Hybrid Rayleigh Research Articles

Toward an Operational Dynamical Model of Lateral Manual Interception Behavior.

We develop a dynamics-based model of discrete movement for lateral manual interception capable of generating movements with realistic kinematics. For the present purposes, we focus on the situation of to-be-intercepted targets moving at constant speed along rectilinear trajectories oriented orthogonally with respect to the interception axis. The proposed phenomenological model is designed to capture the time evolution of empirically observed hand movements along the interception axis under different conditions of target arrival location and target speed-induced time pressure. Pattern formation dynamics combine a Duffing stiffness function, allowing for creating a fixed-point attractor at the perceived location of the target arrival on the interception axis, with a hybrid Rayleigh plus Van der Pol damping function. After parametrizing the model for required movement direction (left/right), amplitude, and duration, it adequately reproduces the (variations in) empirically observed kinematics with a single set of four coefficients for all conditions considered. The model is also demonstrated to inherently incorporate speed-accuracy trade-off characteristics.

Hybrid Rayleigh wave along a nonlocal nonlinear metasurface with two-degree-of-freedom spring-mass resonators

Metasurfaces are devices employing the notion of resonance to transform seismic surface waves into body waves, thereby protecting the subwavelength structures. Using metasurfaces to control surface waves is a rapidly expanding field with intrinsic theoretical value and potential applications everywhere. In this paper, we have combined the concepts of nonlinearity, double mass system, and nonlocal elasticity to unveil the dispersive properties of hybrid Rayleigh waves. To enable a more compact construction for multi-frequency attenuation, two spring-mass resonators coupled with a nonlinear spring are used instead of single-mass resonators. A novel metasurface consisting of an array of nonlinear two-degree-of-freedom (two-mass) spring-mass systems is explored. This metasurface is connected to a nonlocal elastic substrate through a linear elastic spring. The paper provides a simple but effective analytical approach to study the dispersive properties of seismic metasurfaces. The complete explicit solutions are derived for the displacement of spring-mass systems and the Rayleigh waves in the nonlocal host substrate. Two frequency bandgaps are formed due to the presence of a dual spring-mass system in the metasurface. An attempt is made to explain the existence of these multi-frequency bandgaps as a result of the presence of multi-resonators. The effects of nonlinearities (softening and hardening) of the springs, nonlocal elasticity and relative amplitude inputs of the spring-mass system on the frequency (spectral) bandgaps are analyzed in detail via numerous plots.

Acoustics performance of compact micro-perforated panel absorber with grazing flow

This paper presents numerical and experimental investigations into the acoustic behaviour of a micro-perforated panel (MPP) backed by a shallow cavity under a fully developed grazing flow. A three-dimensional time-domain computational fluid dynamics approach is applied alongside hybrid evaluation methods to accurately capture the acoustic behaviour variations of an MPP orifice. Meanwhile, a hybrid Rayleigh's end correction model for T-shaped resonators is utilized to calculate the acoustic reactance of a very shallow cavity and an acoustics impedance model of an orifice backing with shallow cavity at grazing flow is established. The proposed acoustic impedance model of orifice has been validated by experimental study. The practical significance of this study is that it elucidates the influence of cavities upon the acoustic behaviour of MPPs in the presence of grazing flows; furthermore, it proposes an impedance model that is more suitable for predicting the acoustic performance of booming compact meta-structures.

Acoustic behaviour of micro-perforated panel backed by shallow cavity under fully developed grazing flow

This paper presents numerical and experimental investigations into the acoustic behaviour of a micro-perforated panel (MPP) backed by a shallow cavity under a fully developed grazing flow. A three-dimensional time-domain computational fluid dynamics approach is applied alongside hybrid evaluation methods to accurately capture the acoustic behaviour variations of an MPP orifice, considering the interaction of flow dynamics and the acoustics in the orifice and cavity. Meanwhile, a hybrid Rayleigh's end correction model for T-shaped resonators is utilized to calculate the acoustic reactance of a very shallow cavity. The numerical results show that the vertical shear layer is observed alongside the hole and cavity and impinges the bottom of shallow cavity. Subsequently it alters acoustic and flow interaction significantly that leads to variation of acoustic behaviour of orifice. In this regard, an acoustic impedance model of an orifice backing with shallow cavity at grazing flow is established. The proposed acoustic impedance model of orifice has been validated by experimental study. The transmission loss predictions for a compact MPP absorber with single or double cavities agree well with the experimental results for the grazing flow condition. The practical significance of this study is that it elucidates the influence of cavities upon the acoustic behaviour of MPPs in the presence of grazing flow; furthermore, it proposes an impedance model that is more suitable for predicting the acoustic performance of booming compact meta-structures.

Rayleigh Wave Attenuation by a Nonlinear Metasurface with Both Vertical and Horizontal Resonators

It is well known that earthquakes are one of the most catastrophic geological disasters. In recent years, the use of metasurfaces to suppress the propagation of seismic surface waves to protect surface buildings has received extensive attention. However, most of the previous research works are on linear metasurfaces and the effect of vertical resonators. In this work, we propose a nonlinear metasurface, which consists of a linear elastic semi-infinite space with vertical nonlinear and horizontal linear resonators attached to its top surface. Our study shows that the interaction between the dynamics of the resonators and the waves of the semi-infinite space creates a hybrid Rayleigh wave propagating along the surface. First, the dispersion of the hybrid Rayleigh wave is derived analytically. Then, numerical calculations are conducted and the effect of the coupling of the vertical and horizontal resonators on the dispersion is discussed. Afterward, a finite-element simulation is performed to verify the analytical predictions. The results demonstrate that an ultra-wide bandgap for the hybrid Rayleigh wave can be achieved by the designed nonlinear metasurface. This work may help promote the application of metasurfaces in the field of earthquake protection.

Influence of Amplitude-Modulated Force and Nonlinear Dissipation on Chaotic Motions in a Parametrically Excited Hybrid Rayleigh–Van der Pol–Duffing Oscillator

The generation and evolution of chaotic motions in a hybrid Rayleigh–Van der Pol–Duffing oscillator driven by parametric and amplitude-modulated excitation forces are investigated analytically and numerically. By using the Melnikov method, the conditions for the appearance of horseshoe chaos in our system are derived in the case where the modulation frequency [Formula: see text] and the forcing frequency [Formula: see text] are the same [Formula: see text]. The obtained results show that the chaotic region decreases and increases in certain ranges of frequency. The numerical simulations based on the basin of attraction of initial conditions validate the obtained analytical predictions. It is also found that in the case where [Formula: see text] is irrational, the increase of amplitude-modulated force accentuates the fractality of the basin of attraction. The global dynamical changes of our model are numerically examined. It is found that our model displays a rich variety of bifurcation phenomena and remarkable routes to chaos. In addition, the presence of the hybrid Rayleigh–Van der Pol damping force reduces the chaotic domain in the absence of amplitude-modulated force. But when the amplitude-modulated force acts on the system, the chaotic oscillations decrease and disappear. Further, the geometric shape of the chaotic attractors considerably decreases in the presence of the amplitude-modulated excitation force. On the other hand, the system presents transient chaos, torus-chaos and torus of different topologies when [Formula: see text] is irrational.

Single-end hybrid Rayleigh Brillouin and Raman distributed fibre-optic sensing system

Single-end hybrid Rayleigh Brillouin and Raman distributed fibre-optic sensing system

Linear temporal stability analysis on the inviscid sheared convective boundary layer flow

A linear temporal stability analysis is conducted for inviscid sheared convective boundary layer flow, in which the sheared instability with stable stratification coexists with and caps over the thermal instability with unstable stratification. The classic Taylor–Goldstein equation is applied with different stratification factors Js and Jb in the Brunt–Väisälä frequency, respectively. Two shear-thermal hybrid instabilities, the hybrid shear stratified (HSS) and hybrid Rayleigh–Bénard (HRB) modes, are obtained by solving the eigenvalue problems. It is found that the temporal growth rates of the HSS and HRB modes vary differently with increased Jb in two distinct wavenumber (α̃) regions defined by the intersection point between the stability boundaries of the HSS and HRB modes. Based on Jb,cr where the temporal growth rate of the HSS and HRB are equal, a map of the unique critical boundary, which separates the effective regions of the HSS and HRB modes, is constructed and found to be dependent on Js, Jb, and α̃. The examinations of the subordinate eigenfunctions indicate that the shear instability is well developed in the HSS mode, in which the large vortex structures may prevail and suppress the formation of convective rolls; the shear instability in the HRB mode is either “partly developed” when Jb<Jb,cr or “undeveloped” when Jb>Jb,cr, thus only plays a secondary role to modify the dominant convective rolls, and as Jb increases, the eigenfunctions of the HSS mode exhibit different transitional behaviors in the two regions, signifying the “shear enhancement” and “shear sheltering” of the entrainment of buoyancy flux.

Hybrid rayleigh–van der pol–duffing oscillator: Stability analysis and controller

The current study examines the hybrid Rayleigh–Van der Pol–Duffing oscillator (HRVD) with a cubic–quintic nonlinear term and an external excited force. The Poincaré–Lindstedt technique is adapted to attain an approximate bounded solution. A comparison between the approximate solution with the fourth-order Runge–Kutta method (RK4) shows a good matching. In case of the autonomous system, the linearized stability approach is employed to realize the stability performance near fixed points. The phase portraits are plotted to visualize the behavior of HRVD around their fixed points. The multiple scales method, along with a nonlinear integrated positive position feedback (NIPPF) controller, is employed to minimize the vibrations of the excited force. Optimal conditions of the operation system and frequency response curves (FRCs) are discussed at different values of the controller and the system parameters. The system is scrutinized numerically and graphically before and after providing the controller at the primary resonance case. The MATLAB program is employed to simulate the effectiveness of different parameters and the controller on the system. The calculations showed that NIPPF is the best controller. The validations of time history and FRC of the analysis as well as the numerical results are satisfied by making a comparison among them.

Amplitude Equations and Bifurcation Diagrams for Multifrequency Synchronization of Canonical-Dissipative Oscillators

Coupled systems of two canonical-dissipative limit cycle oscillators are considered in the general case and for the case of monofrequency and multifrequency synchronization. Specifically, the oscillator frequency ratios of 1:1, 1:2, and 1:3 are examined and modeled by a hybrid Rayleigh–van der Pol oscillator and an oscillator model suggested by Holt as well as an oscillator model suggested by Fokas and Lagerstrom. It is shown that all three systems exhibit a unique bifurcation diagram that describes limit cycle attractors of monofrequency and multifrequency synchronization. In particular, the relative phase describing the lag between the two oscillators both in the monofrequency and multifrequency case can be tuned by an appropriately defined bifurcation parameter [Formula: see text]. For [Formula: see text] two limit cycle attractors with different relative phases exist that merge at [Formula: see text] into pitchfork bifurcations and give rise to single limit cycle attractors that continue to exist for [Formula: see text]. Similarities and differences to bifurcation diagrams published in previous work of a similar coupled oscillator system, one based on Smorodinsky–Winternitz potentials and exhibiting 1:1 synchronization, are noted.

Position and Velocity Time Delay for Suppression Vibrations of a Hybrid Rayleigh-Van der Pol-Duffing Oscillator

In this paper, we used time delay feedback to minimize the vibrations of a hybrid Rayleigh–van der Pol–Duffing oscillator. This system is a one-degree-offreedom containing the cubic and fifth nonlinear terms and an external force. We applied the multiple scales method to get the solution from first approximation. Graphically and numerically, we studied the system before and after adding time delay feedback at the primary resonance case (Ω ≌ ω). We used MATLAB program to simulate the efficacy of different parameters and the time delay on the main system.

A hybrid Rayleigh and Weibull distribution model for the short-term motion response prediction of moored floating structures

Nonlinearities inherent in the dynamic system lead the motion response of moored floating structure to be non-Gaussian processes, and the short-term motion response prediction based on Rayleigh distribution therefore becomes inaccurate. This paper proposes a probability density function (PDF), termed as the hybrid Rayleigh and Weibull distribution (HRW), to accurately characterize the probability distribution of motion amplitude of moored floating structures. In the HRW model, the Rayleigh distribution is adopted to depict wave frequency (WF) motion amplitude, and the Weibull distribution is employed to describe low frequency (LF) motion amplitude. Since the probability contribution of WF and LF motion amplitude in total motion amplitude depends on the occurrence frequency of WF and LF motion amplitude, a weighting factor related to the mean up-crossing rate of WF and LF motion response is introduced in the HRW model to combine the Rayleigh and Weibull distribution. The proposed HRW model can consider the statistical interference effects of WF and LF motion, and has an advantage of characterizing WF and LF motion amplitude simultaneously. To verify the effectiveness of the proposed HRW model, a case study for a moored semi-submersible was conducted. Numerical calculation results indicate that the proposed HRW model not only yields accurate short-term motion response prediction but also has robustness under severe sea states.

Air Release and Cavitation Modeling with a Lumped Parameter Approach Based on the Rayleigh–Plesset Equation: The Case of an External Gear Pump

In this paper, a novel approach for the simulation of cavitation and aeration in hydraulic systems using the lumped parameter method is presented. The presented approach called the Hybrid Rayleigh–Plesset Equation model is derived from the Rayleigh–Plesset Equation representative of bubble dynamics and overcomes several shortcomings present in existing lumped parameter based cavitation modeling approaches. Models based on static approximations do not consider the non-equilibrium effects of phase change on the system and incorrectly predict the system dynamics. On the other hand, the existing dynamic cavitation modeling strategies account for the non-equilibrium effects of phase change but express the evolution of phases through approximations of the Rayleigh–Plesset Equation (such as exclusion of nonlinear interactions in bubble dynamics), which often lead to physically unrealistic time-scales of bubble growth or dissolution. This paper presents a dynamic model for cavitation which is capable of predicting cavitation in hydraulic systems while preserving the nonlinear dynamics arising from the Rayleigh–Plesset Equation. The derived model determines the evolution of phases in terms of physically realizable parameters such as the bubble radius and the nuclei density, which can be estimated or determined experimentally. The paper demonstrates the effectiveness of the derived modeling approach with the help of numerical simulations of an External Gear Machine. Results from the simulations employing the proposed model are compared with an existing dynamic cavitation modeling approach and validated with experimental results over a range of dynamic parameters.

Nonlinear dynamics of a $$\varvec{\phi ^6}-$$ ϕ 6 - modified Duffing oscillator: resonant oscillations and transition to chaos

The nonlinear dynamics of a hybrid Rayleigh–Van der Pol–Duffing oscillator includes pure and impure quadratic damping are investigated. The multiple timescales method is used to study exhaustively various resonances states. It is noticed that the system presents nine resonances states. The frequency response curves of quintic, third and second superharmonic, and subharmonic resonances states are obtained. Bistability, hysteresis, and jump phenomenon are also obtained. It is pointed out that these resonance phenomena are strongly related to the nonlinear cubic and quadratic damping and to the external force. The numerical simulations are used to make bifurcation sequences displayed by the model for each type of oscillatory. It is noticed that the pure quadratic, impure cubic damping, and external excitation affect regular and chaotic states.

Experimental researches of the hybrid Rayleigh step bearing

The experimental researches for hybrid Rayleigh step bearing at the different regimes of exploitation are investigated. Comparative analysis and the analysis of test data with theoretical calculations of the bearing static characteristics on the basis of thermohydrodynamic lubrication equalizations were carried out. The fundamental aspects of the test, concerning to hybrid bearing, the test procedure at the experimental facility, installed sensors taring, controlling and reading are determined

Identification of constitutive properties of a laminated rotor at rest through a condensed modal functional

Predicting the dynamic behavior of laminated rotors in bending requires the identification of the bending rigidity of the laminated core. An identification of constitutive properties is proposed on the rotor at rest, which is a first step for rotordynamics prediction. Modal parameters predicted and measured are included in a functional based on a hybrid Rayleigh quotient and combined with the Guyan method, the master degrees of freedom corresponding to the measurement points. The laminated core rigidity is extracted through a Levenberg-Marquardt minimization.

Hybrid Rayleigh, Raman and two‐photon excited fluorescence spectral confocal microscopy of living cells

AbstractA hybrid fluorescence–Raman confocal microscopy platform is presented, which integrates low‐wavenumber‐resolution Raman imaging, Rayleigh scatter imaging and two‐photon fluorescence (TPE) spectral imaging, fast ‘amplitude‐only’ TPE‐fluorescence imaging and high‐spectral‐resolution Raman imaging. This multi‐dimensional fluorescence–Raman microscopy platform enables rapid imaging along the fluorescence emission and/or Rayleigh scatter dimensions. It is shown that optical contrast in these images can be used to select an area of interest prior to subsequent investigation with high spatially and spectrally resolved Raman imaging. This new microscopy platform combines the strengths of Raman ‘chemical’ imaging with light scattering microscopy and fluorescence microscopy and provides new modes of correlative light microscopy. Simultaneous acquisition of TPE hyperspectral fluorescence imaging and Raman imaging illustrates spatial relationships of fluorophores, water, lipid and protein in cells. The fluorescence–Raman microscope is demonstrated in an application to living human bone marrow stromal stem cells. Copyright © 2009 John Wiley & Sons, Ltd.