ALBERT

All Library Books, journals and Electronic Records Telegrafenberg

feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
  • 1
    ISSN: 1573-269X
    Keywords: Power systems ; chaos ; bifurcations ; loss of synchronism
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We investigate some of the instabilities in a single-machine quasi-infinite busbar system. The system's behavior is described by the so-called swing equation, which is a nonlinear second-order ordinary-differential equation with additive and multiplicative harmonic terms having the frequency Ω. When Ω≈ω0, where ω0 is the linear natural frequency of the machine, we use digital-computer simulations to exhibit some of the complicated responses of the machine, including period-doubling bifurcations, chaotic motions, and unbounded motions (loss of synchronism). To predict the onset of these complicated behaviors, we use the method of multiple scales to develop an approximate first-order closed-form expression for the period-one responses of the machine. Then, we use various techniques to determine the stability of the analytical solutions. The analytically predicted period-one solutions and conditions for its instability are in good agreement with the digital-computer results.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 2
    ISSN: 1573-269X
    Keywords: Autoparametric resonance ; torus ; chaos ; Hopf bifurcation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An investigation is presented of the response of a three-degree-of-freedom system with quadratic nonlinearities and the autoparametric resonances ω3≈2ω2 and ω2≈2ω1 to a harmonic excitation of the third mode, where the ω m are the linear natural frequencies of the system. The method of multiple scales is used to determine six first-order nonlinear ordinary differential equations that govern the time variation of the amplitudes and phases of the interacting modes. The fixed points of these equations are obtained and their stability is determined. For certain parameter values, the fixed points are found to lose stability due to Hopf bifurcations and consequently the system exhibits amplitude-and phase-modulated motions. Regions where the amplitudes and phases display periodic, quasiperiodic, and chaotic time variations and hence regions where the overall system motion is periodically, quasiperiodically, and chaotically modulated are determined. Using various numerical simulations, we investigated nonperiodic solutions of the modulation equations using the amplitudeF of the excitation as a control parameter. As the excitation amplitudeF is increased, the fixed points of the modulation equations exhibit an instability due to a Hopf bifurcation, leading to limit-cycle solutions of the modulation equations. AsF is increased further, the limit cycle undergoes a period-doubling bifurcation followed by a secondary Hopf bifurcation, resulting in either a two-period quasiperiodic or a phase-locked solution. AsF is increased further, there is a torus breakdown and the solution of the modulation equations becomes chaotic, resulting in a chaotically modulated motion of the system.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 3
    ISSN: 1573-269X
    Keywords: Autoparametric resonance ; combination resonance ; saturation ; phase-locked motions ; quasiperiodic motions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The response of a structure to a simple-harmonic excitation is investigated theoretically and experimentally. The structure consists of two light-weight beams arranged in a T-shape turned on its side. Relatively heavy and concentrated weights are placed at the upper and lower free ends and at the point where the two beams are joined. The base of the ‘T’ is clamped to the head of a shaker. Because the masses of the concentrated weights are much larger than the masses of the beams, the first three natural frequencies are far below the fourth; consequently, for relatively low frequencies of the excitation, the structure has, for all practical purposes, only three degrees of freedom. The lengths and weights are chosen so that the third natural frequency is approximately equal to the sum of the two lower natural frequencies, an arrangement that produces an autoparametric (also called an internal) resonance. A linear analysis is performed to predict the natural frequencies and to aid in the design of the experiment; the predictions and observations are in close agreement. Then a nonlinear analysis of the response to a prescribed transverse motion at the base of the ‘T’ is performed. The method of multiple scales is used to obtain six first-order differential equations describing the modulations of the amplitudes and phases of the three interacting modes when the frequency of the excitation is near the third natural frequency. Some of the predicted phenomena include periodic, two-period quasiperiodic, and phase-locked (also called synchronized) motions; coexistence of multiple stable motions and the attendant jumps; and saturation. All the predictions are confirmed in the experiments, and some phenomena that are not yet explained by theory are observed.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 4
    ISSN: 1573-269X
    Keywords: Chaos ; buckled beam ; parametric resonance ; bifurcations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A nonlinear analysis of the response of a simply-supported buckled beam to a harmonic axial load is presented. The method of multiple scales is used to determine to second order the amplitude- and phase-modulation equations. Floquet theory is used to analyze the stability of periodic responses. The perturbation results are verified by integrating the governing equation using both digital and analog computers. For small excitation amplitudes, the analytical results are in good agreement with the numerical solutions. The large-amplitude responses are investigated by using a digital computer and are compared with those obtained via an analog-computer simulation. The complicated dynamic behaviors that were found include period-multiplying and period-demultiplying bifurcations, period-three and period-six motions, jump phenomena, and chaos. In some cases, multiple periodic attractors coexist, and a chaotic attractor coexists with a periodic attractor. Phase portraits, spectra of the responses, and a bifurcation set of the many solutions are presented.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Nonlinear dynamics 7 (1995), S. 301-315 
    ISSN: 1573-269X
    Keywords: Nonlinear oscillations ; resonance ; modulation ; multifrequency excitation ; carrier frequency
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We study the response of a single-degree-of-freedom system with cubic nonlinearities to an amplitude-modulated excitation whose carrier frequency is much higher than the natural frequency of the system. The only restriction on the amplitude modulation is that it contain frequencies much lower than the carrier frequency of the excitation. We apply the theory to different types of amplitude modulation and find that resonant excitation of the system may occur under some conditions.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 6
    ISSN: 1573-269X
    Keywords: Cable ; autoparametric resonance ; Galerkin procedure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We discuss solution methods for nonlinear vibrations of cables having small initial sag-to-span ratios. One-to-one internal resonances between the in-plane and out-of-plane modes as well as primary resonances of the in-plane mode are considered. Approximate solutions are obtained by two different approaches. In the first approach, the method of multiple scales is applied directly to the governing partial-differential equations and boundary conditions. In the second approach, the equations are first discretized, and then the method of multiple scales is applied to the resulting ordinary-differential equations. It is shown that treatment of the discretized system is inaccurate compared to direct treatment of the partial-differential system. Discrepancies between the two solutions appear even at the first level of approximation. Stability analyses of the amplitude and phase modulation equations for both methods are also performed.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 7
    ISSN: 1573-269X
    Keywords: Power systems ; loss of synchronism ; chaos ; bifurcations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The response of a single-machine quasi-infinite busbar system to the simultaneous occurrence of principal parametric resonance and subharmonic resonance of order one-half is investigated. By numerical simulations we show the existence of oscillatory solutions (limit cycles), period-doubling bifurcations, chaos, and unbounded motions (loss of synchronism). The method of multiple scales is used to derive a second-order analytical solution that predicts (a) the onset of period-doubling bifurcations, which is a precursor to chaos and unbounded motions (loss of synchronism), and (b) saddle-node bifurcations, which may be precursors to loss of synchronism.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 8
    ISSN: 1573-269X
    Keywords: Averaged Lagrangian ; valve ; resonances ; Galerkin procedure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Methods for determining the response of continuous systems with quadratic and cubic nonlinearities are discussed. We show by means of a simple example that perturbation and computational methods based on first discretizing the systems may lead to erroncous results whereas perturbation methods that attack directly the nonlinear partial-differential equations and boundary conditions avoid the pitfalls associated with the analysis of the discretized systems. We describe a perturbation technique that applies either the method of multiple scales or the method of averaging to the Lagrangian of the system rather than the partial-differential equations and boundary conditions.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 9
    ISSN: 1077-3118
    Source: AIP Digital Archive
    Topics: Physics
    Notes: We prepared porous silicon for which the UV reflectance (3.3–6 eV) is nearly eliminated, and exhibits no features at the Si interband bulk transitions 3.3, 4.3, and 5.5 eV. Plating with a thin layer of copper is found to cause recovery of the UV bulk-like crystalline reflectance and interband resonances. This provides evidence that the loss of crystalline absorption is reversible and is not due to a permanent loss in the crystalline structure. This may relate to a recent model in which the optical activity of ultra small nanocrystallites is produced by a new Si–Si crystalline configuration (or phase), distinct from but interconnected to the diamond-like configuration by a potential barrier. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 10
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 77 (1995), S. 4130-4132 
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: HCl, H3PO4, and H2SO4 baths have been used to re-establish the photoluminescence of porous Si whose initial luminescence had been quenched by immersion in CuCl2. HCl had the fastest effect, with luminescence beginning to reappear after typically a few minutes, while the other acids required typically one to two days for dim luminescence to start reappearing. Auger electron spectroscopy (AES) depth profiling showed that after quenching, the Cu profile typically penetrated 2000 to 3000 A(ring) into the porous Si and that the O concentration was greatly enhanced in this region. After re-establishment of the luminescence by acid treatment, the AES depth profiles showed no Cu, but still had an enhanced O region of similar size and concentration. Photoluminescence emission spectra taken in situ during acid treatment with HCl showed a redshift of about 8% in the peak wavelength as the intensity increased. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...