共查询到20条相似文献,搜索用时 15 毫秒
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Richard Bellman Joseph Bentsman Semyon M Meerkov 《Journal of Mathematical Analysis and Applications》1983,97(2):572-589
A method for analysis of nonlinear systems with fast parametric oscillations is presented. Several examples, including classical equations of the theory of oscillations and chemical reactions with vibrating parameters, are considered. 相似文献
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The parametric oscillations of strongly non-linear systems with one degree of freedom are considered using a more general definition of these oscillations than the generally accepted definition. Stability criteria, that are verifiable using the signs of the derivatives of the amplitude-frequency characteristics, are found for the two families of periodic solutions corresponding to the fundamental parametric resonance. A condition is indicated under which the latter are monotonic and, as a result, one of the families is stable and the other is unstable. It is shown that, in a system with a concave non-monotonic elastic characteristic, the stable family loses stability for fairly large amplitudes and this effect is not revealed by the well-known analytical methods of non-linear mechanics. 相似文献
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A.A. Zevin 《Journal of Applied Mathematics and Mechanics》2014,78(1):30-38
The correctness of the existing definitions of the parametric oscillations of linear and non-linear systems is discussed. The possibility of an erroneous choice of the mathematical parametric model instead of the autooscillatory model, connected with the existence in such systems of the same periodic solutions, is pointed out. Some non-local properties of parametric oscillations in Hamiltonian systems are established. It is shown, in particular, that stability regions are convex with respect to the frequency of the parametric excitation (i.e., all the points between the boundaries of neighbouring instability regions correspond to stable solutions). At the critical frequencies of parametric resonance the well-known Rayleigh and Zhuravlev theorems on the behaviour of the frequencies of natural oscillations when the stiffness and inertia changes are generalized. Some additional assertions on the limits of the first instability region for the Hill vector equations are established. 相似文献
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V. M. Babich 《Journal of Mathematical Sciences》1997,86(3):2664-2666
In this paper, the following assertion is illustrated with some examples. In practically all cases, the problem on natural
oscillations for linear holonomic nondissipative mechanical systems reduces to the problem of determining eigenvalues and
eigenelements of the corresponding self-adjoint operator acting in the Hilbert space generated by the quadratic form of the
kinetic energy. Bibliography: 1 title.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 218, 1994, pp. 12–16.
This work was supported by the Russian Foundation of Fundamental Research (Grant 93-011-16148).
Translated by N. S. Zabanikova. 相似文献
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Controllability and observability conditions are derived for a three-mass oscillatory system with nested masses. Modal controllers and observers are constructed that take the system to a prescribed spectral region. Cases are considered when the state vector function or a linear combination of its components is observed.Kiev University. Tadzhik University. Translated from Vychislitel'naya i Prikladnaya Matematika, No. 75, pp. 103–107, 1991. 相似文献
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Inga M. Arkhipova Angelo Luongo 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2016,67(3):69
The effect of damping on the re-stabilization of statically unstable linear Hamiltonian systems, performed via parametric excitation, is studied. A general multi-degree-of-freedom mechanical system is considered, close to a divergence point, at which a mode is incipiently stable and n ? 1 modes are (marginally) stable. The asymptotic dynamics of system is studied via the Multiple Scale Method, which supplies amplitude modulation equations ruling the slow flow. Several resonances between the excitation and the natural frequencies, of direct 1:1, 1:2, 2:1, or sum and difference combination types, are studied. The algorithm calls for using integer or fractional asymptotic power expansions and performing nonstandard steps. It is found that a slight damping is able to increase the performances of the control system, but only far from resonance. Results relevant to a sample system are compared with numerical findings based on the Floquet theory. 相似文献
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Fadi Dohnal 《PAMM》2005,5(1):153-154
The main objective of this contribution is to show the phenomenon of full vibration suppression of a simple two degrees of freedom rotary oscillator by interaction between self-excitation and parametric excitation. One disk is under the influence of self-excitation, modelled by a negative damping coefficient, while the moment of inertia of the second disk is periodically varied in time within an open-loop control with a fixed frequency. Both disks are coupled by a linear spring-element. Parametric excitation develops equations of motion with time-periodic coefficients. Using the averaging method for a firstorder approximation general conditions for full vibration suppression are analytically derived for the two degrees of freedom system with harmonic inertia variation. The approximated analytical stability predictions are verified and compared to results obtained from numerical time integration of the original equations of motion. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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C. R. Bector S. Chandra M. K. Bector 《Journal of Optimization Theory and Applications》1989,60(2):243-260
Using a parametric approach, duality is presented for a minimax fractional programming problem that involves several ratios in the objective function.The first author is thankful to Natural Science and Engineering Research Council of Canada for financial support through Grant A-5319, and the authors are thankful to the anonymous referees for useful suggestions. 相似文献
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A. Ayad 《Journal of Mathematical Sciences》2011,179(6):635-661
In this paper, we present three algorithms: the first one solves zero-dimensional parametric homogeneous polynomial systems
within single exponential time in the number n of unknowns; it decomposes the parameter space into a finite number of constructible
sets and computes the finite number of solutions by parametric rational representations uniformly in each constructible set.
The second algorithm factirizes absolutely multivariate parametic polynomials within single exponential time in n and in the
upper bound d on the degree of the factorized polynomials. The third algorithm decomposes algebraic varieties defined by parametric
polynomial systems of positive dimension into absolutely irreducible components uniformly in the values of the parameters.
The complexity bound for this algorithm is double exponential in n. On the other hand, the lower bound on the complexity of
the problem of resolution of parametric polynomial systems is double exponential in n. Bibliography: 72 titles. 相似文献
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We consider the problem of finding g Mn such that
where Mn is the n-dimensional subspace of the complexHilbert space L2(0, ) spanned by an n-tuple of normalized eigenvectoesof the operator
, corresponding to eigenvalues. The solution is g = Pnf and Pn denotesthe orthoprojector onto Mn. From Grabowski (1991) we know thatPn can be expressed in terms of the Malmquist functions. Wegive an alternative approach, more convenient for applicationof the standard mathematical software. The problem of convergenceas n is discussed from both theoretical and numerical viewpoint.The reslts are illustrated by the problems of finding the optimaladjustment of the proportional controller stabilizing a distributedplant.
Email: pgrab{at}ia.agh.edu.pl 相似文献
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This paper is concerned with generalized second-order contingent epiderivatives of frontier and solution maps in parametric vector optimization problems. Under some mild conditions, we obtain some formulas for computing generalized second-order contingent epiderivatives of frontier and solution maps, respectively. We also give some examples to illustrate the corresponding results. 相似文献
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Siberian Mathematical Journal - 相似文献