Auto-parametric resonance of a continuous-beam-bridge model under two-point periodic excitation:an experimental investigation and stability analysis

The auto-parametric resonance of a continuous-beam bridge model subjected to a two-point periodic excitation is experimentally and numerically investigated in this study.An auto-parametric resonance experiment of the test model is conducted to observe and measure the auto-parametric resonance of a continuous beam under a two-point excitation on columns.The parametric vibration equation is established for the test model using the finite-element method.The auto-parametric resonance stability of the structure is analyzed by using Newmark's method and the energy-growth exponent method.The effects of the phase difference of the two-point excitation on the stability boundaries of auto-parametric resonance are studied for the test model.Compared with the experiment,the numerical instability predictions of auto-parametric resonance are consistent with the test phenomena,and the numerical stability boundaries of auto-parametric resonance agree with the experimental ones.For a continuous beam bridge,when the ratio of multipoint excitation frequency(applied to the columns)to natural frequency of the continuous girder is approximately equal to 2,the continuous beam may undergo a strong auto-parametric resonance.Combined with the present experiment and analysis,a hypothesis of Volgograd Bridge's serpentine vibration is discussed.

Entropic noise induced stability and double entropic stochastic resonance induced by correlated noises

For the activated dynamics of a Brownian particle moving in a confined system with the presence of entropic barriers, this paper investigates a periodic driving and correlations between two noises. Within the two-state approximation, the explicit expressions of the mean first passage time （MFPT） and the spectral power amplification （SPA） axe obtained, respectively. Based on the numerical computations, it is found that： （i） The MFPT as a function of the noise intensity exhibits a maximum with the positive correlations between two noises （λ〉0）, this maximum for MFPT shows the characteristic of the entropic noise induced stability （ENIS） effect. The intensity A of correlations between two noises can enhance the ENIS effect. （ii） The SPA as a function of the noise intensity exhibits a double-peak by tuning the noise correlation intensity λ, i.e., the existence of a double-peak behaviour is the identifying characteristic of the double entropic stochastic resonance phenomenon.

Multiple Resonance and Stability of a Motor-elastic Linkage Mechanism System

The dynamics of a three-phase AC motor-elastic linkage mechanism system is considered. Taking the drive motor and the linkage mechanism as an integrated system, the coupling dynamic equations of the system are established by the finite element method. The multiple resonance and its stability of the system are studied using the method of multiple scales. The first order approximate solutions of the multiple resonance of the system are obtained. An algorithm for determining the stability of resonance is derived. The studies show that the multiple resonance and its stability of the system are not only related to the structure parameters of the linkage mechanism, but also to the electromagnetism parameters of the motor. At last, an experiment is given to verify the results of the theoretical analysis.

Study of Stability and Vibration Reduction in Multi-Tool Ultrasonic Machining under Simultaneous Primary and Internal Resonance

The main object of this paper is the mathematical study of the vibration behavior in ultrasonic machining (USM) described by non-linear differential equations. The ultrasonic machining (USM) consists of the tool holder and the absor-bers representing the tools. This leads to four-degree-of-freedom system subject to multi-external excitation forces. The aim of this project is the reduction of the vibrations in the tool holder and have reasonable amplitudes for the tools represented by the multi-absorbers. Multiple scale perturbation method is applied to obtain the solution up to the second order approximation and to study the stability of the steady state solution near different simultaneous resonance cases. The resulting different resonance cases are reported and studied numerically. The stability of the steady state solution near the selected resonance cases is studied applying both frequency response equations and phase-plane technique. The effects of the different parameters of the system and the absorbers on the system behavior are studied numerically. Optimum working conditions for the tools were obtained. Comparison with the available published work is reported.

Innovate combination of sevoflurane dilution in dimethyl sulfoxide: A stability study by gas chromatography and nuclear magnetic resonance

To investigate physicochemical stability of sevofuranein dimethyl sulfoxide using gas chromatography with a fame ionization detector and nuclear magnetic reso-nance （NMR）.METHODSUndiluted sevoflurane, plus dilutions 1：2, 1：5, 1：10, 1：25, and 1：50 in dimethyl sulfoxide were prepared in a vertical laminar fow cabinet class Ⅱ type B and stored at different temperatures （23 ℃, 6 ℃, and -10 ℃） for 45 d. Sterile 1 mL polypropylene amber syringes to minimize light degradation, caps and needles were used. The presence of sevofurane and its degradation products in the samples was determined by gas chroma-tography with flame ionization detector （260 ℃, 40min）, and by 1H, 19F, and proton-decoupled 19F nuclearmagnetic resonance.RESULTS The gas chromatography analysis showed sevofluraneand dimethyl sulfoxide （DMSO） retention times were 2.7and 13.0 min, respectively. Pure DMSO injection into thecolumn resulted in two additional peaks at 2.1 and 2.8min. The same sevofurane peak at 2.7 min was observedin all the dilutions at -10 ℃, 4 ℃ and 25 ℃. The NMRspectra showed signals consistent with the sevoflurane structure in all the dilutions at -10 ℃, 4 ℃ and 25 ℃. In the 1H spectrum, two signals corresponding to the sevoflurane molecule were observed at 5.12 and 4.16 parts per million （ppm5）. In the 19F-NMR spectrum, two signals were observed at -76.77 ppm and -157.13 ppm. In the 19F NMR CPD, two signals were observed at -76.77 ppm and -157.13 ppm. The first one showed a doublet （JF-F = 3.1 Hz） which integrated by six fluorine nuclei from the hexafluoro-isopropyl group. The second signal was integrated by a fuorine atom and showed a septuplet （JF-F = 3.1 Hz）.CONCLUSIONThis study shows that different concentrations ofsevofurane in dimethyl sulfoxide retain their chemicalcomposition after exposure to different temperaturesfor a period of 45 d.

Improving the UV-light stability of silicon heterojunction solar cells through plasmon-enhanced luminescence downshifting of YVO_(4):Eu^(3+),Bi^(3+)nanophosphors decorated with Ag nanoparticles

The ultraviolet(UV)light stability of silicon heterojunction(SHJ)solar cells should be addressed before large-scale production and applications.Introducing downshifting(DS)nanophosphors on top of solar cells that can convert UV light to visible light may reduce UV-induced degradation(UVID)without sacrificing the power conversion efficiency(PCE).Herein,a novel composite DS nanomaterial composed of YVO_(4):Eu^(3+),Bi^(3+)nanoparticles(NPs)and AgNPs was synthesized and introduced onto the incident light side of industrial SHJ solar cells to achieve UV shielding.The YVO_(4):Eu^(3+),Bi^(3+)NPs and Ag NPs were synthesized via a sol-gel method and a wet chemical reduction method,respectively.Then,a composite structure of the YVO_(4):Eu^(3+),Bi^(3+)NPs decorated with Ag NPs was synthesized by an ultrasonic method.The emission intensities of the YVO_(4):Eu^(3+),Bi^(3+)nanophosphors were significantly enhanced upon decoration with an appropriate amount of~20 nm Ag NPs due to the localized surface plasmon resonance(LSPR)effect.Upon the introduction of LSPR-enhanced downshifting,the SHJ solar cells exhibited an~0.54%relative decrease in PCE degradation under UV irradiation with a cumulative dose of 45 k W h compared to their counterparts,suggesting excellent potential for application in UV-light stability enhancement of solar cells or modules.

Highly sensitive and stable probe refractometer based on configurable plasmonic resonance with nano-modified fiber core

A dispersion model is developed to provide a generic tool for configuring plasmonic resonance spectral characteristics.The customized design of the resonance curve aiming at specific detection requirements can be achieved.According to the model,a probe-type nano-modified fiber optic configurable plasmonic resonance(NMF-CPR)sensor with tip hot spot enhancement is demonstrated for the measurement of the refractive index in the range of 1.3332-1.3432 corresponding to the low-concentration biomarker solution.The new-type sensing structure avoids excessive broadening and redshift of the resonance dip,which provides more possibilities for the surface modification of other functional nanomaterials.The tip hot spots in nanogaps between the Au layer and Au nanostars(AuNSs),the tip electric field enhancement of AuNSs,and the high carrier mobility of the WSe_(2)layer synergistically and significantly enhance the sensitivity of the sensor.Ex-perimental results show that the sensitivity and the figure of merit of the tip hot spot enhanced fiber NMF-CPR sensor can achieve up to 2995.70 nm/RIU and 25.04 RIU^(−1),respectively,which are 1.68 times and 1.29 times higher than those of the conventional fiber plasmonic resonance sensor.The results achieve good agreements with numerical simulations,demonstrate a better level compared to similar reported studies,and verify the correctness of the dispersion model.The detection resolution of the sensor reaches up to 2.00×10^(−5)RIU,which is obviously higher than that of the conventional side-polished fiber plasmonic resonance sensor.This indicates a high detection accuracy of the sensor.The dense Au layer effectively prevents the intermediate nanomaterials from shedding and chemical degradation,which enables the sensor with high stability.Furthermore,the terminal reflective sensing structure can be used as a practical probe and can allow a more convenient operation.

Dynamic stability of parametrically-excited linear resonant beams under periodic axial force

The parametric dynamic stability of resonant beams with various parameters under periodic axial force is studied. It is assumed that the theoretical formulations are based on Euler-Bernoulli beam theory. The governing equations of motion are derived by using the Rayleigh-Ritz method and transformed into Mathieu equations, which are formed to determine the stability criterion and stability regions for parametricallyexcited linear resonant beams. An improved stability criterion is obtained using periodic Lyapunov functions. The boundary points on the stable regions are determined by using a small parameter perturbation method. Numerical results and discussion are presented to highlight the effects of beam length, axial force and damped coefficient on the stability criterion and stability regions. While some stability rules are easy to anticipate, we draw some conclusions： with the increase of damped coefficient, stable regions arise; with the decrease of beam length, the conditions of the damped coefficient arise instead. These conclusions can provide a reference for the robust design of parametricallyexcited linear resonant sensors.

Elucidating solvent effects on the stability of phenoxyl radicals in monohydric alcohols via electron paramagnetic resonance

Research on solvent effects is an important and long-standing topic,but there still is some room,especially for the special solvent effect of fluoroalcohols.In this work,we investigated the stability of phenoxyl radical in monohydric alcohol solvents through in-situ electron paramagnetic resonance detections.The decay behavior of phenoxyl radical showed a reasonable relationship with the mesoscopic structure of alcohols,characterized by smalland wide-angle X-ray scattering.Moreover,the distinct solvent effects of fluoroalcohols were emphasized,and the significant influence of van der Waals distance in the solvents was suggested.Overall,the stability of phenoxyl radical in alcohols was quantified and correlated with the solvent structures.We believe that the established method for stability study on radicals will encourage solvent effect studies on various organic reactions,and the proposed solvent effects in fluoroalcohols may inspire the development of green solvents in both industrial conversions and organic synthesis.

Fiber resonator using negative-curvature anti-resonant fiber with temperature stability

The coupling efficiency of hollow-core fiber changes with temperature,which leads to the decrease of the finesse(F)of fiber resonator and limits the performance of the resonant fiber optic gyroscope(R-FOG)system.Negative-curvature antiresonant fiber(ARF)can maintain single-mode characteristics under the condition of large mode field diameter,achieve efficient and stable fiber coupling,and significantly improve the consistency of the F of the spatial coupling resonator in variable temperature environment.A new type of ARF with a mode field diameter(MFD)of 25μm is used to fabricate a fiber resonator with a length of 5.14 m.In the range of 25℃-75℃,the average F is 31.45.The ARF resonator is used to construct an R-FOG system that shows long-term bias stability(3600 s)of3.1°/h at room temperature,4.6°/h at 75℃.To our knowledge,this is the best reported index of hollow-core fiber resonator and R-FOG system within the temperature variation range of 50℃ test.

NOVEL METHOD FOR DYNAMIC OPTIMIZATION OF STABILITY IN HIGH-SPEED MILLING SYSTEM

Considering the self-excited and forced vibrations in high-speed milling processes, a novel method for dynamic optimization of system stability is used to determine the cutting parameters and structural parameters by increasing the chatter free material removal rate （CF-MRR） and surface finish. The method is hased on the theory of the chatter stability and the semi-bandwidth of the resonant region. The objective function of the method is material removal rate（MRR）,the constraints are chatter stability and surface finish, and the optimizing variables are cutting and structural parameters. The optimization procedure is stated. The method is applied to a milling system and CF-MRR is increased 18.86%. It is shown that the influences of the chatter stability and the resonance are simultaneously considered in the dynamic optimization of the milling system for increasing CF-MRR and the surface finish.

COMPARISON BETWEEN TWO ANALYTICAL MODELS OF HELICOPTER GROUND RESONANCE

The 2-dimensional equivalent model used in helicopter ground resonance analysis is convenient for its simplicity and clarity. The equivalent body mass, the stiffness and the damping are derived from the modal charaCteristics. In this paper, a 3-dimensional space model is constructed to analyse the ground resonance.There is little difference between the calculated results of the 2-dimensional equivalent model and those of the 3-dimensional space model. Hence, the 2-dimensional model is verified for the practical application. Generally, the linear lead-lag damping of the equivalent rotor blade at the modal frequency is derived from the lead-lag damper characteristics by a procedure of iteration. The transformation of the imaginary part of the complex modulus of the viscoelastic damper into a linear velocity damping is complicated in analysis. A method to use the complex modulus directly in the ground resonance analysis is derived and verified.

Principal parametric resonance of axially accelerating rectangular thin plate in magnetic field

Nonlinear parametric vibration and stability is investigated for an axially accelerating rectangular thin plate subjected to parametric excitations resulting from the axial time-varying tension and axial time-varying speed in the magnetic field. Consid- ering geometric nonlinearity, based on the expressions of total kinetic energy, potential energy, and electromagnetic force, the nonlinear magneto-elastic vibration equations of axially moving rectangular thin plate are derived by using the Hamilton principle. Based on displacement mode hypothesis, by using the Galerkin method, the nonlinear para- metric oscillation equation of the axially moving rectangular thin plate with four simply supported edges in the transverse magnetic field is obtained. The nonlinear principal parametric resonance amplitude-frequency equation is further derived by means of the multiple-scale method. The stability of the steady-state solution is also discussed, and the critical condition of stability is determined. As numerical examples for an axially moving rectangular thin plate, the influences of the detuning parameter, axial speed, axial tension, and magnetic induction intensity on the principal parametric resonance behavior are investigated.

DYNAMIC STABILITY OF AXIALLY MOVING VISCOELASTIC BEAMS WITH PULSATING SPEED

Parametric vibration of an axially moving, elastic, tensioned beam with pulsating speed was investigated in the vicinity of subharmonic and combination resonance. The method of averaging was used to yield a set of autonomous equations when the parametric excitation frequency is twice or the combination of the natural frequencies. Instability boundaries were presented in the plane of parametric frequency and amplitude. The analytical results were numerically verified. The effects of the viscoelastic damping, steady speed and tension on the instability boundaries were numerically demonsWated. It is found that the viscoelastic damping decreases the instability regions and the steady speed and the tension make the instability region drift along the frequency axis.

FLOW-INDUCED INTERNAL RESONANCES AND MODE EXCHANGE IN HORIZONTAL CANTILEVERED PIPE CONVEYING FLUID (Ⅱ)

The Newtonian method is employed to obtain nonlinear mathematical model of motion of a horizontally cantilevered and inflexible pipe conveying fluid. The order magnitudes of relevant physical parameters are analyzed qualitatively to establish a foundation on the further study of the model. The method of multiple scales is used to obtain eigenfunctions of the linear free-vibration modes of the pipe. The boundary conditions yield the characteristic equations from which eigenvalues can be derived. It is found that flow velocity in the pipe may induced the 3：1, 2：1 and 1：1 internal resonances between the first and second modes such that the mechanism of flow-induced internal resonances in the pipe under consideration is explained theoretically. The 3：1 internal resonance first occurs in the system and is, thus, the most important since it corresponds to the minimum critical velocity.

PRINCIPAL RESONANCE IN TRANSVERSE NONLINEAR PARAMETRIC VIBRATION OF AN AXIALLY ACCELERATING VISCOELASTIC STRING

To investigate the principal resonance in transverse nonlinear parametric vibration of an axially accelerating viscoelastic string,the method of multiple scales is applied directly to the nonlinear partial differential equation that governs the transverse vibration of the string.To derive the governing equation,Newton's second law,Lagrangean strain,and Kelvin's model are respectively used to account the dynamical relation,geometric nonlinearity and the viscoelasticity of the string material. Based on the solvability condition of eliminating the secular terms,closed form solutions are obtained for the amplitude and the existence conditions of nontrivial steady-state response of the principal parametric resonance.The Lyapunov linearized stability theory is employed to analyze the stability of the trivial and nontrivial solutions in the principal parametric resonance.Some numerical examples are presented to show the effects of the mean transport speed,the amplitude and the frequency of speed variation.

Three-to-one internal resonance in multiple stepped beam systems

In this study, the vibrations of multiple stepped beams with cubic nonlinearities are considered. A three-to-one internal resonance case is investigated for the system. A general approximate solution to the problem is found using the method of multiple scales （a perturbation technique）. The modulation equations of the amplitudes and the phases are derived for two modes. These equations are utilized to determine steady state solutions and their stabilities. It is assumed that the external forcing frequency is close to the lower frequency. For the numeric part of the study, the three-to-one ratio in natural frequencies is investigated. These values are observed to be between the first and second natural frequencies in the cases of the clamped-clamped and clamped-pinned supports, and between the second and third natural frequencies in the case of the pinned-pinned support. Finally, a numeric algorithm is used to solve the three-to-one internal resonance. The first mode is externally excited for the clamped-clamped and clamped-pinned supports, and the second mode is externally excited for the pinned-pinned support. Then, the amplitudes of the first and second modes are investigated when the first mode is externally excited. The amplitudes of the second and third modes are investigated when the second mode is externally excited. The force-response, damping-response, and .frequency- response curves are plotted for the internal resonance modes of vibrations. The stability analysis is carried out for these plots.

Motion Stability Analysis of Non-sinusoidal Oscillation of Mold Driven by Servomotor

The investments of the electro-hydraulic servo system of the mold non-sinusoidal oscillator are great, the modification ratio of the mechanical type is unable to be adjusted online, and some continuous casters suffer from server resonance during the casting. A mold non-sinusoidal oscillation mechanism driven by servomotor is proposed and the prototype is produced in the lab, the investment is low and the modification ratio is can be adjusted online, and the stability problem is studied. At first the dynamics model of the servomotor non-sinusoidal oscillation is established, and the kinematics differential function is deduced. Furthermore, based on the harmonic balance method, the eigenvalues of the system are solved; the criterion of the stability of the system is put forward. In addition, the eigenvalues and harmonic with different oscillating parameters are analyzed. Analytical results show that the real parts of the eigenvalues are positive, the system will be unstable, and the resonance will occur when the positive real parts of the eigenvalues are extremum. A foundation is established for solving the running smooth problem and next application of this mechanism.

Magneto-elastic combination resonances analysis of current-conducting thin plate

Based on the Maxwell equations, the nonlinear magneto-elastic vibration equations of a thin plate and the electrodynamic equations and expressions of electromagnetic forces are derived. In addition, the magneto-elastic combination resonances and stabilities of the thin beam-plate subjected to mechanical loadings in a constant transverse magnetic filed are studied. Using the Galerkin method, the corresponding nonlinear vibration differential equations are derived. The amplitude frequency response equation of the system in steady motion is obtained with the multiple scales method. The excitation condition of combination resonances is analyzed. Based on the Lyapunov stability theory, stabilities of steady solutions are analyzed, and critical conditions of stability are also obtained. By numerical calculation, curves of resonance-amplitudes changes with detuning parameters, excitation amplitudes and magnetic intensity in the first and the second order modality are obtained. Time history response plots, phase charts, the Poincare mapping charts and spectrum plots of vibrations are obtained. The effect of electro-magnetic and mechanical parameters for the stabilities of solutions and the bifurcation are further analyzed, Some complex dynamic performances such as perioddoubling motion and quasi-period motion are discussed.

CO-DIMENSION 2 BIFURCATIONS AND CHAOS IN CANTILEVERED PIPE CONVEYING TIME VARYING FLUID WITH THREE-TO-ONE INTERNAL RESONANCES

The nonlinear behavior of a cantilevered fluid conveying pipe subjected to principal parametric and internal resonances is investigated in this paper.The flow velocity is divided into constant and sinusoidal parts.The velocity value of the constant part is so adjusted such that the system exhibits 3:1 internal resonances for the first two modes.The method of multiple scales is employed to obtain the response of the system and a set of four first-order nonlinear ordinary- differential equations for governing the amplitude of the response.The eigenvalues of the Jacobian matrix are used to assess the stability of the equilibrium solutions with varying parameters.The co- dimension 2 derived from the double-zero eigenvalues is analyzed in detail.The results show that the response amplitude may undergo saddle-node,pitchfork,Hopf,homoclinic loop and period- doubling bifurcations depending on the frequency and amplitude of the sinusoidal flow.When the frequency of the sinusoidal flow equals exactly half of the first-mode frequency,the system has a route to chaos by period-doubling bifurcation and then returns to a periodic motion as the amplitude of the sinusoidal flow increases.