic and cubic nonlinearities, the perturbation solution is expanded up to three orders. The primary resonance of the first and second modes is investigated. Their steady-state solutions are solved, and the stability of these solutions is examined. Response of the system is demonstrated via the frequency response and force-response curves. Results show that jumping, saturation, and hysteresis phenomenon may occur. Moreover, the modulated motion can be found in the case of primary resonance of the first mode. The approximate analytical results are verified by the numerical results.

The nonlinear vibrations of a vertical hard gyroscopic rotor with nonlinear characteristics

Abstract. The paper considers an impact of viscous linear and cubic nonlinear damping of the elastic support on nonlinear vibrations of a vertical hard gyroscopic unbalanced rotor, taking into account nonlinear stiffness of the support material. Analyzing the research results shows that linear and cubic nonlinear damping can significantly suppress the resonance peak of the fundamental harmonic, eliminate the jumping phenomena of the nonlinear system. In non-resonance areas where the velocity is higher than the critical one, cubic nonlinear damping, unlike linear one, can slightly suppress amplitude of the rotor vibration. Therefore, in the high-velocity area, only nonlinear damping can maintain performance of a vibration isolator. In resonance area, an increase in linear or cubic nonlinear damping significantly suppresses the ability to absolute displacement. In non-resonance area, where the rotational velocity is lower than the critical one, they have almost no impact on ability to absolute displacement. In high velocity area, an increase in nonlinear damping may slightly increase the moment of force transmissibility, but linear damping has almost no impact on it. The obtained results can be successfully used to produce passive vibration isolators used for damping the vibrations of rotary machines, including gyroscopic ones.

A lattice Boltzmann simulation of coalescence-induced droplet jumping on superhydrophobic surfaces

The coalescence-induced droplet jumping on superhydrophobic surfaces (SHSs) observed in nature plays a significant role in energy and environmental applications. By using a three-dimensional chemical-potential-based multiphase lattice Boltzmann model, the coalescence-induced jumping of two droplets and multidroplet are systematically simulated and analysed. The results show that the size and the number of droplets and the characteristics of pillared SHSs have a strong influence on the droplet behaviour. The coalesced droplet could only jump under appropriate droplet size and characteristic parameters of SHSs. Furthermore, coalesced droplets are more likely to jump and jump higher on SHSs with larger contact angle and pillar height and smaller distance between two pillars. This work will contribute to understand the phenomenon of the coalescence-induced droplet jumping and provide theoretical guidelines for the design of new SHSs.

A new datum jump detection and mitigation method of Real-Time Service (RTS) clock products

Real-time orbit and clock products are crucial for real-time precise point positioning (PPP) applications. The International Global Navigation Satellite System (GNSS) Service (IGS) launched the Real-Time Service (RTS) in 2013 to provide real-time satellite orbit and clock products which have since found wide applications. Currently, the IGS RTS provides two different types of satellite orbit and clock products: the products generated from individual Analysis Centers such as CLK01, CLK22 and CLK90 and the combination products such as IGS01 and IGS03. These IGS RTS products are different in terms of precision and reliability. First, we verify that the phenomenon of clock datum jumps is obvious in IGS01, which has not been considered by the GNSS community when applying the IGS01 product to the real-time PPP. Afterward, the causes of the clock datum jump are investigated. The results indicate that a switchover of the reference product or a datum jump in the reference product will cause a clock datum jump. In order to solve the clock datum jumps issue, a new clock datum jump detection and mitigation algorithm is proposed. Real-time kinematic PPP experiments are then carried out to validate the proposed satellite clock detection and mitigation algorithm. The positioning results with 27 globally distributed IGS stations show that the root mean square improvements in the north, east and up components are 61.5%, 36.5% and 55.1% after detecting and mitigating the datum jumps.

Multiple-S-Shaped Critical Manifold and Jump Phenomena in Low Frequency Forced Vibration with Amplitude Modulation

Motivated by the forced harmonic vibration of complex mechanical systems, we analyze the dynamics involving different waves in a double-well potential oscillator coupling amplitude modulation control of low frequency. The combination of amplitude modulation factor significantly enriches the dynamical behaviors on the formation of multiple-S-shaped manifold and multiple jumping phenomena that alternate between epochs of slow and fast motion. We can conduct bifurcation analysis to identify two harmonic vibrations. One is that the singular orbit makes multiple jumps to a fast trajectory segment from one attracting equilibrium to another as the expression of slow variable by using the DeMoivre formula. With the increase of tuning frequency, the system exhibits relaxation-type oscillations whose small amplitude oscillations are produced by nonlinear local cycles together with a distinct large amplitude cycle oscillation accounting for the Melnikov threshold values. The tuning frequency may not only affect the asymptotic expressions for the solution curves near fold singularities but also allow for the large amplitude orbit vibrations near fold-cycle singularities. Numerical analysis for computing critical manifolds and their intersections is used to detect the dynamical features in this paper.

Nonlinear breathing vibrations of eccentric rotating composite laminated circular cylindrical shell subjected to temperature, rotating speed and external excitations

In this paper, the nonlinear breathing vibrations of an eccentric rotating composite laminated circular cylindrical shell are studied for the first time, which is subjected to the lateral and temperature excitations. Based on Donnell thin shear deformation theory, von Kármán-type nonlinear relation and Hamilton’s principle, the nonlinear partial differential governing equations of motion are established for the eccentric rotating composite laminated circular cylindrical shell. The nonlinear partial differential governing equations of motion are discretized into a set of coupled nonlinear ordinary differential equations of motion by Galerkin approach. Based on the case of 1:2 internal resonance and principal parametric resonance-1/2 subharmonic resonance, the method of multiple scales is employed to obtain four-dimensional nonlinear averaged equations. Considering the effects of different parameters, for example, the eccentricity ratio, the geometric parameters and the excitations, the nonlinear dynamic behaviors and the jumping phenomena are exhibited for the frequency-response curves and the amplitude-response curves. The periodic and chaotic motions of the eccentric rotating composite laminated circular cylindrical shell are found when the rotating speed corresponds to the internal resonant point at the certain conditions for different lateral and temperature excitations.

Effect of Capacitance Variation on Physical Characteristics of Ferroresonance Severity and Jump Phenomenon Based on Rudenberg Graphical Method

This paper performed the ferroresonance generation experiment with variation of capacitance based on Rudenberg graphical method. The voltage and current measurements were conducted on the transformer primary windings, source voltage, and capacitor. The trend of transformer voltage waveform was then analyzed by using bifurcation diagram. Moreover, the fast Fourier transform (FFT) was applied on the transformer primary voltage. The harmonics spectrum would show the ferroresonance mode. Then, its total harmonics distortion (THD) was calculated. The level of ferroresonance severity involving the values of transformer voltage and overvoltage level as well as THD was mapped based on the quadrant system. The results showed that the appearances of jump phenomenon and different ferroresonance severities could be explained more clearly by using Rudenberg graphical method. In addition, the proposed mapping of ferroresonance responses based on the quadrant system was successful not only to highlight the impact of given variables on ferroresonance but also to categorize more easily its danger level.

Free vibration of truncated conical shells with elastic boundary constraints and added mass

Most of the research on truncated conical shells focuses on the dynamics with classical boundary conditions. However, less attention has been given to the non-classical boundary conditions due to the lack of a unified displacement function, such as a boundary with point constraint or partial constraint, or a boundary with added mass, which exists in engineering practice. In this study, we investigate the free vibration of the truncated conical shell with arbitrary boundary conditions, including elastic and inertia force constraints. The equations of motion with elastic boundary constraints are formulated by employing Hamilton's principle and the thin-walled shallow shell theory of the Donnell type. The solutions of the shells are obtained using Fourier series in circumferential directions and power series in meridional directions, with various boundary conditions achieved through the choice of stiffness, which is a unified solution procedure. The procedure proposed was validated by comparing the results obtained with results available in the literature on classical boundary conditions and with the finite element method results for the non-classical boundary conditions. Numerical simulations were carried out to illustrate the sensitivity of the shell frequency to the stiffness parameters and the moment of inertia effect on frequency, and to present the circumferential modal jumping phenomena with patterns.

A unified Gram-Schmidt-Ritz formulation for vibration and active flutter control analysis of honeycomb sandwich plate with general elastic support

An admissible function constructed by orthogonal polynomials is presented to investigate the vibration and active flutter control of Honeycomb sandwich plate with general elastic support in a supersonic airflow. The control strategies based on the displacement feedback and LQR method are applied by means of pasting the piezoelectric material on the surface of the plate structure. Employing the first-order piston theory to describe the aerodynamic loads, the governing equation of plate system with the piezoelectric actuator is established based on the Hamilton principle. The mode shapes are obtained using the admissible functions, which are a set of characteristic orthogonal polynomials generated directly by employing the Gram-Schmidt process, and the general elastic constraint is modeled using the artificial spring technology. The frequency and mode shape under different boundary are calculated by Rayleigh-Ritz method. The validity of the proposed approach is confirmed by comparing the results with those obtained from FEM and literatures. The phenomenon of mode jumping is observed with the increase of the aerodynamic pressure. The study of active control shows that, the increasement of displacement feedback gain improves the critical dynamic pressure.

Nonlinear Vibrations of Buried Rectangular Plate

We perform an investigation on the vibration response of a simply supported plate buried in glass particles, focusing on the nonlinear dynamic behaviors of the plate. Various excitation strategies, including constant-amplitude variable-frequency sweep and constant-frequency variable-amplitude sweep are used during the testing process. We employ the analysis methods of power spectroscopy, phase diagramming, and Poincare mapping, which reveal many complicated nonlinear behaviors in the dynamic strain responses of an elastic plate in granular media, such as the jump phenomena, period-doubling bifurcation, and chaos. The results indicate that the added mass, damping, and stiffness effects of the granular medium on the plate are the source of the nonlinear dynamic behaviors in the oscillating plate. These nonlinear behaviors are related to the burial depth of the plate (the thickness of the granular layer above plate), force amplitude, and particle size. Smaller particles and a suitable burial depth cause more obvious jump and period-doubling bifurcation phenomena to occur. Jump phenomena show both soft and hard properties near various resonant frequencies. With an increase in the excitation frequency, the nonlinear added stiffness effect of the granular layer makes a transition from strong negative stiffness to weak positive stiffness.

Vibration, Buckling and Aeroelastic Analyses of Functionally Graded Multilayer Graphene-Nanoplatelets-Reinforced Composite Plates Embedded in Piezoelectric Layers

This paper deals with the vibration characteristics and nonlinear aeroelastic response of the functionally graded (FG) multilayer composite plate reinforced with graphene nanoplatelets (GPLs) subjected to in-plane excitations and applied voltage. The different GPL nanofillers distribution patterns across the thickness are discussed, in which the effective Young’s modulus is determined by modified Halpin–Tsai model. Based on high-order shear deformation theory, the motion equations of the FG plate system considering the von Kármán geometric nonlinearity are derived using the Hamilton’s principle. The Galerkin method is applied to discretize the partial differential governing equations into the ordinary differential nonlinear system. The effects of many influential parameters, i.e., GPLs weight fraction, distribution pattern, geometry size, applied voltage and the number of layers, on the vibration and aeroelastic behaviors are presented in detail. Numerical results show that a small amount of GPLs reinforcement can have a significant enhancement effect on the performance of the composite plate structure. Moreover, the in-plane force and aerodynamic pressure play an opposite effect on the dynamic stability, and the jumping phenomena, quasi-periodic motion can be observed with the compressive force increased further.

Coalescence-Induced Jumping of Two Unequal-Sized Nanodroplets.

Coalescence-induced self-propelled jumping of droplets on superhydrophobic surfaces has potential applications for condensation heat transfer enhancement, anti-icing, self-cleaning, antidew, and so forth. However, most of the previous studies focused on two identical droplets which are not commonly encountered in the nature. In this work, coalescence-induced jumping phenomena of two unequal-sized droplets on superhydrophobic surfaces were investigated theoretically and numerically. First, by introducing modified inertial-capillary velocity (uic*) and Ohnesorge number (Oh*) with consideration of radius ratio (r*) of two coalescing droplets, we proposed a generalized inertial-capillary scaling law for the jumping velocity of coalesced droplets, which is expected to be applicable for both two identical droplets and two unequal-sized droplets coalescing on superhydrophobic surfaces. Subsequently, we employed molecular dynamics simulations to investigate the coalescence-induced jumping process of two unequal-sized nanodroplets. Our simulations showed that the dimensionless jumping velocity (vj/uic*) well follows the generalized inertial-capillary scaling law with vj/uic* ≈ 0.127 in a specific Oh* range; however, it rapidly reduces and finally vanishes when the radius ratio of large droplet to small droplet is larger than a certain threshold value. Our simulations also revealed that nonjumping of two unequal-sized droplets with a very large radius ratio is due to that the larger droplet swallows the small one, so that the liquid bridge has no chance to impact the solid surface, and hence the "liquid bridge impacting substrate" mechanism fails in this circumstance.

Energy analysis of droplet jumping induced by multi-droplet coalescence: The influences of droplet number and droplet location

Self-propelled droplet jumping phenomenon during condensation on superhydrophobic surfaces has various engineering applications such as heat transfer enhancement, hotspot cooling and anti-icing/frosting. Since most of the droplet jumping phenomena are induced by multi-droplet rather than two-droplet coalescence, understanding the influences of droplet number and multi-droplet location on the droplet jumping is essential. In this work, droplet jumping induced by multi-droplet coalescence was simulated using the volume of fluid (VOF) method with various coalesced droplet number and locations considered. The simulations showed visualized droplet morphology evolutions during the droplet jumping processes. The changes of several energies, such as surface energy, kinetic energy and jumping energy, were also discussed with the energy conversion efficiencies calculated. The results show that increasing the coalesced droplet number is advantageous for surface energy releasing and the energy conversion efficiency from the surface energy to the jumping energy also increases with increasing coalesced droplet number. Coalescence of droplets with more concentrated location distribution has weaker oscillation during the jumping process, along with less oscillatory kinetic energy, indicating that concentrated droplet distribution is conductive to increase the energy conversion efficiency from the surface energy to the jumping energy.

Condensation and subsequent freezing delays as a result of using femtosecond laser functionalized surfaces

In this paper, the authors report on the use of femtosecond laser surface processing (FLSP) to enhance the anti-icing properties of a commonly used aircraft alloy, Al 7075-O Clad. By changing the surface morphology through FLSP and the surface chemistry through siloxane vapor deposition, the wettability of Al 7075-O Clad was altered. Tall mound and short mound FLSP functionalized surfaces were created through two sets of laser parameters. Condensation and the subsequent freezing of condensates on FLSP Al 7075-O Clad was studied. Both structure height and surface wettability were shown to play a role in the delay of freezing. Freezing occurred on the FLSP superhydrophilic surface faster than on the unprocessed Al 7075-O Clad surface; however, freezing was delayed for all superhydrophobic FLSP surfaces. Tall structure height FLSP functionalized surfaces delayed freezing time longer than short structure height FLSP functionalized surfaces although all were superhydrophobic. It was shown that FLSP functionalized surfaces were able to delay freezing by up to 530 s compared with unprocessed Al 7075-O Clad. The authors also report on self-propelled condensate jumping on FLSP surfaces during the condensing process. The self-propelled jumping phenomena provide a means to promote anti-icing of materials, especially where jumping drops can be swept away in flow conditions.

Global bifurcations of symmetric cross‐ply composite laminated plates with 1:2 internal resonance

AbstractThis paper investigates the global bifurcations and chaotic dynamics for nonlinear oscillations of symmetric cross‐ply composite laminated plates in case of 1:2 internal resonance. The higher‐dimensional Melnikov method and its extensions developed by Kovai and Wiggins is employed to analyze the global bifurcations for composite laminated plates. The explicitly sufficient conditions of the existence of Silnikov‐type homoclinic orbits in perturbed phase space are gained, which may lead to chaotic motions for composite laminated plates. Finally, numerical results obtained by fourth‐order Runge‐Kutta method also indicate that there exist the jumping phenomena and chaotic responses for the nonlinear composite laminated plates, which agree with theoretic predictions.

Pricing mortgage insurance contracts under housing price cycles with jump risk: evidence from the U.K. housing market

ABSTRACTPrevious studies have investigated the determinants of housing price cycles in the housing market; however, we observed the phenomenon of housing price jumps in the 2007 subprime crisis. This paper presents a discussion on the housing price cycle and abnormal price jumps to describe the behavior of housing prices in the United Kingdom. The empirical results show that the impact factors of housing cycles are market risk and the switching factor. Furthermore, the impact factors of jump risks include the bursting of the housing bubble and financial crises. Therefore, in this paper, we employ the Markov switching model with jump risks to value the MI contracts and analyze the influences of housing price cycles, jump risks, risks of market interest rate, and the prepayment risks on MI premiums. The results of sensitivity analysis show that more volatile housing price index returns, as well as longer periods of higher volatility in housing prices, raise MI premiums. Moreover, the MI premium is positively related to the absolute value of the average jump amplitude and the shock frequency of abnormal events. There is the tradeoff between the market interest rate and the prepayment risk. The influences of market interest rate are different on MI premium with/without prepayment risks.

The beginning of time observed in quantum jumps

The phenomenon of quantum jumps observed in a single ion stored in a trap brings to light intimate connections between three different concepts of quantum physics: (i) quantum state trajectories, (ii) Gamow states, and (iii) the arrow of time. In particular, it allows us to identify the starting time of the semigroup time evolution.