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.

Optical pulling force on nanoparticle clusters with gain due to Fano-like resonance

We demonstrate that,in a simple linearly-polarized plane wave,the optical pulling forces on nanoparticle clusters with gain can be induced by the Fano-like resonance.The numerical results based on the full-wave calculation show that the optical pulling forces can be attributed to the recoil forces for the nanoparticle clusters composed of dipolar nanoparticles with three different configurations.Interestingly,the recoil forces giving rise to optical pulling forces are exactly dominated by the coupling term between the electric and magnetic dipoles excited in the nanoparticle clusters,while other higherorder terms have a negligible contribution.In addition,the optical pulling force can be tailored by modulating the Fano-like resonance via either the particle size or the gain magnitude,offering an alternative freedom degree for optical manipulations of particle clusters.

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.

Explicit solution of diffusion master equation under the action of linear resonance force via the thermal entangled state representation

Using the well-behaved features of the thermal entangled state representation, we solve the diffusion master equation under the action of a linear resonance force, and then obtain the infinitive operator-sum representation of the density operator. This approach may also be effective for treating other master equations. Moreover, we find that the initial pure coherent state evolves into a mixed thermal state after passing through the diffusion process under the action of the linear resonance force.

Exciting Forces for a Wave Energy Device Consisting of a Pair of Coaxial Cylinders in Water of Finite Depth

Two coaxial vertical cylinders-one is a riding hollow cylinder and the other a solid cylinder of greater radius at some distance above an impermeable horizontal bottom,were considered.This problem of diffraction by these two cylinders,which were considered as idealization of a buoy and a circular plate,can be considered as a wave energy device.The wave energy that is created and transferred by this device can be appropriately used in many applications in lieu of conventional energy.Method of separation of variables was used to obtain the analytical expressions for the diffracted potentials in four clearly identified regions.By applying the appropriate matching conditions along the three virtual boundaries between the regions,a system of linear equations was obtained,which was solved for the unknown coefficients.The potentials allowed us to obtain the exciting forces acting on both cylinders.Sets of exciting forces were obtained for different radii of the cylinders and for different gaps between the cylinders.It was observed that changes in radius and the gap had significant effect on the forces.It was found that mostly the exciting forces were significant only at lower frequencies.The exciting forces almost vanished at higher frequencies.The problem was also investigated for the base case of no plate arrangement,i.e.,the case having only the floating cylinder tethered to the sea-bed.Comparison of forces for both arrangements was carried out.In order to take care of the radiation of the cylinders due to surge motion,the corresponding added mass and the damping coefficients for both cylinders were also computed.All the results were depicted graphically and compared with available results.

Effects of soil profile and characteristic of exciting force on propagation of ground vibrations

Ground-borne vibrations caused by vibration sources such as road traffic and construction exhibit complicated properties during propagation from the vibration source to the inside of a building. In the present paper, a numerical analysis technique for the system of vibration source and propagation path of ground vibration is developed in order to systematically determine the propagation properties of the vibration as part of developing a predictive technique for exposure evaluations by vibrations in three directions at receiving points of vibration in the human body. First, the exciting forces in three directions for input into the numerical computation are inversely-estimated by using the measured acceleration rec- ords of the measurement points, which are near the vibration source. The thin-layered element method is used for numerical computation of the ground vibration. Then, the calculation results for the ground vibration obtained by using the estimated exciting force are compared with the measured results, and the influence of the stratified structure of the ground on the exciting force and the propagation properties of the ground vibration are studied. From these results, in a prediction of the ground vibration in three directions, it is emphasized that it is necessary to consider the influence of horizontal exciting force, although attention has been paid to only the vertical exciting force for simulating ground vibration.

Characteristics of and Control over Resonance in the Electromotive Force of Electromagnetic Induction

The principles of electromagnetic induction are applied in many devices and systems, including induction cookers, transformers and wireless energy transfer;however, few data are available on resonance in the electromotive force (EMF) of electromagnetic induction. We studied electromagnetic induction between two circular coils of wire: one is the source coil and the other is the pickup (or induction) coil. The measured EMF versus frequency graphs reveals the existence of a resonance/anti-resonance in the EMF of electromagnetic induction through free space. We found that it is possible to control the system’s resonance and anti-resonance frequencies. In some devices, a desired resonance or antiresonance frequency is achieved by varying the size of the resonator. Here, by contrast, our experimental results show that the system’s resonance and anti-resonance frequencies can be adjusted by varying the distance between the two coils or the number of turns of the induction coil.

REGULARITY OF VIBRATION RESPONSE OF MECHANICAL SYSTEM UNDER AFFECT OF VARI-FREQUENCY EXCITING FORCE

The vibration response formulas of the mechanical system under the affect of thevari-frequency exciting force are deduced. It is proved by the theoretical analysis and experimentalresults that the vibration response amplitude of the mechanical system under the affect of thevari-frequency exciting force is far smaller than that under the affect of the constant frequency exciting force on condition that the exciting force amplitudes are just the same;while the vari-fre-quency rate a increases to 5 Hz per second the vibration amplitude will decrease to 10% only as lowas that under the affect of the constant frequency exciting force. All these conclusions will be of significance for revealing the mechanism of suppressing chatter in van-speed cutting and analyzing theexperimental results of sine-wave scanning exciting test.

Forced Resonance of a Slightly-Curved Hydraulic Pipe Fixed at Two Ends

The ideally straight hydraulic pipe is inexistent in reality. The initial curve caused by the manufacturing or the creep deformation during the service life will change the dynamic character of the system. The current work discusses the effect of the initial curve on the hydraulic pipe fixed at two ends for the first time. Based on the governing equation obtained via the generalized Hamilton’s principle,the potential energy changing with the height of the initial curve is discussed. The initial curve makes the potential energy curve asymmetric,but the system is always monostable. The initial curve also has very important influence on natural frequencies. It hardens the stiffness of the first natural mode at first and then has no effect on this mode after a critical value. On the contrast,the second natural frequency is constant before the critical value but increases while the height of the initial curve exceeds the critical value. On account of the initial value,the quadratic nonlinearity appears in the system. Forced resonance is very different from that of the ideally straight pipe under the same condition. Although the 2∶1 internal resonance is established by adjusting the height of the initial curve and the fluid speed,the typical double-jumping phenomenon does not occur under the initial curve given in the current work. This is very different from the straight pipe in the supercritical region. The work here claims that the initial curve of the hydraulic pipe should be taken into consideration. Besides,more arduous work is needed to reveal the dynamic characters of it.

THE ANALYSIS FOR THE AIRFLOW EXCITING-VIBRATION FORCE OF CONTROL STAGE OF STEAM TURBINE

Based on the hydrodynamics, the airflow exciting-vibration force of control stage of steam turbine is studied by using the momentum theorem. A formulation for calculating the air exciting-vibration force of the control stage of steam turbine is deduced first by using theoretical analysis method and taking all the design factors of vane and nozzles into consideration. Moreover, the exciting-vibration forces in different load cases are discussed respectively.

Resonance-Enhanced Photon Excitation Spectroscopy of the Even-Parity 3p^5（2P1/2）nl′ [K′]J （l′=1, 3） Autoionizing Rydberg States of Ar

Metastable 40Ar＊ atoms are produced in the two metastable states 3p54s [3/2]2 and 3p5 4s′ [1/2]0 in a pulsed DC discharge in a beam, and are subsequently excited to the even-parity autoionizing resonance series 3pSnp′[3/2]1,2, 3p5 np′ [1/2]1, and 3p5nf′[5/2]3 using single photon excitation with a pulsed dye laser. The excitation spectra of the even-parity autoion- izing resonance series from the metastable 40Ar＊ are obtained by recording the autoionized Ar＋ ions with time-of-flight ion detection in the photon energy range of 32500-35600 cm-1 with an experimental bandwidth of 〈0.1 cm-1. A wealth of autoionizing resonances are newly observed, from which more precise and systematic spectroscopic data of the level energies and quantum defects are derived.

Influences of Floater Motion on Gap Resonance Triggered by Focused Wave Groups

The current study investigates the hydrodynamic characteristics of gap resonance within a narrow gap formed by two adjacent boxes subjected to incident focused transient wave groups.A two-dimensional(2D)numerical wave tank based on the OpenFOAM package is utilized for this purpose.The weather-side box is fixed while the lee-side box is allowed to heave freely under wave actions.The effects of the focused wave amplitude and spectral peak period on the wave amplification within the gap,motion of the lee-side box,and wave forces(including horizontal and vertical wave forces)acting on each box are systematically examined.For comparison,another structural layout consisting of two fixed boxes is also considered.The results reveal that the release of the heave degree of freedom(DoF)of the lee-side box results in remarkably distinct resonance features.In the heave-box system,both its fluid resonant period and the period corresponding to the maximum heave displacement of the lee-side box are significantly larger(i.e.,1.6-1.7 times)than the fluid resonant period of the fixed-box system.However,the wave amplification factor inside the gap in the heave-box system is significantly lower than that in the fixed-box one.Both the variations of the maximum horizontal and vertical wave forces with the spectral peak period and their magnitudes are also significantly different between the two structural systems.

Relaxation of Ne^(1+)1s^(0)2s^(2)2p^(6)np produced by resonant excitation of an ultraintense ultrafast x-ray pulse

The creation and relaxation of double K-hole states 1s^(0)2s^(2)2p^(6)np(n≥3)of Ne^(1+)in the interaction with ultraintense ultrafast x-ray pulses are theoretically investigated.The x-ray photon energies are selected so that x-rays first photoionize1s^(22)s^(22)p^(6) of a neon atom to create a single K-hole state of 1s2s^(22)p^(6) of Ne^(1+),which is further excited resonantly to double K-hole states of ls^(0)2s^(2)2p^(6)np(n≥3).A time-dependent rate equation is used to investigate the creation and relaxation processes of 1s^(0)2s^(2)2p^(6)np,where the primary microscopic atomic processes including photoexcitation,spontaneous radiation,photoionization and Auger decay are considered.The calculated Auger electron energy spectra are compared with recent experimental results,which shows good agreement.The relative intensity of Auger electrons is very sensitive to the photon energy and bandwidth of x-ray pulses,which could be used as a diagnostic tool for x-ray free electron laser and atom experiments.

HARMONIC, SUBHARMONIC, SUPERHARMONIC, SIMULTANEOUS SUB/SUPER HARMONIC AND COMBINATION RESONANCES OF SELF-EXCITED TWO COUPLED SECOND ORDER SYSTEMS TO MULTI-FREQUENCY EXCITATION

Harmonic, subharmonic, superharmonic, simultaneous sub/super harmonic, and combination resonances of the additive type of self-excited two coupled-second order systems to multi-frequency excitation are investigated. The theoretical results are obtained by the multiple-scales method. The steady state amplitudes for each resonance are plotted, showing the influence of the different parameters. Analysis for each figure is given. Approximate solution corresponding to each type of resonance is determined. Stability analyses are carried out for each case.

Minimizing electrostatic interactions from piezoresponse force microscopy via capacitive excitation

Piezoresponse force microscopy(PFM)has emerged as one of the most powerful techniques to probe ferroelectric materials at the nanoscale,yet it has been increasingly recognized that piezoresponse measured by PFM is often influenced by electrostatic interactions.In this letter,we report a capacitive excitation PFM(ce-PFM)to minimize the electrostatic interactions.The effectiveness of ce-PFM in minimizing electrostatic interactions is demonstrated by comparing the piezoresponse and the effective piezoelectric coefficient measured by ce-PFM and conventional PFM.The effectiveness is further confirmed through the ferroelectric domain pattern imaged via ce-PFM and conventional PFM in vertical modes,with the corresponding domain contrast obtained by ce-PFM is sharper than conventional PFM.These results demonstrate ce-PFM as an effective tool to minimize the interference from electrostatic interactions and to image ferroelectric domain pattern,and it can be easily implemented in conventional atomic force microscope(AFM)setup to probe true piezoelectricity at the nanoscale.

Unnatural parity resonance states in positron-excited hydrogen scattering

The coupled-channels optical method for positron scattering has been applied to investigate resonance states with unnatural parities in a positron-excited hydrogen system. The positronium formation channels and continuum channel are included via a complex equivalent local potential. Resonance states with angular momenta L =- 1 to L = 2 and parities （-1）L＋1 are calculated. Resonance energies and widths are reported and compared with other theoretical calculations. We found that the opening positronium formation channels play an important role in forming nondipole Feshbach resonances.

Seismic evaluation of frequency influence and resonant behavior for lead rubber bearing isolated rigid rectangular liquid tanks

The seismic behavior of a partially filled rigid rectangular liquid tank is investigated under short-and longduration ground motions.A finite element model is developed to analyze the liquid domain by using four-noded quadrilateral elements.The competency of the model is verified with the available results.Parametric studies are conducted for the dynamic parameters of the base-isolated tank,using a lead rubber bearing to evaluate the optimum damping and time period of the isolator.The application of base isolation has reduced the total and impulsive hydrodynamic components of pressure by 80 to 90 percent,and base shear by 15 to 95 percent,depending upon the frequency content and duration of the considered earthquakes.The sloshing amplitude of the base-isolated tank is reduced by 18 to 94 percent for most of the short-duration earthquakes,while it is increased by 17 to 60 percent for the majority of the long-duration earthquakes.Furthermore,resonance studies are carried out through a long-duration harmonic excitation to obtain the dynamic behavior of non-isolated and isolated tanks,using a nonlinear sloshing model.The seismic responses of the base-isolated tank are obtained as higher when the excitation frequency matches the fundamental sloshing frequency rather than the isolator frequency.

Local Bifurcation Analysis of Parameter-Excited Resonance of Pipes under Thermal Load

The stability and local bifurcation of the lateral parameter-excited resonance of pipes induced by the pulsating fluid velocity and thermal load are studied. A mathematical model for a simply supported pipe is developed according to Hamilton principle. The Galerkin method is adopted to discretize the partial differential equations to the ordinary differential equations. The method of multiple scales and the singularity theory are utilized to analyze the stability and bifurcation of the trivial and non-trivial solutions. The transition sets and bifurcation diagrams are obtained both in the unfolding parameter space and physical parameter space, which can reveal the relationship between the thermal field parameter and the dynamic behaviors of the pipe. The numerical results demonstrate the accuracy of the single-mode expansion of the solution and verify the stability and local bifurcation analyses. The critical thermal rates are obtained both by the numerical simulation and the local bifurcation analysis. The natural frequency of lateral vibration decreases as the mean fluid velocity or the thermal rate increases according to the numerical results. The present work can provide valuable information for the design of the pipeline and controllers to prevent structural instability.

Nonlocal effect on resonant radiation force exerted on semiconductor coupled quantum well nanostructures

Based on the microscopic nonlocal optical response theory, the resonant radiation force exerted on a semiconductorcoupled quantum well nanostructure(CQWN), induced by the nonlocal interaction between lasers and electrons in conduction bands, is investigated for two different polarized states. The numerical results show that the spatial nonlocality of optical response can cause a radiation shift(blue-shift) for the spectrum of the resonant radiation force, which is dependent on the CQWN width ratio, the barrier height, and polarized states sensitively. It is also confirmed that the resonant radiation force is steerable by the incident and polarized directions of incident light. This work may provide an advantageous method for detecting internal quantum properties of nanostructures, and open novel and raising possibilities for optical manipulation of nano-objects using laser-induced radiation force.

Resonance enhanced electron impact excitation for P-like Cu XV

Employing both the Dirac R-matrix and the relativistic distorted wave with independent process and isolated reso- nance approaches, we report resonance enhanced electron impact excitation data （specifically, effective collision strengths） among the lowest 41 levels from the n = 3 configurations of Cu XV. The results show that the latter approach can obtain resonance contributions reasonably well for most excitations of Cu XV, though a comparison between the two approaches shows that the close-coupling effects are truly significant for rather weak excitations, especially for two-electron excitations from the 3s3p4 to 3s23p23d configuration. Resonance contributions are significant （more than two orders of magnitude） for many excitations and dramatically influence the line intensity ratios associated with density diagnostics.