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  • 1
    ISSN: 1573-269X
    Keywords: Bouncing ball ; vibrating table ; stability and bifurcation ; period-1 motion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The dynamical behavior of a bouncing ball with a sinusoidally vibrating table is revisited in this paper. Based on the equation of motion of the ball, the mapping for period-1 motion is constructured and thereby allowing the stability and bifurcation conditions to be determined. Comparison with Holmes's solution [1] shows that our range of stable motion is wider, and through numerical simulations, our stability result is observed to be more accurate. The Poincaré mapping sections of the unstable period-1 motion indicate the existence of identical Smale horseshoe structures and fractals. For a better understanding of the stable and chaotic motions, plots of the physical motion of the bouncing ball superimposed on the vibration of the table are presented.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1573-2673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract This paper presents a large anisotropic damage theory of continuum damage mechanics. It is developed via a new hypothesis of incremental complementary elastic energy equivalence. This hypothesis is more versatile and accurate if compared to the original hypothesis of total complementary energy equivalence. To model the large damage, we assumed that it occurs as a series of incremental small damage. An expression for the damage effect tensor M(D) for large damage is derived. It is shown that when the damage is small, that is, D i≪1, the proposed large damage theory reduces to the small damage model of Chow and Wang [1]. To demonstrate this large damage theory, it is applied to model the following cases: (a) uniaxial tension, (b) pure torsion and (c) elastic perfectly-plastic material behavior. In all three cases, the results clearly show that when the damage is small, Chow and Wang's model is recovered. However, for large damage, there are significant differences in predictions. Since this large damage theory is formulated on the basis of the incremental complementary energy, it is applicable to a wider range of problems.
    Type of Medium: Electronic Resource
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  • 3
    ISSN: 1573-269X
    Keywords: resonant-separatrix web ; stochastic layer ; energy spectrum ; Duffing oscillator
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The excitation strength for the onset of a new resonant-separatrix in the stochastic layer of the Duffing oscillator is predicted through the energy change in minimum and maximum energy spectra. The widths of stochastic layers are estimated through the use of the maximum and minimum energy which can be measured experimentally. The energy spectrum approach, rather than the Poincaré mapping section method, is applied to detect the resonant-separatrix web in the stochastic layer, and it is applicable for the onset of resonant layers in nonlinear dynamic systems. The analytical condition for the onset of a new resonant-separatrix in the stochastic layer is also presented. The analytical and numerical predictions are in good agreement.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A general treatment is presented for modelling the dynamics of a flexible multibody system, using a lumped mass finite element approach. The system topology considered here is defined as an arbitrary combination of both rigid and flexible bodies, connected together by joints that permit translation and compliance, in a general tree configuration. An extension to handle closed loop kinematic chains is also indicated. Kane's theory of generalized speeds, which is based on the Lagrange-D'Alembert principle, is used to derive the equations of motion, and this results in a very efficient computer oriented methodology for solving the dynamics of such large mechanical systems. To facilitate numerical computations, these dynamical equations are transformed into a system of first-order differential equations for an explicit formulation of the problem. The accuracy of the proposed formulation is assessed via three examples with known solutions. The results obtained indicate the method is accurate, efficient and versatile for the analysis of a general, flexible multibody system.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
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  • 5
    ISSN: 0029-5981
    Keywords: exact dynamic ; stiffness ; arbitrary beams ; natural frequencies ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, the exact dynamic stiffness matrix is derived for the transverse vibration of beams whose cross-sectional area and moment of inertia vary in accordance to any two arbitrary real-number powers. This variation represents a very large class of arbitrary varying beams and thus, fills the void currently existing in this area of research. With this approach, most beams can be modelled by just one element, and for beams having abrupt profile changes or with very complex profiles, they can be divided into separate distinct parts, with each of the part modelled by just one element, and then assembled together. The method is exact; however, the accuracy of the results depends only on the solver used to solve the exact frequency equation. To demonstrate the procedure, beams of non-linearly varying circular and elliptical cross-sections, and a combination beam consisting of a linear-tapered section, a uniform section and a non-linearly varying-section are analysed for their natural frequencies. Since there are no known solutions for these structures, comparison with finite element results was made and very good agreement was observed. © 1997 by John Wiley & Sons, Ltd.
    Additional Material: 4 Ill.
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  • 6
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a new method of writing finite element programs using the programming approach known as object oriented programming (OOP). More specifically, the C++ language is used to illustrate the key OOP concepts. In addition to the OOP finite element examples, a detailed discussion of OOP techniques in the creation of a generalized matrix library is presented. The C++ language is used in this paper because it is more suited to numerical programs than a pure OOP language such as Smalltalk. The efficiency, flexibility and maintainability of the C++ program are shown to be superior to a comparable version written in a non-OOP language, such as FORTRAN. The matrix library contains a number of matrix objects that are useful for specific types of matrix related problems. Different sparse storage schemes are implemented for each different type of matrix. A large number of functions are provided for each matrix type in order to implement many common matrix operations. In applications, the OOP paradigm allows the functions to be used in a very simple way that is common to all the matrix types. The sample finite element code included in this paper is primarily intended to illustrate the key concepts of OOP style. This paper explains how to set up a finite element hierarchy, material hierarchy and how to integrate this with the matrix hierarchy (library). Thus, a completely object oriented finite element program can be written.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
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  • 7
    Publication Date: 2019-07-13
    Description: We describe a probe-class mission concept that provides an unprecedented view of the X-ray sky, performing timing and 0.2-30 keV spectroscopy over timescales from microseconds to years. The Spectroscopic Time-Resolving Observatory for Broadband Energy X-rays (STROBE-X) comprises three primary instruments. The first uses an array of lightweight optics (3-m focal length) that concentrate incident photons onto solid state detectors with CCD-level (85-130 eV) energy resolution, 100 ns time resolution, and low background rates to cover the 0.2-12 keV band. This technology is scaled up from NICER, with enhanced optics to take advantage of the longer focal length of STROBE-X. The second uses large-area collimated silicon drift detectors, developed for ESA's LOFT, to cover the 2-30 keV band. These two instruments each provide an order of magnitude improvement in effective area compared with its predecessor (NICER and RXTE, respectively). Finally, a sensitive sky monitor triggers pointed observations, provides high duty cycle, high time resolution, high spectral resolution monitoring of the X-ray sky with approx. 20 times the sensitivity of the RXTE ASM, and enables multi-wavelength and multi-messenger studies on a continuous, rather than scanning basis.For the first time, the broad coverage provides simultaneous study of thermal components, non-thermal components, iron lines, and reflection features from a single platform for accreting black holes at all scales. The enormous collecting area allows detailed studies of the dense matter equation of state using both thermal emission from rotation-powered pulsars and harder emission from X-ray burst oscillations. The combination of the wide-field monitor and the sensitive pointed instruments enables observations of potential electromagnetic counterparts to LIGO and neutrino events. Additional extragalactic science, such as high quality spectroscopy of clusters of galaxies and unprecedented timing investigations of active galactic nuclei, is also obtained.
    Keywords: Astrophysics
    Type: MSFC-E-DAA-TN46013 , AAS HEAD Divisional Meeting; 20-24 Aug. 2017; Sun Valley, ID; United States
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  • 8
    Publication Date: 2019-07-13
    Description: Millisecond pulsars (MSPs) are a growing class of gamma-ray emitters. Pulsed gamma-ray signals have been detected from more than 40 MSPs with the Fermi Large Area Telescope (LAT). The wider radio beams and more compact magnetospheres of MSPs enable studies of emission geometries over a broader range of phase space than non-recycled radio-loud gamma-ray pulsars. We have modeled the gamma-ray light curves of 40 LAT-detected MSPs using geometric emission models assuming a vacuum retarded-dipole magnetic field. We modeled the radio profiles using a single-altitude hollow-cone beam, with a core component when indicated by polarimetry; however, for MSPs with gamma-ray and radio light curve peaks occurring at nearly the same rotational phase, we assume that the radio emission is co-located with the gamma rays and caustic in nature. The best-fit parameters and confidence intervals are determined using amaximum likelihood technique.We divide the light curves into three model classes, with gamma-ray peaks trailing (Class I), aligned (Class II), or leading (Class III) the radio peaks. Outer gap and slot gap (two-pole caustic) models best fit roughly equal numbers of Class I and II, while Class III are exclusively fit with pair-starved polar cap models. Distinguishing between the model classes based on typical derived parameters is difficult. We explore the evolution of the magnetic inclination angle with period and spin-down power, finding possible correlations. While the presence of significant off-peak emission can often be used as a discriminator between outer gap and slot gap models, a hybrid model may be needed.
    Keywords: Astrophysics
    Type: GSFC-E-DAA-TN17872 , The Astrophysical Journal Supplement Series; 213; 1; 6
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  • 9
    Publication Date: 2019-07-12
    Description: We report the discovery of nine previously unknown gamma-ray pulsars in a blind search of data from the Fermi Large Area Telescope (LAT). The pulsars were found with a novel hierarchical search method originally developed for detecting continuous gravitational waves from rapidly rotating neutron stars. Designed to find isolated pulsars spinning at up to kHz frequencies, the new method is computationally efficient, and incorporates several advances, including a metric-based gridding of the search parameter space (frequency, frequency derivative and sky location) and the use of photon probability weights. The nine pulsars have spin frequencies between 3 and 12 Hz, and characteristic ages ranging from 17 kyr to 3 Myr. Two of them, PSRs Jl803-2149 and J2111+4606, are young and energetic Galactic-plane pulsars (spin-down power above 6 x 10(exp 35) ergs per second and ages below 100 kyr). The seven remaining pulsars, PSRs J0106+4855, J010622+3749, Jl620-4927, Jl746-3239, J2028+3332,J2030+4415, J2139+4716, are older and less energetic; two of them are located at higher Galactic latitudes (|b| greater than 10 degrees). PSR J0106+4855 has the largest characteristic age (3 Myr) and the smallest surface magnetic field (2x 10(exp 11)G) of all LAT blind-search pulsars. PSR J2139+4716 has the lowest spin-down power (3 x l0(exp 33) erg per second) among all non-recycled gamma-ray pulsars ever found. Despite extensive multi-frequency observations, only PSR J0106+4855 has detectable pulsations in the radio band. The other eight pulsars belong to the increasing population of radio-quiet gamma-ray pulsars.
    Keywords: Astrophysics
    Type: GSFC.JA.6037.2012 , GSFC.JA.0377.2012 , GSFC.JA.7328.2012
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  • 10
    Publication Date: 2019-07-12
    Description: We have discovered five millisecond pulsars (MSPs) in a survey of 14 unidentified Ferm;'LAT sources in the southern sky using the Parkes radio telescope. PSRs J0101-6422, J1514-4946, and J1902-5105 reside in binaries, while PSRs J1658-5324 and J1747-4036 are isolated. Using an ephemeris derived from timing observations of PSR JOl01-6422 (P=2.57ms, DH=12pc/cubic cm ), we have detected gamma-ray pulsations and measured its proper motion. Its gamma-ray spectrum (a power law of Gamma = 0.9 with a cutoff at 1.6 GeV) and efficiency are typical of other MSPs, but its radio and gamma-ray light curves challenge simple geometric models of emission. The high success rate of this survey -- enabled by selecting gamma-ray sources based on their detailed spectral characteristics -- and other similarly successful searches indicate that a substantial fraction of the local population of MSPs may soon be known.
    Keywords: Astronomy
    Type: GSFC.JA.01107.2012
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