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J.G. Papastavridis 《Journal of sound and vibration》1985,103(1):83-98
This paper presents a variational derivation of the adiabatic periodic motion theorems and related time-integral-of-energy results, including the virial theorem, and some of their applications to linear and non-linear oscillators. Specifically, (i) first, the Maupertuis-Euler-Langrange (MEL) action principle is formulated for the most general (scleronomic and holonomic) system; in the derivation the time-dependent system parameters are treated just like additional generalized co-ordinates and subjected to similar variations; (ii) next, combination of MEL's principle with the first law of thermodynamics yields the adiabatic theorem; subsequent specializations of it lead to additional energetic equations; (iii) the theory is then applied to the one d.o.f. linear and non-linear oscillator; the effects of linear friction and of a harmonic external force are also discussed; useful relations for the adiabatically varying system parameters are thus obtained. 相似文献
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Stavros G. Papastavridis Markos V. Koutras 《Annals of the Institute of Statistical Mathematics》1992,44(4):605-612
A consective k-out-of-n system consists of n linearly or cycliccally ordered components such that the system fails if and only if at least k consecutive components fail. In this paper we consider a maintained system where each component is repaired independently of the others according to an exponential distribution. Assuming general lifetime distributions for system's components we prove a limit theorem for the time to first failure of both linear and circular systems. 相似文献
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J.G. Papastavridis 《Journal of sound and vibration》1982,80(4):447-459
Hamilton's principle is applied to analyze the problem of the stability of equilibrium of a discrete, holonomic, and scleronomic mechanical system under conservative and non-conservative (position and/or velocity dependent) forces. At the stability limit, the vanishing of the second order terms (in the deviations from equilibrium) of the total action change functional leads to the condition that the matrix of a certain quadratic form be singular; this yields the eigenvalue (frequency-load) curve. The flutter loads follow by setting the frequency derivative of the determinant of this matrix equal to zero; the energetic interpretation of this latter is also given. When the non-conservative forces go to zero it is shown that one recovers the well-known discrete conservative system stability criterion. An application follows, and finally in an Appendix various relevant time-integral equalities are summarized and interpreted. 相似文献
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Summary A sequence of independent experiments is performed, each one producing a letter from a given alphabet. We study the number of overlapping appearances of a given pattern of letters and we prove that, under quite general conditions, the number of overlapping appearances of long patterns is approximately distributed according to a Pólya-Aeppli distribution. 相似文献
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Stavros Papastavridis 《manuscripta mathematica》1979,29(1):85-92
Let M be an n-dimensional, differential, compact and closed manifold and let c be a characteristic class of degree greater or equal to (n+1)/2. We will prove that if the class c anihilates all the characteristic numbers of M, where it enters as a factor, then the manifold M is cobordant to a manifold in which the class c is zero. Also, we will examine the case of manifolds with an extra structure. 相似文献
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Rotation in a general relativistic framework is examined. This concept, combined with the appropriate mechanical work concept, is used to show how the Euclidean group of transformations, serving as an invariance requirement associated with the principle of objectivity, can lead to erroneous conclusions. 相似文献
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J.G. Papastavridis 《Journal of sound and vibration》1983,90(1):51-58
The relation between the static and kinetic variational methods of the stability of equilibrium analysis of conservative systems and the corresponding static and kinetic Rayleigh's principles is reexamined. Specifically made explicit are the connections between (i) the virtual work principle (for the adjacent equilibrium configuration) and Rayleigh's principle of extremum critical loads and buckled modes, and (ii) Hamilton's principle (for the adjacent non-equilibrium configuration) and Rayleigh's principle of extremum frequencies and mode shapes, through simple familiar examples. These connections are found by considering, in addition to the familiar mode amplitude variations, variations of the load which in turn produce variations in the space (i) and time (ii) domain lengths, respectively; one is thus led to a variable endpoints variational problem (instead of the customary fixed endpoints one) which, by invoking the energetics of these adjacent configurations, is simplified and finally brought to the standard Rayleigh's principle form. 相似文献
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J.G. Papastavridis 《Journal of sound and vibration》1983,87(4):573-587
In this paper the Hamiltonian Action-based stability ideas of Routh are combined with Trefftz's variational formulation of the adjacent configuration method of static buckling into a comprehensive time-integral-of-energy-based extremum criterion of kinetic stability. Specifically, if the action functional along a fundamental path is a minimum for an arbitrarily long time interval of integration then the path is unstable, whereas if it ceases to do so at some point, then the path is stable up to that point; this latter leads to a direct method for approximate stability limit calculations. Some relevant analytical tools are also discussed, and finally applications of the criteria to the stability of equilibrium, and that of the steady state of Duffing's (cubic and harmonically-forced) oscillator are presented. 相似文献