Excitation Of Parametric Resonance Research Articles

Graviton to photon conversion via parametric resonance

We study the parametric resonance excitation of the electromagnetic field by a gravitational wave. We show that there is narrow band resonance. For an electromagnetic field in the vacuum the resonance occurs only in the second band, and its strength is thus suppressed by two powers of amplitude of the gravitational wave. On the other hand, in the case of an electromagnetic field in a medium with the speed of light smaller than 1 (in natural units), there is a band of Fourier modes which undergo resonance in the first band.

Asymptotics of Long Standing Waves in One-Dimensional Basins with Shallow Coasts: Theory and Experiment

We construct time-periodic asymptotic solutions of the one-dimensional system of nonlinear shallow water equations in a basin of variable depth \(D\left( x \right)\) with two shallow coasts (which means that the function \(D\left( x \right)\) vanishes at the points defining the coast) or with one shallow coast and a vertical wall. Such solutions describe standing waves similar to the well-known Faraday waves in basins with vertical walls. In particular, they approximately describe seiches in elongated basins. The construction of such solutions consists of two stages. First, time-harmonic exact and asymptotic solutions of the linearized system generated by the eigenfunctions of the operator \(d{\text{/}}dxD(x)d{\text{/}}dx\) are determined, and then, using a recently developed approach based on the simplification and modification of the Carrier–Greenspan transformation, solutions of nonlinear equations are reconstructed in parametric form. The resulting asymptotic solutions are compared with experimental results based on the parametric resonance excitation of waves in a bench experiment.

Excitation of the σl_l = 90° resonance by the cavity rf accelerating fields

In rf linacs the longitudinal focalization is done by si-nusoidal forces and at high accelerating fields the zero-current longitudinal phase advance per longitudinal fo-cusing period σ0l_l can be high. The nonlinear compo-nents of the sinusoidal rf field (sextupolar, octupolar and higher order components) can then excite parametric resonances, including the 4th-order resonance (σl_l = 90°) when σ0l_l is higher than 90°, inducing strong longitudinal emittance growths and acceptance reductions. As pointed out in previous papers, the longitudinal beam dynamics is therefore complex, even when the space-charge forces are ignored. The parametric resonance excitation by the rf field is analyzed before discussing the additional effect of the space-charge forces, in particular to explain why the zero-current longitudinal phase advance per trans-verse focusing period σ0l_t is not a relevant parameter. Examples are given in the SPIRAL2 linac case.

Detection of thermal size-dependent dynamic instability of rotating CNTRC microbeams with damping under parametric resonance excitation

Small-scale dynamic instability analysis of a rotating nanocomposite damped microbeam reinforced with carbon nanotube exposed to a temperature growth is addressed in this research. The modified couple stress theory, along with the Timoshenko beam hypothesis is explored to develop the motion equations. The practical thermo-mechanical characteristics are determined by resorting to the modified rule for mixtures. The Chebyshev–Ritz approach is exerted on the nonlinear motion equations to achieve the discretized form of the motion equations. The influence of structural damping is integrated into the governing equations. Considering a varying rotating speed, a possible instability resulting from principal parametric resonance stimulation is examined using the Bolotin's route and the Floquet hypothesis. The influences of the material length scale constant, distribution type of carbon nanotubes, temperature, and the damping constant on the dynamic instability boundaries are investigated. The outcomes enlighten that a rotating nanocomposite microbeam with O distribution pattern for carbon nanotubes is more sensitive to the changing temperature.

Application of the Chebyshev–Ritz route in determination of the dynamic instability region boundary for rotating nanocomposite beams reinforced with graphene platelet subjected to a temperature increment

The Chebyshev–Ritz route is exploited for the sake of the examination of the principal parametric resonance instability boundary of a rotating nanocomposite beam subjected to a temperature rising. The parametric resonance excitation is because of a time varying rotational speed. It is assumed that the rotating speed oscillates harmonically about a constant value. Resorting to the Halpin–Tsai micromechanical, the practical mechanical and thermal characteristics are estimated. The Newton–Raphson scheme is utilized to determine the prestressed configuration. The structural damping influence is incorporated to the motion equations. By the assumption that the frequency of the harmonically varying term of the rotating speed is approximately twice the one of the natural frequencies, the principal parametric resonance excitation is activated. The Bolotin’s technique alongside the Floquet theory are utilized to define the instability region boundaries. The impacts of various effectual parameters including the graphene platelet weight fraction, and its dispersion pattern, the design value of the damping constant, the boundary condition type, and the rotating speed on the instability region are examined. It is inferred that by the increment of the weight fraction of the graphene platelet as well as the design value of the damping ratio, the critical excitation amplitude increases.

Methods of Parametric Resonance Excitation in the Scheme of an Optical Magnetometric Sensor

Methods of Parametric Resonance Excitation in the Scheme of an Optical Magnetometric Sensor

Possible dynamics of Josephson junction arrays connected to high-Q tank circuit

Serial Josephson junction arrays connected to high-Q tank circuit are analysed and discussed. Numerical simulation of the systems shows two possible oscillation modes above resonance frequency when the tank impedance is capacitive. These are the inphase oscillation mode and the collectively antiphase oscillation mode. This fact is responsible for complicate switching dynamics, which can block parametric resonance excitation. Stability domains of the modes depend on McCumber parameter of the junctions. Increase in this parameter is favourable to the inphase mode. When the inphased oscillations are feasible, the resonance peak-like peculiarities on IV curve and Shapiro steps can be described with the analytic theory derived earlier for one-junction case and extended over the array systems.

Electro-thermal excitation of parametric resonances in double-clamped micro beams

We report on a simple yet efficient approach allowing direct electrothermal excitation of parametric resonance (PR) in double-clamped flexible nano- and microscale beams. The application of a time-harmonic voltage between the beam's ends leads to the electric current and Joule's heating of the entire beam, which induces a time-periodic axial stress and results in excitation of the structure lateral vibrations through the PR mechanism. The proposed approach has an advantage, simplifying fabrication and integration and reducing the influence of residual stress, and thermal mismatch, unlike conventional piezoelectric, photothermal, or electrostatic actuation approaches, which require additional piezoelectric layers, light sources, or electrodes in the proximity of a vibrating beam. Single crystal silicon, nominally 500 μm long, 30 μm wide, and 5 μm thick beams were fabricated by deep reactive ion etching and operated at a pressure of ≈1.9 mTorr. The experimental results, consistent with the reduced order and numerical model predictions, demonstrate the feasibility of the suggested excitation scenario, which could be implemented in resonant sensors, timing devices, signal processing, and micro and nanomechanical logical elements.

Efficient primary and parametric resonance excitation of bistable resonators

We experimentally demonstrate an efficient approach to excite primary and parametric (up to the 4th) resonance of Microelectromechanical system MEMS arch resonators with large vibrational amplitudes. A single crystal silicon in-plane arch microbeam is fabricated such that it can be excited axially from one of its ends by a parallel-plate electrode. Its micro/nano scale vibrations are transduced using a high speed camera. Through the parallel-plate electrode, a time varying electrostatic force is applied, which is converted into a time varying axial force that modulates dynamically the stiffness of the arch resonator. Due to the initial curvature of the structure, not only parametric excitation is induced, but also primary resonance. Experimental investigation is conducted comparing the response of the arch near primary resonance using the axial excitation to that of a classical parallel-plate actuation where the arch itself forms an electrode. The results show that the axial excitation can be more efficient and requires less power for primary resonance excitation. Moreover, unlike the classical method where the structure is vulnerable to the dynamic pull-in instability, the axial excitation technique can provide large amplitude motion while protecting the structure from pull-in. In addition to primary resonance, parametrical resonances are demonstrated at twice, one-half, and two-thirds the primary resonance frequency. The ability to actuate primary and/or parametric resonances can serve various applications, such as for resonator based logic and memory devices.

Inner-shell magnetic dipole transition in Tm atoms: A candidate for optical lattice clocks

We consider a narrow magneto-dipole transition in the $^{169}$Tm atom at the wavelength of $1.14\,\mu$m as a candidate for a 2D optical lattice clock. Calculating dynamic polarizabilities of the two clock levels $[\text{Xe}]4f^{13}6s^2 (J=7/2)$ and $[\text{Xe}]4f^{13}6s^2 (J=5/2)$ in the spectral range from $250\,$nm to $1200\,$nm, we suggest the "magic" wavelength for the optical lattice at $807\,$nm. Frequency shifts due to black-body radiation (BBR), the van der Waals interaction, the magnetic dipole-dipole interaction and other effects which can perturb the transition frequency are calculated. The transition at $1.14\,\mu$m demonstrates low sensitivity to the BBR shift corresponding to $8\times10^{-17}$ in fractional units at room temperature which makes it an interesting candidate for high-performance optical clocks. The total estimated frequency uncertainty is less than $5 \times 10^{-18}$ in fractional units. By direct excitation of the $1.14\,\mu$m transition in Tm atoms loaded into an optical dipole trap, we set the lower limit for the lifetime of the upper clock level $[\text{Xe}]4f^{13}6s^2 (J=5/2)$ of $112\,$ms which corresponds to a natural spectral linewidth narrower than $1.4\,$Hz. The polarizability of the Tm ground state was measured by the excitation of parametric resonances in the optical dipole trap at $532\,$nm.

Excitation of parametric resonances in mechanisms with rheonomic constraints subject to the joint effect of fast and slow variations of parameters

As applied to the dynamics of machines with rheonomic constraints, the dynamic stability conditions are studied within the frequency range of parametric resonances, with due account taken of impulse and slow variations of parameters. A modification is suggested for the conditional oscillator method, and the level of dissipation is determined on its basis, which is necessary to suppress parametric resonances and eliminate the amplitude modulation of oscillations within the kinematic cycle. Given properly selected parameters, the stability conditions are demonstrated to be independent of dissipation.

Current-driven non-linear magnetodynamics in exchange-biased spin valves

This work investigates the excitation of parametric resonance in exchange-biased spin valves (EBSVs). Using a mechanical point contact, high density dc and microwave currents were injected into the EBSV sample. Observing the reflected microwave power and the small rectification voltage that develops across the contact allows detecting the current-driven magnetodynamics not only in the bulk sample but originating exclusively from the small contact region. In addition to ferromagnetic resonance (FMR), parametric resonance at twice the natural FMR frequency was observed. In contrast to FMR, this non-linear resonance was excited only in the vicinity of the point contact where current densities are high. Power-dependent measurements displayed a typical threshold-like behavior of parametric resonance and a broadening of the instability region with increasing power. Parametric resonance showed a linear shift as a function of applied dc bias which is consistent with the field-like spin-transfer torque induced by current on magnetic moments in EBSV.

Construction of screener oriented on application of parametric resonance

The problem with obtaining high efficiency screening process in the coal, metal mining, building and other industries lead to invent new constructions of the screeners. The rapid progress of screening techniques and screen design was observed in the past and nowadays the development of screen is stabilized and most of equipment produced by various machines companies is very similar. In spite of this, there is always a need to improve the performance of screens. Increase capacity and efficiency of screening process on the one hand, and decrease its ecological footprint are the main goals of development of a new screening equipment. The screening machines inventive method is parametric resonance excitation of the screen sieve mesh. The model of laboratory screener based on parametric resonance for fine granular materials is presented in this paper. The working principle of the screener is included showing, that the parametric resonance screener could obtain a complex motion of the sieve, which is desirable with processing naturally wet fine granular materials.

Acceptance of the quadrupole mass filter in the upper stability island under biharmonic excitation

Dynamic characteristics of the quadrupole mass filter (QMF) with the parametric resonance excitation of ion oscillations by a low additional HF voltage are studied by numerical methods. The upper stability island formed by instability bands that follow the isolines of stability parameters of the unperturbed first stability band is considered. Isolines of characteristic indices on the island’s parameter plane are calculated. Ion trajectories at characteristic points near the x and y island boundaries, which have the form of beats, are presented. Parameters of the ellipses are determined as functions of the initial phase at which the ions enter the HF field. These parameters are shown to be periodic with a period of π with respect to the phase shift between the main and additional HF voltages. As a result, the QMF acceptance and, consequently, transmittance have maxima as functions of the phase shift. Therefore, to increase the QMF transmittance, the biharmonic signal must be synchronized.

Vibration influence on fluid interfaces

This work concerns the vibration influence on the stability and dynamics of fluid interfaces. Resonance phenomena (Faraday ripple, parametric waves under horizontal vibrations, the stability of the interface of liquid and its saturated vapor in the near critical state) are discussed. The thresholds of excitation of parametric resonance are determined and non-linear behavior is investigated. Mean effects of high frequency vibrations with various polarizations on the behavior of planar (terrestrial conditions) and cylindrical interfaces (space conditions) are analyzed. The shape and amplitude of the relief developing on the interfaces after stability loss are defined. The mechanisms of generation of mean flows near a fluid interface by high frequency vibrations are studied. To cite this article: D.V. Lyubimov et al., C. R. Mecanique 332 (2004).

Squeezed field generation by nonlinear bounded quantum oscillators

A new, effective method of squeezing is presented, based on the parametric resonance excitation of nonlinear bounded oscillators as vibration modes of multiatomic molecules.

Modeling of particle motion in a betatron chamber during the excitation of parametric resonance by free radial oscillations

There is a dynamical modeling of the amplitudes and phases of free radial oscillations of electrons at parametric resonance. The solutions obtained are discussed and compared with the solutions found by other methods.

On the convective instability of a thermal boundary layer

When the surface temperature of a liquid is a harmonic function of time with a frequencyω, a temperature wave propagates into the liquid. The amplitude of this wave decreases exponentially with distance from the surface. The temperature oscillation is essentially concentrated in a layer of the order of (2χ/ω)1/2, where x is the thermal conductivity of the liquid (thermal boundary layer). Depending on the phase, at certain positions below the surface the temperature gradient is directed downwards and if its magnitude is sufficiently large (the magnitude is a function of the amplitude and frequency of the surface oscillations) the liquid can become unstable with respect to the onset of convection. In that case the convective motion may spread beyond the initial unstable layer. For low frequencies the stability condition can be derived from the usual static Rayleigh criterion, on the basis of the Rayleigh number and the average temperature gradient of the unstable layer. This quasi-static approach, used by Sal'nikov [1], is appropriate to those cases in which the period of the temperature oscillations is much larger than the characteristic time of the perturbations. But when these times are of the same order, the problem must be analyzed in dynamic terms. The stability problem must then be formulated as a problem of parametricresonance excitation of velocity oscillations due to the action of a variable parameter-the temperature gradient.