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.

Dielectronic recombination and resonant transfer excitation processes for helium-like krypton

The relativistic configuration interaction method is employed to calculate the dielectronic recombination（DR） cross sections of helium-like krypton via the 1s2lnl ＇（n = 2,3,...,15） resonances.Then,the resonant transfer excitation（RTE） processes of Kr 34＋ colliding with H,He,H 2,and CH x（x = 0-4） targets are investigated under the impulse approximation.The needed Compton profiles of targets are obtained from the Hartree-Fock wave functions.The RTE cross sections are strongly dependent on DR resonant energies and strengths,and the electron momentum distributions of the target.For H 2 and H targets,the ratio of their RTE cross sections changes from 1.85 for the 1s2l2l ＇ to 1.88 for other resonances,which demonstrates the weak molecular effects on the Compton profiles of H 2.For CH x（x = 0-4） targets,the main contribution to the RTE cross section comes from the carbon atom since carbon carries 6 electrons;as the number of hydrogen increases in CH x,the RTE cross section almost increases by the same value,displaying the strong separate atom character for the hydrogen.However,further comparison of the individual orbital contributions of C（2p,2s,1s） and CH 4（1t 2,2a 1,1a 1） to the RTE cross sections shows that the molecular effects induce differences of about 25.1%,19.9%,and 0.2% between 2p-1t 2,2s-2a 1,and 1s-1a 1 orbitals,respectively.

Xe-Kr laser induced collisional ionization system and experimental preparation of its initial state: Four-photon resonant excitation

This paper proposes a novel one-colour Xe-Kr laser induced collisional ionization system. Considering the level scheme of the system, it finds that the initial state of the reaction--the four 4f levels with even J of Xe-can be prepared through method of four-photon resonant excitation by dye laser with wavelength of -440 nm. Absorption of an additional photon （the transfer laser） of the same wavelength will complete the laser induced collisional ionization process. The resonance enhanced ionization spectrum of Xe by four laser photons at -440nm is measured through time-of-flight mass spectrometry, this aims at the preparation of the initial state of the system proposed. The Stark broadening of the measured spectrum is observed and consistent with the previous study. Analysis of the measured resonance ionization spectrum implies the feasibility of -440 nm four-photon resonant excitation of the initial 4f state of the Xe Kr system proposed in this paper, which prepares for a further experiment of laser induced collisional ionization.

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.

Exploration of magnetic field generation of H_(3)^(2+)by direct ionization and coherent resonant excitation

Coherent electronic dynamics are of great significance in photo-induced processes and molecular magnetism.We theoretically investigate electronic dynamics of triatomic molecule H_(3)^(2+) by circularly polarized pulses,including electron density distributions,induced electronic currents,and ultrafast magnetic field generation.By comparing the results of the coherent resonant excitation and direct ionization,we found that for the coherent resonant excitation,the electron is localized and the coherent electron wave packet moves periodically between three protons,which can be attributed to the coherent superposition of the ground A′state and excited E+state.Whereas,for the direct single-photon ionization,the induced electronic currents mainly come from the free electron in the continuum state.It is found that there are differences in the intensity,phase,and frequency of the induced current and the generated magnetic field.The scheme allows one to control the induced electronic current and the ultrafast magnetic field generation.

Dielectronic recombination and resonant transfer excitation processes for helium-like krypton

The relativistic configuration interaction method is employed to calculate the dielectronic recombination(DR) cross sections of helium-like krypton via the 1s2lnl ’(n = 2,3,...,15) resonances.Then,the resonant transfer excitation(RTE) processes of Kr 34+ colliding with H,He,H 2,and CH x(x = 0-4) targets are investigated under the impulse approximation.The needed Compton profiles of targets are obtained from the Hartree-Fock wave functions.The RTE cross sections are strongly dependent on DR resonant energies and strengths,and the electron momentum distributions of the target.For H 2 and H targets,the ratio of their RTE cross sections changes from 1.85 for the 1s2l2l ’ to 1.88 for other resonances,which demonstrates the weak molecular effects on the Compton profiles of H 2.For CH x(x = 0-4) targets,the main contribution to the RTE cross section comes from the carbon atom since carbon carries 6 electrons;as the number of hydrogen increases in CH x,the RTE cross section almost increases by the same value,displaying the strong separate atom character for the hydrogen.However,further comparison of the individual orbital contributions of C(2p,2s,1s) and CH 4(1t 2,2a 1,1a 1) to the RTE cross sections shows that the molecular effects induce differences of about 25.1%,19.9%,and 0.2% between 2p-1t 2,2s-2a 1,and 1s-1a 1 orbitals,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.

On the Temperature Profile of the Thermally Excited Resonant Silicon Micro Structural Pressure Sensor

According to the sensing structure of a practical silicon resonant pressure micro sensor whose preliminary sensing unit is a square silicon diaphragm and the final sensing unit is a silicon beam resonator, its operating mechanism is analyzed. The thermal resistor acts as the excited unit, and the piezoresistive unit acts as the detector, for the above micro sensor. By using the amplitude and phase conditions, the self exciting closed loop system is investigated based on the operating mechanism for the abov...

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.

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.

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.

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.

Resonance-Enhanced Photon Excitation Spectroscopy of the Even-Parity Autoionizing Rydberg States of Xe

Xenon atoms were produced in their metastable states 5p^56s[3/2]2 and 5p^56s＇[1/2]0 in a pulsed DC discharge in a beam, and subsequently excited to the even-parity autoionizing Rydberg states 5p^5np＇ [3/2] 1,[1/2] 1, and 5p^5nf＇ [5/2] 3 using single photon excitation. The excitation spectra of the even-parity autoionizing resonance series from the metastable 129Xe were obtained by recording the autoionized Xe＋ with time-of-flight ion detection in the photon energy range of 28000-42000 cm-1. A wealth of autoionizing resonances were newly observed, from which more precise and systematic spectroscopic data of the level energies and quantum defects were derived.

Internal resonance of an axially transporting beam with a two-frequency parametric excitation

This paper investigates the transverse 3:1 internal resonance of an axially transporting nonlinear viscoelastic Euler-Bernoulli beam with a two-frequency parametric excitation caused by a speed perturbation.The Kelvin-Voigt model is introduced to describe the viscoelastic characteristics of the axially transporting beam.The governing equation and the associated boundary conditions are obtained by Newton’s second law.The method of multiple scales is utilized to obtain the steady-state responses.The RouthHurwitz criterion is used to determine the stabilities and bifurcations of the steady-state responses.The effects of the material viscoelastic coefficient on the dynamics of the transporting beam are studied in detail by a series of numerical demonstrations.Interesting phenomena of the steady-state responses are revealed in the 3:1 internal resonance and two-frequency parametric excitation.The approximate analytical method is validated via a differential quadrature method.

On rotational normal modes of the Earth：Resonance,excitation,convolution, deconvolution and all that

Earth＇s Coriolis force profoundly alters the eigen frequencies, eigen functions, and excitation of rotational normal modes. Some rotational modes of the solid mantle-fluid outer core-solid inner core Earth system are confirmed observationally and some remain elusive. Here we bring together from literature assertions about an excited resonance system in terms of the Green＇s function and temporal convolution. We raise caveats against taking the face values of the oscillational motion which have been ＂masqueraded＂ by the convolution, necessitating deconvolution for retrieving the excitation function which reflects the true variability. Lastly we exemplify successful applications of the deconvolution in estimating resonance complex frequencies.

Studies of Electron Energy Distribution Function (EEDF) in Lithium Vapor Excitation at 2S→3D Two-Photon Resonance

We have developed a computational model which quantitatively studies the Electron Energy Distribution Function (EEDF) in laser excited lithium vapor at 2s→3d two-photon resonance. A kinetic model has been constructed which includes essentially all the important collisional ionization, photoionization, electron collisions and radiative interactions that come into play when lithium vapor (density range 1013?- 1014 cm-3) is subject to a sudden pulse of intense laser radiation (power range 105?- 106 W·cm-2) at wavelength 639.1 nm and pulse duration 20 ns. The applied computer simulation model is based on the numerical solution of the time-dependent Boltzman equation and a set of rate equations that describe the rate of change of the formed excited states populations. Using the measured values for the cross-sections and rate coefficients of each physical process considered in the model available in literature, relations are obtained as a function of the electron energy and included in the computational model. We have also studied the time evolution and the laser power dependences of the ion population (atomic and molecular ions) as well as the electron density which are produced during the interaction. The energy spectra of the electrons emerging from the interaction contains a number of peaks corresponding to the low-energy electrons produced by photoionization and collisional ionization such as assosicative and Penning ionization processes. The non-equilibrium shape of these electrons occurs due to relaxation of fast electrons produced by super-elastic collisions with residual excited lithium atoms. Moreover, a reasonable agreement between McGeoch results and our calculations for the temporal behaviour of the electron density is obtained.

Excitation of Zonal Flows by ion-temperature-gradient Modes Excited by the Fluid Resonance

We apply the reductive perturbation method to the simple electrostatic ion-temperature-gradient mode in an advanced fluid description. The fluid resonance turns out to play a major role for the excitation of zonal flows. This is the mechanism recently found to lead to the low-to-high （L-H） mode transition and to the nonlinear Dimits upshift in transport code simulations. It is important that we have taken the nonlinear temperature dynamics from the Reynolds stress as the convected diamagnetic flow. This has turned out to be the most relevant effect as found in transport simulations of the L-H transition, internal transport barriers and Dimits shift. This is the first time that an analytical method is applied to a system which numerically has been found to give the right experimental dynamics.

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.

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.

High order correlation polarization potential for vibrational excitation scattering of diatomic molecules by low-energy electrons

This paper introduces a correlation-polarization potential with high order terms for vibrational excitation in electron-molecule scattering. The new polarization potential generalizes the two-term approximation so that it can better reflect the dependence of correlation and polarization effects on the position coordinate of the scattering electron. It applies the new potential on the vibrational excitation scattering from N2 in an energy range which includes the ^2Ⅱg shape resonance. The good agreement of theoretical resonant peaks with experiments shows that polarization potentials with high order terms are important and should be included in vibrational excitation scattering.