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41.
In this paper,a new approach is devoted to find novel analytical and approximate solutions to the damped quadratic nonlinear Helmholtz equation(HE)in terms of the Weiersrtrass elliptic function.The exact solution for undamped HE(integrable case)and approximate/semi-analytical solution to the damped HE(non-integrable case)are given for any arbitrary initial conditions.As a special case,the necessary and sufficient condition for the integrability of the damped HE using an elementary approach is reported.In general,a new ansatz is suggested to find a semi-analytical solution to the non-integrable case in the form of Weierstrass elliptic function.In addition,the relation between the Weierstrass and Jacobian elliptic functions solutions to the integrable case will be derived in details.Also,we will make a comparison between the semi-analytical solution and the approximate numerical solutions via using Runge-Kutta fourth-order method,finite difference method,and homotopy perturbation method for the first-two approximations.Furthermore,the maximum distance errors between the approximate/semi-analytical solution and the approximate numerical solutions will be estimated.As real applications,the obtained solutions will be devoted to describe the characteristics behavior of the oscillations in RLC series circuits and in various plasma models such as electronegative complex plasma model. 相似文献
42.
The authors investigate limit-cycle oscillations of a wing/store configuration. Unlike typical aeroelastic studies that are based upon a linearized form of the governing equations, herein full system nonlinearities are retained, and include transonic flow effects, coupled responses from the structure, and store-related kinematics and dynamics. Unsteady aerodynamic loads are modeled with the equations from transonic small disturbance theory. The structural dynamics for the cantilevered wing are modeled by the nonlinear equations of motion for a beam. The effects of general store-placement are modeled by the nonlinear equations of motion related to the position-induced nonlinear kinematics. Chordwise deformations of the wing surface, as well as pylon and store flexibility, are assumed negligible. Nonlinear responses are studied by examining bifurcation and related response characteristics using direct simulation. Particular attention is given to cases for which large-time, time-dependent behavior is dependent on initial conditions, as observed for some configurations in flight test. Comparisons of results in which selective nonlinearities are excluded indicate that the accurate prediction of nonlinear responses such as limit cycle oscillations (LCOs) may depend upon consideration of all nonlinearities related to the full system. 相似文献
43.
Zhenjun Yang 《Acta Mechanica Sinica》2006,22(3):243-256
The scaled boundary finite element method (SBFEM) is a recently developed numerical method combining advantages of both finite element methods (FEM) and boundary element methods (BEM) and with its own special features as well. One of the most prominent advantages is its capability of calculating stress intensity factors (SIFs) directly from the stress solutions whose singularities at crack tips are analytically represented. This advantage is taken in this study to model static and dynamic fracture problems. For static problems, a remeshing algorithm as simple as used in the BEM is developed while retaining the generality and flexibility of the FEM. Fully-automatic modelling of the mixed-mode crack propagation is then realised by combining the remeshing algorithm with a propagation criterion. For dynamic fracture problems, a newly developed series-increasing solution to the SBFEM governing equations in the frequency domain is applied to calculate dynamic SIFs. Three plane problems are modelled.
The numerical results show that the SBFEM can accurately predict static and dynamic SIFs, cracking paths and load-displacement curves, using only a fraction of degrees of freedom generally needed by the traditional finite element methods.The project supported by the National Natural Science Foundation of China (50579081) and the Australian Research Council (DP0452681)The English text was polished by Keren Wang. 相似文献
44.
In this paper, linear stability and chaotic motion of a time-delayednonlinear vehicle system are studied. The stability is determined bycomputing the spectrum associated with a system of linear retardedfunctional differential equations, which reveals that a loss ofstability occurs following a Hopf bifurcation. Beyond the critical valuefor linear stability, the system exhibits limit cycle motions.Subharmonic, quasi-periodic and chaotic motions are observed for asystem excited by a periodic disturbance. 相似文献
45.
Jeļena Leičūnaite Igors KļimenkovsJorens Kviesis Dzintars ZačsJuris Pauls Kreišmanis 《Comptes Rendus Chimie》2010,13(10):1335-1340
A new series [CnOmmim]Cl of imidazolium cation-based ionic liquids (ILs), with an ether functional group on the alkyl side-chain, has been prepared. The possibility of analyzing the ionic liquids by high performance liquid chromatography (HPLC) was investigated on mixed-mode reversed/cation exchange stationary phase with the aqueous-acetonitrile mobile phase. Elution parameters, such as retention factor, selectivity and column efficiency, were studied as functions of mobile phase composition and pH. The ILs were characterized by elemental analysis, and infrared, UV and 1H, 13C NMR spectroscopy. 相似文献
46.
Determination of fungicides in wine by mixed-mode solid phase extraction and liquid chromatography coupled to tandem mass spectrometry 总被引:1,自引:0,他引:1
A novel procedure for the determination of nine selected fungicides (metalaxyl-M, azoxystrobin, myclobutanil, flusilazole, penconazole, tebuconazole, propiconazole, diniconazole and difenoconazole) in wine samples is presented. Sample enrichment and purification is simultaneously performed using mixed-mode, anion exchange and reversed-phase, OASIS MAX solid-phase extraction (SPE) cartridges. Analytes were determined by liquid chromatography coupled to tandem mass spectrometry using atmospheric pressure electrospray ionization (LC-ESI-MS/MS). Parameters affecting the chromatographic determination and the extraction-purification processes were thoroughly investigated. Under optimized conditions, 10 mL of wine were firstly diluted 1:1 with ultrapure water and then passed through the mixed-mode SPE cartridge at a flow of ca. 5 mLmin(-1). After a washing step with 5 mL of an aqueous NH(4)OH solution (5%, w:v), analytes were recovered with just 1 mL of methanol and injected in the LC-MS/MS system without any additional purification. The selective extraction process avoided significant changes in the ionization efficiency for red and white wine extracts in comparison with pure standards in methanol. Performance of the method was good in terms of precision (RSDs<11%) and accuracy (absolute recoveries>72%, determined against pure standards in methanol) reporting method LOQs in the range of 0.01-0.79 ngmL(-1) for target compounds, which are far below the EU maxima residue levels (MRLs) for fungicides in vinification grapes and wine. Several commercial wines from different geographic areas in Spain were analyzed. In most samples, metalaxyl-M and azoxystrobin were found at concentrations up to several ngmL(-1). 相似文献
47.
We have studied the optical oscillations and transitions in two-dimensional graded square photonic lattices (GSPL) formed by evanescently coupled optical waveguide arrays with parabolic confinements in all transverse directions. When we retain only the orthogonal couplings, decoupled one-dimensional models can be used to obtain the various normal modes, which correspond to a variety of optical oscillations. Six different combinations of Bloch oscillation (BO), dipole oscillation (DO), and reflections from the boundaries of finite lattice are classified on the phase diagram. If we include the diagonal couplings, transitions among various oscillations are obtained with the Hamiltonian optics approach and confirmed by the field-evolution analysis. We studied in detail a typical example in which a switching occurs from the constituent BO and DO to both DOs in the two orthogonal directions. The method to analyze the complex field evolution in GSPL can be extended to similar systems with different types of lattices and/or confinements. 相似文献
48.
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50.
We investigate how models for neutrino–nucleus cross sections based on different assumptions for the nuclear dynamics affect the forecasted sensitivities to neutrino oscillation parameters at future neutrino facilities. We limit ourselves to the quasi-elastic regime, where the neutrino cross sections can be evaluated with less uncertainties, and discuss the sensitivity reach to θ13 and δ at a prototype low-γ β-beam, mostly sensitive to the quasi-elastic regime. 相似文献