Resonance Case Research Articles

Resonance in the Cart-Pendulum System—An Asymptotic Approach

The major objective of this research is to study the planar dynamical motion of 2DOF of an auto-parametric pendulum attached with a damped system. Using Lagrange’s equations in terms of generalized coordinates, the fundamental equations of motion (EOM) are derived. The method of multiple scales (MMS) is applied to obtain the approximate solutions of these equations up to the second order of approximation. Resonance cases are classified, in which the primary external and internal resonance are investigated simultaneously to establish both the solvability conditions and the modulation equations. In the context of the stability conditions of these solutions, the equilibrium points are obtained and graphically displayed to derive the probable steady-state solutions near the resonances. The temporal histories of the attained results, the amplitude, and the phases of the dynamical system are depicted in graphs to describe the motion of the system at any instance. The stability and instability zones of the system are explored, and it is discovered that the system’s performance is stable for a significant number of its variables.

Unbounded solutions for asymmetric oscillations in the degenerate resonant case

In this paper, we are concerned with the existence of unbounded solutions of the asymmetric equationx″+ax+−bx−=f(t), where x+=max⁡{x,0}, x−=max⁡{−x,0}, a and b are two different positive constants satisfying 1/a+1/b=2n/m with m and n relatively prime, f(t) is a continuous 2π periodic function, and the discriminative functionΦf(θ)=∫02πC(nmθ+nt)f(nt)dt,θ∈R has some degenerate zeros, where C(t) is the solution ofx″+ax+−bx−=0 with the initial conditions C(0)=1,C′(0)=0. Especially, when a=4,b=1,f(t)=±1/45+cos⁡4t, the existence of unbounded solutions will be proved.

Eternally non-Markovian dynamics of a qubit interacting with a single-photon wavepacket

An evolution of a two-level system (qubit) interacting with a single-photon wave packet is analyzed. It is shown that a hierarchy of master equations gives rise to phase covariant qubit evolution. The temporal correlations in the input field induce nontrivial memory effects for the evolution of a qubit. It is shown that in the resonant case whenever time-local generator is regular (does not display singularities) the qubit evolution never displays information backflow. However, in general the generator might be highly singular leading to intricate non-Markovian effects. A detailed analysis of the exponential profile is provided which allows to illustrate all characteristic feature of the qubit evolution.

Amplitude resonance response and feedback control of cantilever beams with tip-mass under aerodynamic load

The dynamic of a cantilever beam with tip mass is studied under an aerodynamic loading. The effects of coupling is investigated by tacking into account the fluid flow. Using the multiple time scale method, the approximative solutions are found and the study of their stability is made by the Routh-Hurwitz stability criterion. The influence of parameters on the system is studied at the harmonic and subharmonic resonances. The results show that, the effects of tip mass can be neglected in harmonic resonance case, while they are more important in subharmonic resonance cases. The results equally demonstrate that an increase of the stable state fluid velocity reduces the amplitude of vibrations. In addition, the hysteresis phenomenon studies show that it is principally induced by nonlinearity coefficients. Finally, time-delay feedback control is applied and the effects of controlling are observed on amplitude response curve at the harmonic resonance, from where we note that optimized choice of control parameters can be useful in controlling vibrations.

Normal forms and near-axis expansions for Beltrami magnetic fields

A formal series transformation to Birkhoff–Gustavson normal form is obtained for toroidal magnetic field configurations in the neighborhood of a magnetic axis. Bishop's rotation minimizing coordinates are used to obtain a local orthogonal frame near the axis in which the metric is diagonal, even if the curvature has zeros. We treat the cases of vacuum and force-free (Beltrami) fields in a unified way, noting that the vector potential is essentially the Poincaré–Liouville one-form of Hamiltonian dynamics, and the resulting magnetic field corresponds to the canonical two-form of a non-autonomous one-degree-of-freedom system. Canonical coordinates are obtained and Floquet theory is used to transform to a frame in which the lowest order Hamiltonian is autonomous. The resulting magnetic axis can be elliptic or hyperbolic, and resonant elliptic cases are treated. The resulting expansion for the field is shown to be well-defined to all orders, and is explicitly computed to degree four. An example is given for an axis with constant torsion near a 1:3 resonance.

Interlayer exciton mediated second harmonic generation in bilayer MoS2

Second-harmonic generation (SHG) is a non-linear optical process, where two photons coherently combine into one photon of twice their energy. Efficient SHG occurs for crystals with broken inversion symmetry, such as transition metal dichalcogenide monolayers. Here we show tuning of non-linear optical processes in an inversion symmetric crystal. This tunability is based on the unique properties of bilayer MoS2, that shows strong optical oscillator strength for the intra- but also interlayer exciton resonances. As we tune the SHG signal onto these resonances by varying the laser energy, the SHG amplitude is enhanced by several orders of magnitude. In the resonant case the bilayer SHG signal reaches amplitudes comparable to the off-resonant signal from a monolayer. In applied electric fields the interlayer exciton energies can be tuned due to their in-built electric dipole via the Stark effect. As a result the interlayer exciton degeneracy is lifted and the bilayer SHG response is further enhanced by an additional two orders of magnitude, well reproduced by our model calculations. Since interlayer exciton transitions are highly tunable also by choosing twist angle and material combination our results open up new approaches for designing the SHG response of layered materials.

Theoretical modeling on the combination resonance of size-dependent microbeams

The combination resonance of size-dependent microbeams is investigated. Two harmonic forces act on the microbeam, and combination resonance is observed while the excitation frequencies differ from the resonant frequency. Microbeams with two different sources of nonlinearities including three kinds of boundary conditions, clamped-free (nonlinearity comes from large curvature and nonlinear inertial), clamped-clamped, and hinged-hinged (nonlinearity originates from mid-plane stretching-bending coupling), are taken into consideration to have a deep understanding of this phenomenon. A traveling load acting on the microbeam is presented as a special case of combination resonance. The modal discretization technique is applied to discretize the equations of motion, and then the Lindstedt–Poincare method, a perturbation approach, is employed to solve the resultant equations. The conditions for combination resonance are presented, and frequency-response curves and time histories at the resonance point are obtained for microbeams of each boundary condition. Results reveal that different sources of nonlinearities result in different performances of combination resonance. The free vibration part constitutes a large percentage of the final response. Furthermore, the situation of coexistence of combination resonance and superharmonic (or subharmonic) resonance is determined. The special case demonstrates a higher amplitude than the common combination resonance for all the boundary conditions. Parametric studies are then carried out to discuss the effects of the length scale parameter, excitation force as well as its position, and damping on the performance of the microbeam.

Unsteady aerodynamics of flexible wings in transverse gusts

Unsteady aerodynamics of two flexible cantilevered wings in transverse gusts has been studied by means of force, velocity, and deformation measurements. The first bending frequencies of the wings were in the range of gust frequencies tested. The deformation measurements revealed that plunge angle due to the bending deflections is generally small. However, it becomes large at the resonant conditions and significantly attenuates the amplitude of the effective gust angle perceived by the wing, although the unsteady lift is difficult to measure accurately for the resonant cases. As the gust frequency increases, the more flexible wing experiences more separated flow during the cycle. Nevertheless, for both flexible wings, the lift amplitude normalized by the gust amplitude is smaller than those of the rigid wings with separated flows. When the maximum effective angle of attack is smaller than a critical value, the lift amplitude normalized by the gust amplitude is close to the theoretical predictions for attached flows and the effect of the gust reduced frequency is small. In contrast, above the critical value of the maximum effective angle of attack, the normalized lift can be amplified or attenuated, depending on the gust reduced frequency.

Enhanced Vibration Isolation with Prestressed Resonant Auxetic Metamaterial.

Metamaterials designate structures with properties exceeding bulk materials. Since the end of the 1990s, they have attracted ever-growing attention in many research fields such as electromagnetics, acoustics, and elastodynamics. This paper presents a numerical and experimental study on a locally resonant auxetic metamaterial for vibration isolation. The designed materials combine different mechanisms—such as buckling, local resonances, and auxetism—to generate enhanced isolation properties. This type of structure could help to improve the isolation for machines, transportation, and buildings. First, the static properties of the reference and resonant structures are compared. Dispersion curves are then analysed to describe their periodic dynamic behaviour. An experimental validation carried out on a specially designed test bench is then presented and compared to corresponding finite structure simulation. As a result, huge bandgaps are found for the resonant case and strong isolation properties are also confirmed by the experimental data.

Bifurcation study on a degenerate double van der Waals cirque potential energy surface using Lagrangian descriptors

In this paper, we explore the dynamics of a Hamiltonian system after a double van der Waals potential energy surface degenerates into a single well. The energy of the system is increased from the bottom of the potential well up to the dissociation energy, which occurs when the system becomes open. In particular, we study the bifurcations of the basic families of periodic orbits of this system as the energy increases using Lagrangian descriptors and Poincaré maps. We investigate the capability of Lagrangian descriptors to find periodic orbits of bifurcating families for the case of resonant, saddle–node and pitchfork bifurcations.

Заболеваемость несовершеннолетних правонарушителей в Хабаровском крае и ЕАО

Recently, resonant cases have often arisen with the participation of children who commit unlawful acts. Participants in these crimes are most often children - victims of social maladjustment and child neglect, who are subject to an increased risk of the prevalence and severity of diseases (compared to the child population as a whole) due to the unfavorable socio-economic background of their life and upbringing, due to their aggravated socio-medical history of their parents. As a rule, these children elude the attention of the district out-patient clinic service: they fundamentally refuse to visit a pediatrician at an early stage of the development of the disease and undergo preventive medical examinations, which subsequently leads to a greater burden of somatic morbidity

Analyzing the Stability for the Motion of an Unstretched Double Pendulum near Resonance

This work looks at the nonlinear dynamical motion of an unstretched two degrees of freedom double pendulum in which its pivot point follows an elliptic route with steady angular velocity. These pendulums have different lengths and are attached with different masses. Lagrange’s equations are employed to derive the governing kinematic system of motion. The multiple scales technique is utilized to find the desired approximate solutions up to the third order of approximation. Resonance cases have been classified, and modulation equations are formulated. Solvability requirements for the steady-state solutions are specified. The obtained solutions and resonance curves are represented graphically. The nonlinear stability approach is used to check the impact of the various parameters on the dynamical motion. The comparison between the attained analytic solutions and the numerical ones reveals a high degree of consistency between them and reflects an excellent accuracy of the used approach. The importance of the mentioned model points to its applications in a wide range of fields such as ships motion, swaying buildings, transportation devices and rotor dynamics.

Instability in large bounded domains—branched versus unbranched resonances

We study transitions from convective to absolute instability near a trivial state in large bounded domains for prototypical model problems in the presence of transport and negative nonlinear feedback. We identify two generic scenarios, depending on the nature of the linear mechanism for instability, which both lead to different, universal bifurcation diagrams. In the first, classical case of a linear branched resonance the transition is hard, that is, small changes in a control parameter lead to a finite-size state. In the second, novel case of an unbranched resonance, the transition is gradual. In both cases, the bifurcation diagram is determined by interaction of the leading edge of an invasion front with upstream boundary conditions. Technically, we analyze this interaction in a heteroclinic gluing bifurcation analysis that uses geometric desingularization of the trivial state.

Energy transport in degenerate anisotropic electron plasma

AbstractDegenerate plasmas have gained increasing attention in the last decade due to their great importance in various areas of physics, such as semiconductors, metals, microelectronics, and carbon nanotubes, and in the astrophysical environments. In this article, energy transport of right circularly polarized wave (RCPW) is studied in anisotropic degenerate plasma. The energy flux is examined for both the limits: resonant and non‐resonant. We discuss how the energy flux is significantly affected by degenerate temperature anisotropy. It is found that the RCPW transfers its energy rapidly when the parallel temperature is larger than the perpendicular temperature. Moreover, it is also found that the wave delivers its energy over a longer distance in the resonant case as compared with the non‐resonant. The results obtained in this investigation may have application for laboratory degenerate plasmas.

Multiple Series Representations of N-fold Mellin-Barnes Integrals.

Mellin-Barnes (MB) integrals are well-known objects appearing in many branches of mathematics and physics, ranging from hypergeometric functions theory to quantum field theory, solid-state physics, asymptotic theory, etc. Although MB integrals have been studied for more than one century, until now there has been no systematic computational technique of the multiple series representations of N-fold MB integrals for N>2. Relying on a simple geometrical analysis based on conic hulls, we show here a solution to this important problem. Our method can be applied to resonant (i.e., logarithmic) and nonresonant cases and, depending on the form of the MB integrand, it gives rise to convergent series representations or diverging asymptotic ones. When convergent series are obtained, the method also allows, in general, the determination of a single "master series" for each series representation, which considerably simplifies convergence studies and/or numerical checks. We provide, along with this Letter, a Mathematica implementation of our technique with examples of applications. Among them, we present the first evaluation of the hexagon and double box conformal Feynman integrals with unit propagator powers.

On Oscillating Solutions of a Countable System of Differential Equations in the Resonance Case

On Oscillating Solutions of a Countable System of Differential Equations in the Resonance Case

Thermoplasmonics of metal layers and nanoholes

Since the early 2000s, the experimental and theoretical studies of photothermal effects in plasmonics have been mainly oriented toward systems composed of nanoparticles, mostly motivated by applications in biomedecine, and have overlooked the case of plasmonic resonances of nanoholes in metal layers (also called nanopores or nano-apertures). Yet, more and more applications based on plasmonic nanoholes have been reported these last years (e.g., optical trapping, molecular sensing, and surface-enhanced Raman scattering), and photothermal effects can be unexpectedly high for this kind of systems, mainly because of the very large amount of metal under illumination, compared with nanoparticle systems. Nanoholes in metal layers involve a fully different photothermodynamical picture, and few of what is known about nanoparticles can be applied with nanoholes. A plasmonic nanohole mixes localized and surfaces plasmons, along with heat transport in a two-dimensional highly conductive layer, making the underlying photothermodynamical physics particularly complex. This Tutorial is aimed to provide a comprehensive description of the photothermal effects in plasmonics when metal layers are involved, based on experimental, theoretical, and numerical results. Photothermal effects in metal layers (embedded or suspended) are first described in detail, followed by the study of nanoholes, where we revisit the concept of absorption cross section and discuss the influences of parameters such as layer thickness, layer composition, nanohole size and geometry, adhesion layer, thermal radiation, and illumination wavelength.

Polarization characteristics of the transmitted light in a graphene planar dielectric structure

In a planar multilayer dielectric structure with graphene inserted as a boundary surface current, the optical transport properties for the transverse electric/magnetic mode have been investigated using the matrix transfer method . When an arbitrarily polarized wave transmits through the dielectric layers, the phase difference of the transmitted light between two vertical polarization directions at the terahertz frequency region is variable. The similar dependence of phase difference at zero points on the graphene Fermi energy and the number of graphene layers offers an efficient and reliable experiment method for identifying graphene flakes. The graphene broadening width can be applied to tune the value of the phase difference, but not the positions with zero phase difference. The ellipticity can be determined by the phase difference and the incident linearly polarized direction. This phenomenon is similar to the presence of the cyclotron resonance case in a traditional two dimensional electron gas . • The elliptically polarized wave is obtained in linearly polarized incident light. • The phases of the transmitted wave are different for pure TE/TM mode. • Graphene systematic parameters can be determined via the phase difference. • Proposing an efficient experiment way for identifying graphene flakes.

Study of a Stripper Header for Grain Harvesting as a Vibrating System

Introduction. Grain losses caused by stripping defects are the main problem to be solved in designing a stripper header. To reduce these losses, a design of a stripper header with a vibration drive is proposed. This device combines the processes of stripping grain crops and the vibration effect of the stripping fingers upon the ears of plants. The most important stage of the mathematical description of these processes is composing the differential equation of the stripping fingers motion. Materials and Methods. A computational-graphic diagram of an oscillatory system with one degree of freedom is proposed. To compose the differential equation of the stripping fingers motion, a method based on the application of the Lagrange equation was used. The oscillations of the system under studying arise from the motion of a point in the system according to a given law. The problem of kinematic excitation is reduced to the problem of force perturbation. This stage of the study was carried out without taking into account the resistance forces. Results. An equation for motion of stripping fingers making vibrational reciprocating movements is obtained. It is proposed to select the elastic element in the design scheme and consider a more general case of the stripping fingers movement. In this case, the movement of the stripping fingers is considered to be difficult. A characteristic feature of the mathematical description is the presence of a generalized force of potential forces. The differential equation of motion of a comb in the presence of an elastic element and the solution of this equation are composed. Discussion and Conclusion. Forced oscillations of a system without resistance, excited by a harmonic disturbing force, are harmonic oscillations with constant amplitude. On close values of the angular frequency of vibration of the drive output link and the root of the ratio of the stiffness coefficient of the elastic element to the stripping fingers mass, the case of resonance takes place. The system parameters must be selected so as to avoid this negative phenomenon.

Fano resonance for applications

Fano resonance is a universal phenomenon observed in many areas where wave propagation and interference are possible. Fano resonance arises from the interference of broad and narrow spectra of radiation and becomes an important tool for many applications in the physical, chemical, and biological sciences. At the beginning of this paper, we consider Fano resonances in individual particles, primarily of spherical and cylindrical shapes, and discuss their connection with the physics of bound states in the continuum that determine the high quality factors of resonators. Further, we discuss two areas in which structures with Fano resonances have already found or will find real application in the nearest future—sensors and lasers. The penultimate section concerns our future, which will be associated with the complete replacement of electronic processing, transmission, and storage of information with optical devices as many hope. It is believed that this sophisticated goal can be achieved with devices that implement the slow-light regime associated with the phenomenon of electromagnetically induced transparency, which can be considered as a special case of Fano resonance. The review completes with one more promising topic related to quantum electrodynamics in structures with Fano cavities.