Simultaneous Parametric and Internal Resonances in Systems Involving Strong Non-Linearities

Ibrahim, R. A.; El-Sayad, M. A.

doi:10.1006/jsvi.1999.2277

Cited by 31 publications

(4 citation statements)

References 14 publications

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“…Under combined parametric resonance the system behaves like a soft system in the absence of impact and as a hard system in the presence of impact. Under simultaneous parametric and internal resonance conditions the system response was studied using the multiple scales method by [31] and by applying the Lie group transformations [35]. Both studies lead to the same system response characteristics.…”

Section: Sloshing Hydrodynamic Impactmentioning

confidence: 99%

Liquid Sloshing Dynamics With Aerospace Applications

Ibrahim¹

2001

International Conference on Aerospace Sciences and Aviation Tec

183

316

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Liquid containers constitute major components in a number of dynamical systems such as aerospace vehicles, road tankers, liquefied natural gas carriers, and elevated water towers. The dynamic behavior of these systems is greatly affected by the dynamics of the free liquid surface. The basic problem of liquid sloshing involves the estimation of hydrodynamic pressure distribution, forces, moments and natural frequencies of the free liquid surface. These parameters have direct effect on the dynamic stability and performance of moving containers. The aerospace technology has promoted the research activities in many problems pertaining to liquid sloshing and the special NASA research monograph edited by Abramson [1] documents these problems. Recently, Ibrahim, et al, [2] presented an extensive review of recent advances in liquid sloshing dynamics and the present paper is an abridged form. A liquid free surface in partially filled containers can experience a wide spectrum of motions such as planar, non-planar, rotational, quasi-periodic, chaotic, and disintegration. Since the early 1960's, the problem of liquid sloshing dynamics has been of major concern to aerospace engineers studying the influence of liquid propellant sloshing on the flight performance or jet vehicles. Since then, new areas of research activities have emerged. Thft modem theory of nonlinear dynamics has indeed promoted further studies and uncovered complex nonlinear phenomena. These include rotary sloshing, Faraday waves. nonlinear liquid sloshing interaction with elastic structures, internal resonance effects, stochastic sloshing dynamics, hydrodynamic sloshing impact dynamics, g-jitter under microgravity field, cross-waves, and spatial resonance. The dynamic stability of liquid gas tankers and ship cargo tankers, and liquid hydrodynamic impact loading are problems of current interest to the designers of such systems. FREE AND FORCED FREE-SURFACE MOTIONS Fluid Field Equations The general equations of motion for a fluid in closed containers can be simplified by assuming that the container is rigid and impermeable, and the fluid is inviscid, incompressible, and initially irrotational. Capillary or surface tension effects will be

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Section: Sloshing Hydrodynamic Impactmentioning

confidence: 99%

Liquid Sloshing Dynamics With Aerospace Applications

Ibrahim¹

2001

International Conference on Aerospace Sciences and Aviation Tec

183

316

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“…where is an integer and b is a positive constant parameter usually estimated from experimental measurement. Such representation was proposed in vibro-impact problems by Hunt and Crossley [3] and in simulating liquid sloshing impact in moving containers [4][5].…”

Section: Power-law Phenomenological Modelingmentioning

confidence: 99%

Modeling of Dynamic Systems With Vibro-Impact Interaction and Discontinuity Mapping

Ibrahim

2014

The International Conference on Applied Mechanics and Mechanica

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This paper presents an overview of selected modeling techniques of vibro-impact dynamics. Vibro-impact dynamics has occupied a wide spectrum of studies by dynamicists, physicists, and mathematicians. These studies may be classified into three main categories: modeling, mapping and applications. The main techniques used in modeling of vibro-impact systems include phenomenological modeling, Hertzian models, and non-smooth coordinate transformations developed by Zhuravlev and Ivanov. One of the most critical situations impeded in vibro-impact systems is the grazing bifurcation. Grazing bifurcation is usually studied through discontinuity mapping techniques, which are useful to uncover the rich dynamics in the process of impact interaction. Complex dynamic phenomena of vibro-impact systems such as sub-harmonic oscillations, chaotic motion, and coexistence of different attractors for the same excitation and system parameters but under different initial conditions will be discussed.

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“…where n 1 is an integer and b a positive constant parameter, usually estimated from the experimental measurement. Such representation was proposed in vibro-impact problems by Hunt and Crossley [33] and in simulating liquid sloshing impact in moving containers [34][35][36]. With reference to the schematic diagram shown in Fig.…”

Section: Power-law Phenomenological Modellingmentioning

confidence: 99%

Modelling and analysis of ship roll oscillations interacting with stationary icebergs

Grace

Ibrahim

2008

Proceedings of the Institution of Mechanical Engineers, Part C:

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Impact dynamic interaction of ships with solid ice or stationary rigid structures is a serious problem that affects the safe operation and navigation in arctic regions. The purpose of this study is to present two analytical models of impact interaction between ship roll dynamics and one-side rigid barrier. These models are the phenomenological modelling represented by a power law in stiffness and damping forces, and Zhuravlev non-smooth coordinate transformation. Extensive numerical simulations are carried out for all initial conditions covered by the ship grazing orbit for different values of excitation amplitude and frequencies 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, chaotic impact motion, and unbounded rotational motion. The results are summarized in the bifurcation diagram in terms of response-excitation amplitudes plane. The stability fraction index is obtained for different values of excitation frequency based on the ratio of the area of bounded roll oscillations to the total area of the grazing orbit.

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Simultaneous Parametric and Internal Resonances in Systems Involving Strong Non-Linearities

Cited by 31 publications

References 14 publications

Liquid Sloshing Dynamics With Aerospace Applications

Liquid Sloshing Dynamics With Aerospace Applications

Modeling of Dynamic Systems With Vibro-Impact Interaction and Discontinuity Mapping

Modelling and analysis of ship roll oscillations interacting with stationary icebergs

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