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Chaotic Motion (chaotic + motion)
Selected AbstractsExperimental and theoretical simulations of seismic poundings between two adjacent structuresEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 4 2003K. T. Chau Abstract Shaking table tests have been carried out to investigate the pounding phenomenon between two steel towers of different natural frequencies and damping ratios, subject to different combinations of stand-off distance and seismic excitations. Both harmonic waves and ground motions of the 1940 El Centro earthquake are used as input. Subjected to sinusoidal excitations, poundings between the two towers could appear as either periodic or chaotic. For periodic poundings, impact normally occurs once within each excitation cycle or within every other excitation cycle. A type of periodic group poundings was also observed for the first time (i.e. a group of non-periodic poundings repeating themselves periodically). Chaotic motions develop when the difference of the natural frequency of the two towers become larger. Under sinusoidal excitations, the maximum relative impact velocity always develops at an excitation frequency between the natural frequencies of the two towers. Both analytical and numerical predictions of the relative impact velocity, the maximum stand-off distance, and the excitation frequency range for pounding occurrences were made and found to be comparable with the experimental observations in most of the cases. The stand-off distance attains a maximum when the excitation frequency is close to that of the more flexible tower. Pounding appears to amplify the response of the stiffer structure but suppress that of the more flexible structure; and this agrees qualitatively with previous shaking table tests and theoretical studies. Copyright © 2003 John Wiley & Sons, Ltd. [source] On the design of energy,momentum integration schemes for arbitrary continuum formulations.INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2004Applications to classical, chaotic motion of shells Abstract The construction of energy,momentum methods depends heavily on three kinds of non-linearities: (1) the geometric (non-linearity of the strain,displacement relation), (2) the material (non-linearity of the elastic constitutive law), and (3) the one exhibited in displacement-dependent loading. In previous works, the authors have developed a general method which is valid for any kind of geometric non-linearity. In this paper, we extend the method and combine it with a treatment of material non-linearity as well as that exhibited in force terms. In addition, the dynamical formulation is presented in a general finite element framework where enhanced strains are incorporated as well. The non-linearity of the constitutive law necessitates a new treatment of the enhanced strains in order to retain the energy conservation property. Use is made of the logarithmic strain tensor which allows for a highly non-linear material law, while preserving the advantage of considering non-linear vibrations of classical metallic structures. Various examples and applications to classical and non-classical vibrations and non-linear motion of shells are presented, including (1) chaotic motion of arches, cylinders and caps using a linear constitutive law and (2) large overall motion and non-linear vibration of shells using non-linear constitutive law. Copyright © 2004 John Wiley & Sons, Ltd. [source] Mass components in ordered and in chaotic motion in galactic N -body modelsMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 2 2002N. Voglis ABSTRACT Two self-consistent (N -body) non-rotating equilibrium models of elliptical galaxies with smooth central density profiles (called ,Q' and ,C' models) are constructed, starting from quiet and clumpy cosmological initial conditions, respectively. Both models are triaxial. The Q model has an E7 maximum ellipticity in the inner parts and tends to E6 or E5 maximum ellipticity in the outer parts. The C model has a maximum ellipticity E4 in the inner parts and tends to an E2 or E1 in the outer parts. For each model, we identify the particles moving in chaotic orbits with the Lyapunov number exceeding a particular threshold (namely, 10,2.8, in units of the inverse radial periods of the particular orbits). At energy levels in the deepest 30 per cent of the potential well, no chaotic orbits were detected in the above limit of chaoticity. In the Q model, the detected chaotic part is 32 per cent of the total mass. This part has a nearly spherical distribution. It imposes limitations on the maximum ellipticity of the system, in spite of the fact that only a part of less than about 8 per cent of the total mass moves in chaotic orbits and is able to develop chaotic diffusion within a Hubble time. In the C model, the detected chaotic part is about 26 per cent of the total mass, but only less than 2 per cent can develop chaotic diffusion within a Hubble time. These chaotic components produce surface density profiles flatter than the profiles of the rest of the mass, particularly in the Q model. The two profiles intersect at a given distance, where the overall profile forms an observable hump, especially if the surface density profiles are taken along the shortest axis of the projection. [source] Identification of chaos in a regenerative cutting process by the 0-1 testPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2009Grzegorz Litak We examine the regenerative cutting process by using a single degree of freedom non-smooth model with a friction component and a time delay term. Instead of the standard Lyapunov exponent calculations, we propose a statistical 0-1 test for chaos. This approach reveals the nature of the cutting process signaling regular or chaotic dynamics. We are able to show that regular or chaotic motion occur in the investigated model depending on the delay time. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] The evolution of chaos in active galaxy models with an oblate or a prolate dark halo componentASTRONOMISCHE NACHRICHTEN, Issue 3 2010N.D. Caranicolas Abstract The evolution of chaotic motion in a galactic dynamical model with a disk, a dense nucleus and a flat biaxial dark halo component is investigated. Two cases are studied: (i) the case where the halo component is oblate and (ii) the case where a prolate halo is present. In both cases, numerical calculations show that the extent of the chaotic regions decreases exponentially as the scale-length of the dark halo increases. On the other hand, a linear relationship exists between the extent of the chaotic regions and the flatness parameter of the halo component. A linear relationship between the critical value of the angular momentum and the flatness parameter is also found. Some theoretical arguments to support the numerical outcomes are presented. An estimation of the degree of chaos is made by computing the Lyapunov Characteristic Exponents. Comparison with earlier work is also made (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Ordered and chaotic spiral armsASTRONOMISCHE NACHRICHTEN, Issue 9-10 2008P.A. Patsis Abstract The stellar flow at the arms of spiral galaxies is qualitatively different among different morphological types. The stars that reinforce the spiral arms can be either participating in an ordered or in a chaotic flow. Ordered flows are associated with normal (non-barred) spiral galaxies. Typically they are described with precessing ellipses corresponding to stable periodic orbits at successive energies (Jacobi constants). On the contrary, the spiral arms in barred-spiral systems may be supported by stars in chaotic motion. The trajectories of these stars are associated with the invariant manifolds of the unstable Lagrangian points (L1,2). Response and orbital models indicate that this kind of spirals either stop at an azimuth smaller than , /2, or present large gaps at about this angle. Chaotic spirals appear in strong bars having (L1,2) close to the ends of the bar. The arms of barred-spiral systems with corotation away from the end of the bar can be either as in the case of normal spirals, or supported by banana-like orbits surrounding the stable Lagrangian points (L4,5). We find also models combining ordered and chaotic flows. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] On modelling and analysis of gear drives with nonlinear couplingsPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2006Miroslav Byrtus The paper deals with modelling of vibration of shaft systems with gears and rolling-element bearings using the modal synthesis method with DOF number reduction. The influence of the nonlinear bearing and gearing contact forces with the possibility of the contact interruption is respected. The gear drive nonlinear vibrations caused by internal excitation generated in gear meshing, accompanied by impact and chaotic motions are studied. The theory is applied to a simple test-gearbox. (© 2006 WILEY-VCH Verlag GmbH & Co. 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