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1.
Nonlinear Dynamics - It is highly desired yet challenging to obtain analytical approximate solutions to strongly nonlinear oscillators accurately and efficiently. Here we propose a new approach,... 相似文献
2.
Separatrices and limit cycles of strongly nonlinear oscillators by the perturbation-incremental method 总被引:1,自引:0,他引:1
The perturbation-incremental method is applied to determine the separatrices and limit cycles of strongly nonlinear oscillators. Conditions are derived under which a limit cycle is created or destroyed. The latter case may give rise to a homoclinic orbit or a pair of heteroclinic orbits. The limit cycles and the separatrices can be calculated to any desired degree of accuracy. Stability and bifurcations of limit cycles will also be discussed. 相似文献
3.
A new method for the periodic solution of strongly nonlinear system is given. By using this method, the existance and stability
of the periodic solution can be decided, and the approximate expression of the periodic solution can also be found.
The project supported by the National Natural Science Foundation of China 相似文献
4.
Numerical method in dynamic response of nonlinear systems 总被引:1,自引:0,他引:1
A kind of modal synthesis techniques, which is applicable to vibration analysis for linear substructures with nonlinear coupling attachments, has been extended to nonlinear dynamic analysis of large complex structural systems[9]. In this paper, a process is suggested to dynamic analysis of large complex structural systems with nonlinear characteristics of each substructure. At the end of this paper, an example shows the defendable accuracy of the results and high efficiency of this process.This paper was collected in Proceedings of Symposium on Nonlinear Mechanics, Vol. IV, 1982, Wuxi, China (in Chinese). 相似文献
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I.IntroductionInthelasttwodecades,theresponseofstochasticallyexcitednonlinearsystemshavebeenresearcheddeeplyandwidely.Manyexactandapproximatemethodsofpredictingtheresponseofnonlinearsystemstorandomexcitationshavebeenprop0sedl']'l21.Becauseofv4riousreasons… 相似文献
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Nonlinear Dynamics - In this paper, a novel fractional equivalent linearization (NFEL) approach is developed by introducing fractional derivative term into the conventional equivalent linear... 相似文献
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A non-linear seales method is presented for the analysis of strongly non-linear oseillators of the form % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaamXvP5wqonvsaeHbfv3ySLgzaGqbdiqb-Hha4zaadaGaey4kaSIa% am4zaiaacIcacqWF4baEcaGGPaGae8xpa0JaeqyTduMaamOzaiaacI% cacqWF4baEcqWFSaalcuWF4baEgaGaaiaabMcaaaa!4FEC!\[\ddot x + g(x) = \varepsilon f(x,\dot x{\text{)}}\], where g(x) is an arbitrary non-linear function of the displacement x. We assumed that % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaamXvP5wqonvsaeHbfv3ySLgzaGqbdiab-Hha4jaacIcacqWF0baD% cqWFSaalcqaH1oqzcaGGPaGaeyypa0Jae8hEaG3aaSbaaSqaaiaaic% daaeqaaOGaaiikaiabe67a4jaacYcacqaH3oaAcaGGPaGaey4kaSYa% aabmaeaacqaH1oqzdaahaaWcbeqaaiaad6gaaaaabaGaamOBaiabg2% da9iaaigdaaeaacaWGTbGaeyOeI0IaaGymaaqdcqGHris5aOGae8hE% aG3aaSbaaSqaaiab-5gaUbqabaGccaGGOaGaeqOVdGNaaiykaiabgU% caRiaad+eacaGGOaGaeqyTdu2aaWbaaSqabeaacaWGTbaaaOGaaiyk% aaaa!67B9!\[x(t,\varepsilon ) = x_0 (\xi ,\eta ) + \sum\nolimits_{n = 1}^{m - 1} {\varepsilon ^n } x_n (\xi ) + O(\varepsilon ^m )\], where % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiaabsgacqaH+oaEcaGGVaGaaeizaiaadshacqGH9aqpdaaeWaqa% aiabew7aLnaaCaaaleqabaGaamOBaaaaaeaacaWGUbGaeyypa0JaaG% ymaaqaaiaad2gaa0GaeyyeIuoakiaadkfadaWgaaWcbaGaamOBaaqa% baGccaGGOaGaeqOVdGNaaiykaaaa!4FFC!\[{\text{d}}\xi /{\text{d}}t = \sum\nolimits_{n = 1}^m {\varepsilon ^n } R_n (\xi )\], % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiaabsgacqaH3oaAcaGGVaGaaeizaiaadshacqGH9aqpdaaeWaqa% aiabew7aLnaaCaaaleqabaGaamOBaaaaaeaacaWGUbGaeyypa0JaaG% imaaqaaiaad2gaa0GaeyyeIuoakiaadofadaWgaaWcbaGaamOBaaqa% baGccaGGOaGaeqOVdGNaaiilaiabeE7aOjaacMcaaaa!5241!\[{\text{d}}\eta /{\text{d}}t = \sum\nolimits_{n = 0}^m {\varepsilon ^n } S_n (\xi ,\eta )\], and R
n,S
nare to be determined in the course of the analysis. This method is suitable for the systems with even non-linearities as well as with odd non-linearities. It can be viewed as a generalization of the two-variable expansion procedure. Using the present method we obtained a modified Krylov-Bogoliubov method. Four numerical examples are presented which served to demonstrate the effectiveness of the present method. 相似文献
8.
A perturbation-incremental method is extended for the analysis of strongly non-linear non-autonomous oscillators of the form , where g(x) and are arbitrary non-linear functions of their arguments, and ε can take arbitrary values. Limit cycles of the oscillators can be calculated to any desired degree of accuracy and their stabilities are determined by the Floquet theory. Branch switching at period-doubling bifurcation along a frequency-response curve is made simple by the present method. Subsequent continuation of an emanating branch is also discussed. 相似文献
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E. N. Pelinovskii S. Kh. Shavratskii 《Journal of Applied Mechanics and Technical Physics》1974,15(5):628-631
The damping of a nonsinusoidal wave in systems described by a Klein-Gordon equation is investigated by the method of averaging. An explicit solution is given for an initial-value problem. It is shown that in certain cases the prolonged existence of a steady-state wave is impossible. Dissipation can lead to the damping out of the wave. The characteristic features of the boundary-value problem are discussed. Formulas are obtained describing the damping of single pulses (solitons).Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 55–59, September–October, 1974. 相似文献
12.
Nonlinear Dynamics - The hyperbolic perturbation method is applied to determining the homoclinic and heteroclinic solutions of cubic strongly nonlinear autonomous oscillators of the form... 相似文献
13.
The paper deals with the analysis of stochastic mechanical systems with one degree of freedom and proposes a simple procedure to obtain a representation of the dynamical response. In particular, approximate solution of the FPK equation is obtained for a system subjected to a stochastic force term. The resolving procedure is implemented with reference to a polynomial expansion of the restoring force function. Numerical tests are performed with reference to Duffing and van der Pol oscillators, showing good agreement with simulated response. 相似文献
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The solution of the constrained multibody system equations of motion using the generalized coordinate partitioning method requires the identification of the dependent and independent coordinates. Using this approach, only the independent accelerations
are integrated forward in time in order to determine the independent coordinates and velocities. Dependent coordinates are
determined by solving the nonlinear constraint equations at the position level. If the constraint equations are highly nonlinear,
numerical difficulties can be encountered or more Newton–Raphson iterations may be required in order to achieve convergence
for the dependent variables. In this paper, a velocity transformation method is proposed for railroad vehicle systems in order to deal with the nonlinearity of the constraint equations when the vehicles
negotiate curved tracks. In this formulation, two different sets of coordinates are simultaneously used. The first set is
the absolute Cartesian coordinates which are widely used in general multibody system computer formulations. These coordinates
lead to a simple form of the equations of motion which has a sparse matrix structure. The second set is the trajectory coordinates
which are widely used in specialized railroad vehicle system formulations. The trajectory coordinates can be used to obtain
simple formulations of the specified motion trajectory constraint equations in the case of railroad vehicle systems. While
the equations of motion are formulated in terms of the absolute Cartesian coordinates, the trajectory accelerations are the
ones which are integrated forward in time. The problems associated with the higher degree of differentiability required when
the trajectory coordinates are used are discussed. Numerical examples are presented in order to examine the performance of
the hybrid coordinate formulation proposed in this paper in the analysis of multibody railroad vehicle systems. 相似文献
16.
Analytical and numerical studies of multi-degree-of-freedom(MDOF) nonlinear stochastic or deterministic dynamic systems have long been a technical challenge.This paper presents a highly-efficient method for determining the stationary probability density functions(PDFs) of MDOF nonlinear systems subjected to both additive and multiplicative Gaussian white noises. The proposed method takes advantages of the sufficient conditions of the reduced Fokker-Planck-Kolmogorov(FPK) equation when constructi... 相似文献
17.
A generalized hyperbolic perturbation method is presented for homoclinic solutions of strongly nonlinear autonomous oscillators,in which the perturbation procedure is improved for those systems whose exact homoclinic generating solutions cannot be explicitly derived.The generalized hyperbolic functions are employed as the basis functions in the present procedure to extend the validity of the hyperbolic perturbation method.Several strongly nonlinear oscillators with quadratic,cubic,and quartic nonlinearity are studied in detail to illustrate the efficiency and accuracy of the present method. 相似文献
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Summary Exact stationary solutions are constructed for nonlinear dynamic systems subjected to stochastic excitation. The results are then applied to both classical and nonclassical stochastic vibration systems. 相似文献