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  • nonlinear oscillations  (9)
  • nonlinear vibrations  (8)
  • 1
    ISSN: 1573-269X
    Keywords: Cables ; active control ; nonlinear oscillations ; bifurcation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The nonlinear oscillations of a controlled suspended elastic cable under in-plane excitation are considered. Active control realized by longitudinal displacement of one support is introduced in order to reduce the transverse in-plane and out-of-plane vibrations. Linear and quadratic enhanced velocity feedback control laws are chosen and their effects on the cable motion are investigated using a two degree-of-freedom model. Perturbation analysis is performed to determine the in-plane steady-state solutions and their stability under an out-of-plane disturbance. The analysis is extended to the bifurcated two-mode steady-state oscillations in the region of parametric excitation. The dependence of the control effectiveness on the system parameters is investigated in the case of the first symmetric mode and the range of oscillation amplitudes in which the proposed control ensures a dissipation of energy is determined. Although control based only on in-plane response quantities is effective in reducing oscillations with a prevailing in-plane component, addition of out-of-plane measures has to be considered when the motion is characterized by two comparable components.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1573-269X
    Keywords: Ship dynamics ; nonlinear oscillations ; parametric excitation ; effects of bending and torsional elasticity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An enhanced mechanical model for simulating ship body oscillations and both the induced fluxural and twisting vibrations of the hull in the case of longitudinal seas is presented. The onset of parametric rolling, which may result from nonlinearly coupled heave-pitch-roll motions, and the effects of bending and torsional elasticity of the hull are considered in detail. It is shown that in the above sea conditions the flexural and/or twisting vibrations are likely to occur under a mechanism similar to that of parametric rolling.
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Nonlinear dynamics 6 (1994), S. 301-316 
    ISSN: 1573-269X
    Keywords: Valve mechanism of internal combustion engine ; parametric and forcing excitation ; nonlinear oscillations ; local and global bifurcations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper we study in detail problems of nonlinear oscillations of valve mechanism at internal combustion engine. The practical measurement indicates that stiffness of valve mechanism is not constant but is a function of the rotational angle of the cam. For simplicity of analysis we replace valve mechanism of internal combustion engine with a nonlinear oscillator of single degree of freedom under combined parametric and forcing excitation. We use the method of multiple scales and normal form theory to study local and global bifurcations of valve mechanism at internal combustion engine.
    Type of Medium: Electronic Resource
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  • 4
    ISSN: 1573-269X
    Keywords: Symmetry ; structural dynamics ; nonlinear vibrations ; group theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We show in this work that use of group-theoretic ideas can greatly simplify the procedure for finding both linear vibration modes and frequencies and locating solution branches for nonlinear vibration problems. These methods can be employed in both analytic and numerical settings, and they lead to dramatic increases in solving efficiency via block diagonalization. For the class of problems studied here (in which gyroscopic effects are present), we demonstrate that the original structural symmetry group can be employed to analyze the dynamics of the system despite the loss of reflection symmetry. This allows for a simpler and more intuitive implementation of the group representation techniques. In addition, we explain how ideas from bifurcation theory can be included with symmetry analysis to prove the existence of solution branches for nonlinear vibration problems. These examples provide great insight to the many advantages of using group-theoretic methods in structural vibrations problems.
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Nonlinear dynamics 20 (1999), S. 309-317 
    ISSN: 1573-269X
    Keywords: nonlinear oscillations ; chaos ; control ; input-output linearization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The control of chaotic oscillations is investigated in this paper. A control methodology, termed input-output linearization, is modified by locally linearizing the nonlinear control law in the small neighborhood of the control goal. Its suitability for controlling chaotic oscillators is analyzed. The forced Duffing oscillator is treated as a numerical example of controlling chaotic motion to a given fixed point and a given period-2 motion. The control signals and time needed to achieve the desired goals of the modified method are compared with those of the original method. The robustness of the control law is demonstrated.
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  • 6
    ISSN: 1573-269X
    Keywords: Experimental analysis ; cables ; nonlinear vibrations ; modal interaction ; bifurcations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An experimental model of an elastic cable carrying eight concentrated masses and hanging at in-phase or out-of-phase vertically moving supports is considered. The system parameters are adjusted to approximately realize multiple 1:1 and 2:1 internal resonance conditions involving planar and nonplanar, symmetric and antisymmetric modes. Response measurements are made in various frequency ranges including meaningful external resonance conditions. A ‘local’ analysis of the system response is made on the basis of numerous amplitude-frequency and amplitude-forcing plots obtained in different ranges of the control parameter space. Attention is mainly devoted to the detection of the main features of the regular motions exhibited by the system, and to the analysis of the relevant phenomena of nonlinear modal interaction, competition, and local bifurcation between planar and nonplanar regular responses. The resulting picture appears very rich and varied.
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  • 7
    ISSN: 1573-269X
    Keywords: Beam ; gravity effect ; method of multiple scales ; nonlinear oscillations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A critical problem in designing large structures for space applications, such as space stations and parabolic antennas, is the limitation of testing these structures and their substructures on earth. These structures will exhibit very high flexibilities due to the small loads expected to be encountered in orbit. It has been reported in the literature that the gravitational sag effect under dead weight is of extreme importance during ground tests of space-station structural components [1–4]. An investigation of a horizontal, pinned-pinned beam with complete axial restraint and undergoing large-amplitude oscillations about the statically deflected position is presented here. This paper presents a solution for the frequency-amplitude relationship of the nonlinear free oscillations of a horizontal, immovable-end beam under the influence of gravity. The governing equation of motion used for the analysis is the Bernoulli-Euler type modified to include the effects of mid-plane stretching and gravity. Boundary conditions are simply supported such that at both ends there is no bending moment and no transverse and axial displacements. These boundary conditions give rise to an initial tension in the statically deflected shape. The displacement function consists of an assumed space mode using a simple sine function and unknown amplitude which is a function of time. This assumption provides for satisfaction of the boundary conditions and leads to an ordinary differential equation which is nonlinear, containing both quadratic and cubic functions of the amplitude. The perturbation method of multiple scales is used to provide an approximate solution for the fundamental frequency-amplitude relationship. Since the beam is initially deflected the small-amplitude fundamental natural frequency always increases relative to the free vibration situation provided in zero gravity. The nonlinear equation provides for interactions between frequency and amplitude in that both hardening and softening effects arise. The coefficient of the quadratic term in the nonlinear equation arises from the static (dead load) portion of the deflection. This quadratic term, depending upon its magnitude, introduces a softening effect that overcomes the hardening term (due to initial axial tension developed by deflection) for large slenderness ratios. For very large slender, immovable-end beams, the fundamental natural frequency is greater than that of beams without axial constraints undergoing small amplitude oscillations. This phenomenon is attributed to the stiffening effect of the statically-induced axial tension. However, the stiffening effect of axial tension in beams with slenderness ratios greater than approximately 392 undergoing large-amplitude symmetric-mode oscillations is overpowered by the presence of gravitational loading.
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  • 8
    ISSN: 1573-269X
    Keywords: Beams ; nonlinear oscillations ; flexural-torsional dynamics ; torsional response ; nonlinear resonance
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Nonlinear coupling between torsional and both in-plane and out-of-plane flexural motion is examined for inextensional beams (or beam-like structures) whose torsional and flexural eigenfrequencies are of the same order. The analysis presented here is based on a consistent set of nonlinear differential equations which contain both curvature and inertia nonlinearities, and account for torsional dynamics. Response characteristics, including stability, are determined for cantilever beams subjected to a lateral periodic excitation. The beam's response in the presence of a one-to-one internal resonance involving a torsional frequency and an in-plane bending frequency is investigated in detail.
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Nonlinear dynamics 1 (1990), S. 131-141 
    ISSN: 1573-269X
    Keywords: Ship dynamics ; nonlinear vibrations ; parametric excitation ; heave-pitch-roll motion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Two different models for simulating the ship motion in longitudinal or oblique seas are presented and studied in detail. Particular attention is devoted to the parametrically induced rolling which may be established by means of the nonlinear coupling between both heave-roll and/or pitch-roll motions. It is proved that the phenomenon is likely to occur with this mechanism when the roll frequency is subharmonic of the encounter wave frequency and when the vertical motions become resonant.
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    Nonlinear dynamics 19 (1999), S. 193-235 
    ISSN: 1573-269X
    Keywords: cylinder gyroscopes ; nonlinear vibrations ; energy transfer
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we model and analyze nonlinear oscillations which are known to exist in some Coriolis-based gyroscopes due to large amplitude excitation in the drive loop. A detailed derivation of a dynamic model for a cylinder gyroscope including geometric nonlinearities is given, and the energy transfer between the system's modes is analyzed using a perturbation theory and by proposing a simplified model. The model is also simulated, and the results are shown to give an accurate description of the experimental results. This work is carried out in order to gain a better understanding of the gyroscope's dynamics, and is intended to be a starting point for designing nonlinear observers and vibration controllers for the gyroscope in order to increase the performance.
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