ALBERT

All Library Books, journals and Electronic Records Telegrafenberg

Your email was sent successfully. Check your inbox.

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

Proceed reservation?

Export
  • 11
    ISSN: 1573-269X
    Keywords: Composite beams ; flexural-flexural-torsional-extensional vibrations ; nonlinear equations of motion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Newton's second law is used to develop the nonlinear equations describing the extensional-flexural-flexural-torsional vibrations of slewing or rotating metallic and composite beams. Three consecutive Euler angles are used to relate the deformed and undeformed states. Because the twisting-related Euler angle ϕ is not an independent Lagrangian coordinate, twisting curvature is used to define the twist angle, and the resulting equations of motion are symmetric and independent of the rotation sequence of the Euler angles. The equations of motion are valid for extensional, inextensional, uniform and nonuniform, metallic and composite beams. The equations contain structural coupling terms and quadratic and cubic nonlinearities due to curvature and inertia. Some comparisons with other derivations are made, and the characteristics of the modeling are addressed. The second part of the paper will present a nonlinear analysis of a symmetric angle-ply graphite-epoxy beam exhibiting bending-twisting coupling and a two-to-one internal resonance.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 12
    ISSN: 1573-269X
    Keywords: Internal resonances ; bifurcations ; quasiperiodic motions ; chaos
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We present a collection of experimental results on the influence of modal interactions (i.e., internal or autoparametric resonances) on the nonlinear response of flexible metallic and composite structures subjected to a range of resonant excitations. The experimental results are provided in the form of frequency spectra, Poincaré sections, pseudo-phase planes, dimension calculations, and response curves. Experimental observations of transitions from periodic to chaotically modulated motions are also presented. We also discuss relevant analytical results. The current study is also relevant to other internally resonant structural systems.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 13
    ISSN: 1573-269X
    Keywords: Flexible robotic manipulator ; advanced composites ; mathematical modeling ; finite element method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A dynamic model for a two degree-of-freedom planar robot arm is derived in this study. The links of the arm, connected to prismatic and revolute joints, are considered to be flexible. They are assumed to be fabricated from either aluminum or laminated composite materials. The model is derived based on the Timoshenko beam theory in order to account for the rotary inertia and shear deformation. These effects are significant in modeling flexible links connected to prismatic joints. The deflections of the links are approximated by using a shear-deformable beam finite element. Hamilton's principle is implemented to derive the equations describing the combined rigid and flexible motions of the arm. The resulting equations are coupled and highly nonlinear. In view of the large number of equations involved and their geometric nonlinearity (topological and quadratic), the solution of the equations of motion is obtained numerically by using a stiff integrator. The digital simulation studies examine the interaction between the flexible and the rigid body motions of the robot arm, investigate the improvement in the accuracy of the model by considering the flexibility of all rather than some of the links of the arm, assess the significance of the rotary inertia and shear deformation, and illustrate the advantages of using advanced composites in the structural design of robotic manipulators.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 14
    Electronic Resource
    Electronic Resource
    Springer
    Nonlinear dynamics 2 (1991), S. 235-262 
    ISSN: 1573-269X
    Keywords: Burgers' equation ; stabilizability ; optimal controls ; approximations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A stabilization problem for Burgers' equation is considered. Using linearization, various controllers are constructed which minimize certain weighted energy functionals. These controllers produce the desired degree of stability for the closed-loop nonlinear system. A numerical scheme for computing the feedback gain functional is developed and several numerical experiments are performed to illustrate the theoretical results.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 15
    Electronic Resource
    Electronic Resource
    Springer
    Nonlinear dynamics 2 (1991), S. 317-317 
    ISSN: 1573-269X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 16
    Electronic Resource
    Electronic Resource
    Springer
    Nonlinear dynamics 2 (1991), S. 353-365 
    ISSN: 1573-269X
    Keywords: Chaotic motions ; diagnostics ; specepstrum
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A technique based on the power cepstrum has been developed to analyze and characterize data of various nonlinear and chaotic motions. For repeatability and ready availability, nonlinear response data of a Duffing oscillator and van der Pol oscillator, generated numerically by the fourth order Runge-Kutta algorithm, were used in the investigation. Results obtained by the proposed technique using spectrum, cepstrum, and specepstrum which is defined as the spectrum of the logarithmic cepstrum, indicate that it is superior to methods previously available in the literature.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 17
    ISSN: 1573-269X
    Keywords: Railway dynamics ; limit-cycles ; bifurcations ; chaos
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A dicone moving on a pair of cylindrical rails can be considered as a simplified model of a railway wheelset. Taking into account the non-linear friction laws of rolling contact, the equations of motion for this non-linear mechanical system result in a set of differential-algebraic equations. Previous simulations performed with the differential-algebraic solver DASSL, [2], and experiments, [7], indicated non-linear phenomena such as limit-cycles, bifurcations as well as chaotic behaviour. In this paper the non-linear phenomena are investigated in more detail with the aid of special in-house software and the path-following algorithm PATH [10]. We apply Poincaré sections and Poincaré maps to describe the structure of periodic, quasiperiodic and chaotic motions. The analyses show that part of the chaotic behaviour of the non-linear system can be fully understood as a non-linear iterative process. The resulting stretching and folding processes are illustrated by series of Poincaré sections.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 18
    ISSN: 1573-269X
    Keywords: Beams ; free vibration ; nonlinear oscillation ; quadrature method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The quadrature method (OM) has been used in structural analysis only in recent years. In this study, OM is applied to flexural vibration analysis of a geometrically nonlinear beam. The numerical results by OM agree with the results by the finite element method. It is believed that this is the first attempt to solve a nonlinear dynamic problem by the quadrature method.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 19
    ISSN: 1573-269X
    Keywords: Hopf bifurcation ; multiple scales ; limit cycles ; internal resonance
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We study motions near a Hopf bifurcation of a representative nonconservative four-dimensional autonomous system with quadratic nonlinearities. Special cases of the four-dimensional system represent the envelope equations that govern the amplitudes and phases of the modes of an internally resonant structure subjected to resonant excitations. Using the method of multiple scales, we reduce the Hopf bifurcation problem to two differential equations for the amplitude and phase of the bifurcating cyclic solutions. Constant solutions of these equations provide asymptotic expansions for the frequency and amplitude of the bifurcating limit cycle. The stability of the constant solutions determines the nature of the bifurcation (i.e., subcritical or supercritical). For different choices of the control parameter, the range of validity of the analytical approximation is ascertained using numerical simulations. The perturbation analysis and discussions are also pertinent to other autonomous systems.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 20
    ISSN: 1573-269X
    Keywords: Fixed point algorithm ; quasi-periodic response ; bifurcation to chaos
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Steady-state solutions of a piecewise-linear oscillator under multi-forcing frequencies are obtained using the fixed point algorithm (FPA). Stability analysis is also performed using the same technique. For the periodic solutions of a piecewise-linear oscillator with single forcing frequency, the harmonic balance method (HBM) is also used along with the FPA. Although both FPA and HBM generate accurate solutions, it is observed that the HBM failed to converge to solutions in the superharmonic range of the forcing frequency. The fixed point algorithm was also applied to the oscillator under multifrequency excitation. The algorithm proved to be very effective in obtaining torus solutions and in locating corresponding bifurcation thresholds. A piecewise-linear oscillator model of an offshore articulated loading platform (ALP) subjected to two incommensurate wave frequencies is found to exhibit chaotic behavior. A second order Poincaré mapping technique reveals the hidden fractal-like nature of the resulting chaotic response. A parametric study is performed for the response of the ALP.
    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...