Optimal Control of Mechanical Oscillations

Kovaleva, Agnessa

doi:10.1007/978-3-540-49258-0

Cited by 26 publications

(20 citation statements)

References 51 publications

(123 reference statements)

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“…Formulas (17) coincide with the definition of the homoclinic separatrix of the rocking oscillator obtained, e.g., in [1,2]. The phase portrait of system (8) is shown in Fig.…”

Section: The Separatrix Of Rocking Oscillationsmentioning

confidence: 96%

“…2. The domain of bounded oscillations is circumscribed by the diamond-shape separatrix (17); escape from the inner domain of the bounded oscillations to the outer area of unbounded unstable motion corresponds to the passage from stable oscillations to overturning of the block.…”

Section: The Separatrix Of Rocking Oscillationsmentioning

confidence: 99%

“…It follows from (16), (17) that the critical angular displacement ϕ = α 1 n 2 /n 2 1 and velocity ω = ϕn 1 have the form…”

Section: The Separatrix Of Rocking Oscillationsmentioning

confidence: 99%

See 2 more Smart Citations

Stability and control of random rocking motion of a multidimensional structure: the Melnikov approach

Kovaleva

2009

Nonlinear Dyn

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This paper investigates the controlled dynamics of a structure consisting of a free standing rigid block with an attached chain of uniaxially moving point masses. Rocking motion is excited by motion of the ground; instability is associated with overturning of the structure as a whole. The control task is to minimize the probability of overturning. The stochastic Melnikov method is used to obtain a necessary condition of instability, estimate an upper bound to the probability of overturning, and find a convenient control strategy. The paper is restricted to the consideration of seismic vulnerability of the structure. A similar approach can be applied to systems with wind or wave excitations.

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“…Formulas (17) coincide with the definition of the homoclinic separatrix of the rocking oscillator obtained, e.g., in [1,2]. The phase portrait of system (8) is shown in Fig.…”

Section: The Separatrix Of Rocking Oscillationsmentioning

confidence: 96%

Section: The Separatrix Of Rocking Oscillationsmentioning

confidence: 99%

See 1 more Smart Citation

Stability and control of random rocking motion of a multidimensional structure: the Melnikov approach

Kovaleva

2009

Nonlinear Dyn

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“…Note that using the classic Dirac delta function in (6) would be unjustified due to the discontinuous factor z |z | at z = 0. Accordingly, the term (1 − e)z |z |δ − (z) provides only approximate description for the energy loss at the barrier, z = 0, which is justified under the condition (1 − e) 1, as indicated in many references (see, e.g., [28,[30][31][32]). Although the model still includes singularity due to the localized energy dissipation, the corresponding term (the last one on the left-hand side of (6)) has a relatively small integral effect due to the factor (1 − e).…”

Section: Constraint Eliminating Coordinate (Model 1)mentioning

confidence: 99%

Inelastic impact dynamics of ships with one-sided barriers. Part I: analytical and numerical investigations

2011

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This two-part paper deals with impact interaction of ships with one-sided ice barrier during roll dynamics. The first part presents analytical and numerical studies for the case of inelastic impact. An analytical model of a ship roll motion interacting with ice is developed based on Zhuravlev and Ivanov non-smooth coordinate transformations. These transformations have the advantage of converting the vibro-impact oscillator into an oscillator without barriers such that the corresponding equation of motion does not contain any impact term. Such approaches, however, account for the energy loss at impact times in different ways. The present work, in particular, demonstrates that the impact dynamics may have qualitatively different response characteristics to different dissipation models. The difference between localized and distributed equivalent damping approaches is discussed. Extensive numerical simulations are carried out for all initial conditions covered by the ship grazing orbit for different values of excitation amplitude and frequency of external wave roll moment. The basins of attraction of safe operation are obtained and reveal the coexistence of different response regimes such as non-impact periodic oscillations, modulation impact motion, period added impact oscillations, I.M. Grace · R.A. Ibrahim ( ) · V.N. Pilipchuk

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“…Periodic Optimal Control problems are motivated by a lot of applications (see for instance [9,14,18,21] and their references). It is for instance known in industry that a periodic control can give a better production process than a static one [17,26].…”

Section: Introductionmentioning

confidence: 99%

On some general almost periodic Optimal Control problems: links with periodic problems and necessary conditions

Pennequin

2007

ESAIM: COCV

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Abstract.In this paper, we are concerned with periodic, quasi-periodic (q.p.) and almost periodic (a.p.) Optimal Control problems. After defining these problems and setting them in an abstract setting by using Abstract Harmonic Analysis, we give some structure results of the set of solutions, and study the relations between periodic and a.p. problems. We prove for instance that for an autonomous concave problem, the a.p. problem has a solution if and only if all problems (periodic with fixed or variable period, q.p. or a.p.) have a constant solution. After that, we give some first order necessary conditions (weak Pontryagin) in the space of Harmonic Synthesis and we also give in this space an existence result.

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Optimal Control of Mechanical Oscillations

Abstract: Kovaleva, A.S. (Agnessa Solomonova), Optimal control of mechanical oscillations A. Kovaleva; translated by V. Silberschmidt (Foundations of engineering mechanics) Includes bibliographical references and index

Cited by 26 publications

References 51 publications

Stability and control of random rocking motion of a multidimensional structure: the Melnikov approach

Stability and control of random rocking motion of a multidimensional structure: the Melnikov approach

Inelastic impact dynamics of ships with one-sided barriers. Part I: analytical and numerical investigations

On some general almost periodic Optimal Control problems: links with periodic problems and necessary conditions

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