共查询到20条相似文献,搜索用时 453 毫秒
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B. Lani-Wayda 《Journal of Mathematical Fluid Mechanics》1999,1(4):388-408
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Tatsuhiro Takahashi Jun Watanabe Keiji Minagawa Jun-ichi Takimoto Kenji Iwakura Prof. Kiyohito Koyama 《Rheologica Acta》1995,34(2):163-171
The effect of ionic interaction on linear and nonlinear viscoelastic properties was investigated using poly(ethylene-co-methacrylic acid) (E/MAA) and its ionomers which were partially neutralized by zinc or sodium. Dynamic shear viscosity and step-shear stress relaxation studies were performed. Stress relaxation moduli G(t, y) of the E/MAA and its sodium or zinc ionomers were factorized into linear relaxation moduli G°(t) and damping functions h(y). The relaxation modulus at the smallest strain in each ionomer agreed with the linear relaxation modulus calculated from storage modulus G and loss modulus G. In the linear region, the ionic interaction shifted the relaxation time longer with keeping the same relaxation time distribution as E/MAA. In the nonlinear region, the ionic interaction had no influence on h(y) when the ion content was low. At higher ion content, however, the ion bonding enhanced the strain softening of h(y). 相似文献
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H. J. Choe 《Journal of Mathematical Fluid Mechanics》2000,2(2):151-184
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A (3+1)-dimensional nonlinear Schrödinger equation with variable-coefficient dispersion/diffraction and cubic-quintic-septimal nonlinearities is studied, two families of analytical light bullet solutions with two types of \({{\mathcal {PT}}}\)-symmetric potentials are obtained. The coefficient of the septimal nonlinear term strongly influences the form of light bullet. The direct numerical simulation indicates that light bullet solutions in different cubic-quintic-septimal nonlinear media exhibit different property of stability, and under different \({\mathcal {PT}}\)-symmetric potentials they also show different stability against white noise. These stabilities of evolution originate from subtle interplay among dispersion, diffraction, nonlinearity and \({\mathcal {PT}}\)-symmetric potential. Moreover, compression and expansion of light bullets in the hyperbolic dispersion/diffraction system and periodic modulation system are investigated numerically. The evolution of light bullet in periodic modulation system is more stable than that in the hyperbolic dispersion/diffraction system. 相似文献
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J. Neustupa 《Journal of Mathematical Fluid Mechanics》1999,1(4):309-325
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朱位秋 《应用数学和力学(英文版)》1990,11(2):165-175
The exact solutions for stationary responses of one class of the second order and three classes of higher order nonlinear systems to parametric and/or external white noise excitations are constructed by using Fokker-Planck-Kolmogorov equation approach. The conditions for the existence and uniqueness and the behavior of the solutions are discussed. All the systems under consideration are characterized by the dependence of nonconservative forces on the first integrals of the corresponding conservative systems and are called generalized-energy-dependent (G.E.D.) systems. It is shown taht for each of the four classes of G.E.D. nonlinear stochastic systems there is a family of non-G.E.D. systems which are equivalent to the G.E.D. system in the sense of having identical stationary solution. The way to find the equivalent stochastic systems for a given G.E.D. system is indicated and as an example, the equivalent stochastic systems for the second order G.E.D. nonlinear stochastic system are given. It is pointed out and illustrated with example that the exact stationary solutions for many non-G.E.D. nonlinear stochastic systems may be found by searching the equivalent G.E.D. systems.Project Supported by The National Natural Science Foundation of China. Accepted by XVIIth International Congress of Theoretical and Applied Mechanics. 相似文献
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In this paper, we study the robust finite \(L_2 \) -gain control for a class of cascade switched nonlinear systems with parameter uncertainty. Each subsystem of the switched system under consideration is composed of a zero-input asymptotically stable nonlinear part which is a lower dimension switched system, and of a linearizable part. The uncertainty appears in the control channel of each subsystem. We give sufficient conditions under which the nonlinear feedback controllers are derived to guarantee that the \(L_2 \) -gain of the closed-loop switched system is less than a prespecified value for all admissible uncertainty under arbitrary switching. Moreover, we also develop the \(L_2\) -gain controllers for the switched systems with nonminimum phase case. 相似文献
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The following is a well-known problem of statistical physics: can a dynamic system of oscillators with nonlinear coupling be described approximately by statistical laws? This problem was studied for the first time by Fermi, Ulam, and Pasta [1] for the following system of equations describing coupled oscillators:
$$\begin{gathered} x^{..} _i = x_{i + 1} - 2x_i + x_{i - 1} + \alpha [(x_{i + 1} - x_i )^2 ] - (x_i ..x_{i - 1} )^2 ], \hfill \\ (i = 1,...,N;\alpha< 1).(0.1) \hfill \\ \end{gathered} $$ 相似文献
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This paper investigates the stability and stabilization problem of fractional-order nonlinear systems for \(0<\alpha <2\). Based on the fractional-order Lyapunov stability theorem, S-procedure and Mittag–Leffler function, the stability conditions that ensure local stability and stabilization of a class of fractional-order nonlinear systems under the Caputo derivative with \(0<\alpha <2\) are proposed. Finally, typical instances, including the fractional-order nonlinear Chen system and the fractional-order nonlinear Lorenz system, are implemented to demonstrate the feasibility and validity of the proposed method. 相似文献
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Gerasimos G. Rigatos 《Nonlinear dynamics》2014,76(2):1335-1354
The paper proposes a solution to the problem of observer-based adaptive fuzzy control for MIMO nonlinear dynamical systems (e.g. robotic manipulators). An adaptive fuzzy controller is designed for a class of nonlinear systems, under the constraint that only the system’s output is measured and that the system’s model is unknown. The control algorithm aims at satisfying the $H_\infty $ tracking performance criterion, which means that the influence of the modeling errors and the external disturbances on the tracking error is attenuated to an arbitrary desirable level. After transforming the MIMO system into the canonical form, the resulting control inputs are shown to contain nonlinear elements which depend on the system’s parameters. The nonlinear terms which appear in the control inputs are approximated with the use of neuro-fuzzy networks. Moreover, since only the system’s output is measurable the complete state vector has to be reconstructed with the use of a state observer. It is shown that a suitable learning law can be defined for the aforementioned neuro-fuzzy approximators so as to preserve the closed-loop system stability. With the use of Lyapunov stability analysis, it is proven that the proposed observer-based adaptive fuzzy control scheme results in $H_{\infty }$ tracking performance. 相似文献
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This paper is concerned with the output feedback \(\mathcal {H}_\infty \) control problem for a class of stochastic nonlinear systems with time-varying state delays; the system dynamics is governed by the stochastic time-delay It \(\hat{o}\) -type differential equation with state and disturbance contaminated by white noises. The design of the output feedback \(\mathcal {H}_\infty \) control is based on the stochastic dissipative theory. By establishing the stochastic dissipation of the closed-loop system, the delay-dependent and delay-independent approaches are proposed for designing the output feedback \(\mathcal {H}_\infty \) controller. It is shown that the output feedback \(\mathcal {H}_\infty \) control problem for the stochastic nonlinear time-delay systems can be solved by two delay-involved Hamilton–Jacobi inequalities. A numerical example is provided to illustrate the effectiveness of the proposed methods. 相似文献
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An experimental investigation focusing on the nonlinear stages of planar jet shear layer transition is presented. Experimental results for transition under both natural and low level artificial forcing conditions are presented and compared. The local spectral dynamics of the jet shear layer is modeled as a nonlinear system based upon a frequency domain, second-order Volterra functional series representation. The local linear and nonlinear wave coupling coefficients are estimated from time-series streamwise velocity fluctuation data. From the linear coupling coefficient, the mean dispersion characteristics and spatial growth rates may be obtained. With the estimation of the nonlinear power transfer function, the total, linear and quadratic nonlinear spectral energy transfer may be locally estimated. When these measures are used in conjunction with the local quadratic bicoherency and linear-quadratic coupling bicoherency, the local system output power may be completely characterized and the effect of nonlinearity on local mean flow distortion assessed. Particular attention is focused upon quantifying the linear and nonlinear power transfer that characterizes the different stages of the jet shear layer transition for both natural and excited flows. The quadratic power transfer that occurs with deviation from the perfect resonant wavenumber matching condition is clarified as is the dynamic mechanism of subharmonic resonance. The mechanism of spectral broadening is described and contrasted for natural and artificially excited flows. 相似文献
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Gear-motor system is a typically nonlinear system because of many nonlinear factors, such as time-varying meshing stiffness, backlash, and the nonlinear relationship between the electric motor torque and speed. At present, the nonlinear analytical methods can only be used for simplified gear dynamic model. Though the numerical methods can be used for the complicated dynamic model, the quantitative analysis of stability is difficult and rarely conducted. Therefore, a kind of trajectory-based stability preserving dimension reduction (TSPDR) methodology is proposed to investigate nonlinear dynamic characteristics of the gear-motor system. In the TSPDR methodology herein, the complementary cluster center of inertia-relative motion (CCCOI-RM) transformation is chosen and the stability margins are specially defined for distinguishing the stable motion modes of the motor-gear system, to make the TSPDR methodology used in the nonlinear analysis of the gear-motor system. Furthermore, the critical values are obtained for alteration of different motion modes and the nonlinear characteristics of each motion modes are analyzed. At last, combined with modal analysis, the relationship between the stability and resonance of the gear-motor system is revealed. 相似文献
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M. D. Gunzburger 《Journal of Mathematical Fluid Mechanics》2000,2(3):219-266
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Nonlinear damping suspension is a promising method to be used in a rotor-bearing system for vibration isolation between the bearing and environment. However, the nonlinearity of the suspension may influence the stability of the rotor-bearing system. In this paper, the motions of a flexible rotor in short journal bearings with nonlinear damping suspension are studied. A computational method is used to solve the equations of motion, and the bifurcation diagrams, orbits, Poincaré maps, and amplitude spectra are used to display the motions. The results show that the effect of the nonlinear damping suspension on the motions of the rotor-bearing system depends on the speed of rotor: (a) For low speeds, the rotor- bearing system presents the same motion pattern under the nonlinear damping ( \(p=0.5, 2, 3\) ) suspension as for the linear damping ( \(p=1\) ) suspension; (b) For high speeds, the effect of nonlinear damping depends on a combination of the damping exponent and damping coefficient. The square root damping model ( \(p=0.5\) ) shows a wider stable speed range than the linear damping for large damping coefficients. The quadratic damping ( \(p=2\) ) shows similar results to linear damping with some special damping coefficients. The cubic damping ( \(p=3\) ) shows more stable response than the linear damping in general. 相似文献