相似文献
8.
We consider the dynamics of roller-coaster type experimental models used as analog devices for nonlinear oscillators. It is shown how to chose the shape of the track in order to achieve a desired oscillator equation, in terms of the are length coordinate or its projection onto the horizontal. Explicit calculations are carried out for the linear oscillator, the so-called escape equation, the two-well Duffing oscillator, and the pendulum. 相似文献
9.
In this paper we analyze the vibrations of nonlinear structures by means of the novel approach of isogeometric finite elements. The fundamental idea of isogeometric finite elements is to apply the same functions, namely B-Splines and NURBS (Non-Uniform Rational B-Splines), for describing the geometry and for representing the numerical solution. In case of linear vibrational analysis, this approach has already been shown to possess substantial advantages over classical finite elements, and we extend it here to a nonlinear framework based on the harmonic balance principle. As application, the straight nonlinear Euler–Bernoulli beam is used, and overall, it is demonstrated that isogeometric finite elements with B-Splines in combination with the harmonic balance method are a powerful means for the analysis of nonlinear structural vibrations. In particular, the smoother k-method provides higher accuracy than the p-method for isogeometric nonlinear vibration analysis. 相似文献
10.
11.
In this paper, outcomes of the study on the Bäcklund transformation, Lax pair, and interactions of nonlinear waves for a generalized (2 + 1)-dimensional nonlinear wave equation in nonlinear optics, fluid mechanics, and plasma physics are presented. Via the Hirota bilinear method, a bilinear Bäcklund transformation is obtained, based on which a Lax pair is constructed. Via the symbolic computation, mixed rogue–solitary and rogue–periodic wave solutions are derived. Interactions between the rogue waves and solitary waves, and interactions between the rogue waves and periodic waves, are studied. It is found that (1) the one rogue wave appears between the two solitary waves and then merges with the two solitary waves; (2) the interaction between the one rogue wave and one periodic wave is periodic; and (3) the periodic lump waves with the amplitudes invariant are depicted. Furthermore, effects of the noise perturbations on the obtained solutions will be investigated. 相似文献12.
In this paper, by Darboux transformation and symbolic computation we investigate the coupled cubic–quintic nonlinear Schrödinger equations with variable coefficients, which come from twin-core nonlinear optical fibers and waveguides, describing the effects of quintic nonlinearity on the ultrashort optical pulse propagation in the non-Kerr media. Lax pair of the equations is obtained, and the corresponding Darboux transformation is constructed. One-soliton solutions are derived; some physical quantities such as the amplitude, velocity, width, initial phases, and energy are, respectively, analyzed; and finally an infinite number of conservation laws are also derived. These results might be of some value for the ultrashort optical pulse propagation in the non-Kerr media. 相似文献
13.
Nonlinear Dynamics - We use Whitham’s averaged Lagrangian method extended with the multiple-scale formalism to derive a sixth-order nonlinear Schrödinger equation for the complex... 相似文献
14.
To reduce additional mass, this work proposes a nonlinear energy sink(NES)with an inertial amplifier(NES-IA) to control the vertical vibration of the objects under harmonic and shock excitations. Moreover, this paper constructs pure nonlinear stiffness without neglecting the gravity effect of the oscillator. Both analytical and numerical methods are used to evaluate the performance of the NES-IA. The research findings indicate that even if the actual mass is 1% of the main oscillator, the NES-IA... 相似文献
15.
Nonlinear Schr?dinger-type equations can model the nonlinear waves in fluids, plasmas, nonlinear optics and atmosphere. In this paper, integrable coupled nonlinear Schr?dinger-type equations are investigated. With the aid of symbolic computation, the equations are transformed into their bilinear forms, by virtue of which the multi-soliton solutions are derived. Soliton interactions are analyzed, the elastic interactions are seen, while the dark, anti-dark, M- and W-shape solitons are exhibited with some parameters selected. The propagating solitons can preserve their properties after the interaction, and the profiles of them depend on the corresponding dispersion relations. The amplitudes, velocities of the solitons are found to be influenced by the coefficient of the original equations, which is detailed in the paper. 相似文献
16.
The gearboxes of machines generally operate under a time-varying state rather than under steady-state conditions. However, it is difficult to investigate the nonlinear dynamics of a time-varying gear system. A gear system model of a railway vehicle was proposed in consideration of its time-varying mesh stiffness, nonlinear backlash, transmission error, time-varying external excitation, and rail irregularity. To obtain the nonlinear behaviors of a time-varying stochastic gear system, a quasi-static analysis was performed to observe its doubling-periodic bifurcation, chaotic motion, and transition from a lower to a higher power periodic motion. Based on the energy comparison results, the time-varying stochastic gear system was degraded to a time-varying system to simplify the calculation. Furthermore, the nonlinear response of the time-varying system was computed using the Runge–Kutta method and was compared with the results of a quasi-static analysis that employed a short-time Fourier transform method. The results of the quasi-static analysis were consistent with the results of the time–frequency analysis for the time-varying gear system except for the result at 3180 r/min, which represented a short period wherein the process transitioned to chaos. Hence, the comparison demonstrates the applicability of the quasi-static analysis for the nonlinear behavior analysis of a time-varying stochastic system. 相似文献
17.
Numerical solutions of a nonlinear Schrödinger equation is obtained using the differential quadrature method based on polynomials for space discretization and Runge–Kutta of order four for time discretization. Five well-known test problems are studied to test the efficiency of the method. For the first two test problems, namely motion of single soliton and interaction of two solitons, numerical results are compared with earlier works. It is shown that results of other test problems agrees the theoretical results. The lowest two conserved quantities and their relative changes are computed for all test examples. In all cases, the differential quadrature Runge–Kutta combination generates numerical results with high accuracy. 相似文献
18.
Patricio Aviles 《Archive for Rational Mechanics and Analysis》1987,97(2):141-170
We obtain theorems of Phragmén-Lindelöf type for the following classes of elliptic partial differential inequalities in an arbitrary unbounded domain \(\Omega \subseteq \mathbb{R}^n ,{\text{ }}n \geqq 2\)
19.
In this paper, combining the techniques of ε-generalized gradient projection and Armjio’s line search, we present a new algorithm for the nonlinear minimax problems. At each iteration, the improved search direction is generated by an ε-generalized gradient projection explicit formula. Under some mild assumptions, the algorithm possesses global and strong convergence. Finally, some preliminary numerical results show that the proposed algorithm performs efficiently. 相似文献
20.
The multi-coupled nonlinear factors existing in the giant magnetostrictive actuator (GMA) have a serious impact on its output characteristics. If the structural parameters are not properly designed, it is easy to fall into the nonlinear instability, which has seriously hindered its application in many important fields. The electric–magnetic-machine coupled dynamic mathematical model for GMA is established according to J-A dynamic hysteresis model, ampere circuit law, nonlinear quadratic domain model and structure dynamics equation. Nonlinear dynamic analysis method is applied to study the nonlinear dynamic behaviour of the key structure parameters to reveal their influence on the system stability. The design principle of structural parameters is obtained by studying stability of GMA, which provides theoretical basis and technical support for the structural stability design. 相似文献
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