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451.
A stochastic averaging method is proposed for nonlinear energy harvesters subjected to external white Gaussian noise and parametric excitations. The Fokker–Planck–Kolmogorov equation of the coupled electromechanical system of energy harvesting is a three variables nonlinear parabolic partial differential equation whose exact stationary solutions are generally hard to find. In order to overcome difficulties in solving higher dimensional nonlinear partial differential equations, a transformation scheme is applied to decouple the electromechanical equations. The averaged Itô equations are derived via the standard stochastic averaging method, then the FPK equations of the decoupled system are obtained. The exact stationary solution of the averaged FPK equation is used to determine the probability densities of the displacement, the velocity, the amplitude, the joint probability densities of the displacement and velocity, and the power of the stationary response. The effects of the system parameters on the output power are examined. The approximate analytical outcomes are qualitatively and quantitatively supported by the Monte Carlo simulations. 相似文献
452.
S.E. Strigin 《Physics letters. A》2018,382(33):2256-2258
We discuss the parametric oscillatory instability in a Fabry–Perot cavity of the Einstein Telescope. Unstable combinations of elastic and optical modes for two possible configurations of gravitational wave third-generation detector are deduced. The results are compared with the results for gravitational wave interferometers LIGO and LIGO Voyager. 相似文献
453.
This work examines dynamical behavior of a nonlinear oscillator with symmetric potential that models a quarter-car forced by the road profile under parametric excitation. The parametric resonance of a harmonically excited nonlinear quarter-car model with position and velocity time-delayed active control are investigated. We focus on the influence of delay and parametric excitation in the system. The influence of parametric excitation, time-delay and feedback gain parameters on the stability of the steady state response are investigated. By means of Melnikov's method, conditions for onset of chaos resulting from heteroclinic bifurcation is derived analytically and numerically. 相似文献
454.
Free vibrations of a beam-mass-spring system with different boundary conditions are analyzed both analytically and numerically.In the analytical analysis,the system is divided into three subsystems and the effects of the spring and the point mass are considered as internal boundary conditions between any two neighboring subsystems.The partial differential equations governing the motion of the subsystems and internal boundary conditions are then solved using the method of separation of variables.In the numerical analysis,the whole system is considered as a single system and the effects of the spring and point mass are introduced using the Dirac delta function.The Galerkin method is then employed to discretize the equation of motion and the resulting set of ordinary differential equations are solved via eigenvalue analysis.Analytical and numerical results are shown to be in very good agreement. 相似文献
455.
456.
Tunable line emission (LE) over a large wavelength region (340–980 nm) is obtained by pumping thick crystals of β-barium borate (BBO) with picosecond pulses at 532 nm. Phenomena of group velocity dispersion, diffraction and phase matching take place simultaneously such that the radiation shows specific features that are characteristic of (i) strongly coupled fundamental and harmonic fields, (ii) amplified phase matched superfluorescence, (iii) conical emission and (iv) four wave mixing. 相似文献
457.
Analytical derivations and numerical calculations are employed to gain insight into the parametric resonance of a stochastically driven van der Pol oscillator with delayed feedback. This model is the prototype of a self-excited system operating with a combination of narrow-band noise excitation and two time delayed feedback control. A slow dynamical system describing the amplitude and phase of resonance, as well as the lowest-order approximate solution of this oscillator is firstly obtained by the technique of multiple scales. Then the explicit asymptotic formula for the largest Lyapunov exponent is derived. The influences of system parameters, such as magnitude of random excitation, tuning frequency, gains of feedback and time delays, on the almost-sure stability of the steady-state trivial solution are discussed under the direction of the signal of largest Lyanupov exponent. The non-trivial steady-state solution of mean square response of this system is studied by moment method. The results reveal the phenomenon of multiple solutions and time delays induced stabilization or unstabilization, moreover, an appropriate modulation between the two time delays in feedback control may be acted as a simple and efficient switch to adjust control performance from the viewpoint of vibration control. Finally, theoretical analysis turns to a validation through numerical calculations, and good agreements can be found between the numerical results and the analytical ones. 相似文献
458.
Parametric search is a useful tool in geometric optimization. Invented by Nimrod Megiddo in 1983, it has been widely used
in computational geometry. Unfortunately, this technique has rarely been used in the combinatorial optimization community
in China. In this paper, we introduce parametric search via three new geometric optimization applications. 相似文献
459.
Nonlinear oscillations with parametric excitation solved by homotopy analysis method 总被引:1,自引:0,他引:1
An analytical technique, namely the homotopy analysis method (HAM), is used to solve problems of nonlinear oscillations with parametric excitation. Unlike perturbation methods, HAM is not dependent on any small physical parameters at all, and thus valid for both weakly and strongly nonlinear problems. In addition, HAM is different from all other analytic techniques in providing a simple way to adjust and control convergence region of the series solution by means of an auxiliary parameter h. In the present paper, a periodic analytic approximations for nonlinear oscillations with parametric excitation are obtained by using HAM, and the results are validated by numerical simulations. 相似文献
460.
Zhiwei Zhang Howard E. Rockette 《Annals of the Institute of Statistical Mathematics》2006,58(4):687-706
We consider parameter estimation in parametric regression models with covariates missing at random. This problem admits a
semiparametric maximum likelihood approach which requires no parametric specification of the selection mechanism or the covariate
distribution. The semiparametric maximum likelihood estimator (MLE) has been found to be consistent. We show here, for some
specific models, that the semiparametric MLE converges weakly to a zero-mean Gaussian process in a suitable space. The regression
parameter estimate, in particular, achieves the semiparametric information bound, which can be consistently estimated by perturbing
the profile log-likelihood. Furthermore, the profile likelihood ratio statistic is asymptotically chi-squared. The techniques
used here extend to other models. 相似文献