Non-linear oscillations of a four-degree-of-freedom model of a suspended cable under multiple internal resonance conditions

Benedettini, F.; Rega, Giuseppe; Alaggio, Rocco

doi:10.1006/jsvi.1995.0232

Cited by 146 publications

(83 citation statements)

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“…(29) together with modal relationships (7) and nonlinear frequencies (12). Instead of Eqs, (7), (12) the set of algebraic equations (6) may be taken for numerical convenience.…”

Section: Numerical Calculationsmentioning

confidence: 99%

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Nonlinear normal modes of a self-excited system driven by parametric and external excitations

Warmiński

2010

Nonlinear Dyn

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“…(29) together with modal relationships (7) and nonlinear frequencies (12). Instead of Eqs, (7), (12) the set of algebraic equations (6) may be taken for numerical convenience.…”

Section: Numerical Calculationsmentioning

confidence: 99%

“…in sagged cable dynamics [ 12]- [ 14] or gear systems [ 15], vibrations of bars, beams and plates [ 16] as well as in microelectromechanical systems (MEMS) [ 17]. If the considered structure is additionally damped by a nonlinear force e.g.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear normal modes of a self-excited system driven by parametric and external excitations

Warmiński

2010

Nonlinear Dyn

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“…Much research has been carried out into both linear and nonlinear dynamics of such systems. Benedettini et al [1,2] intensively studied linear and nonlinear vibrations of cables and devoted their attention especially to the problem of coupling "in-plane" and "out-of plane" vibrations. Two further papers [3,4] present the experimental set-up which enables such coupling to be investigated for a cable with eight lumped masses.…”

Section: Introductionmentioning

confidence: 99%

Compensation of top horizontal displacements of a riser

et al. 2016

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The nonlinear dynamic problem of catenary risers is solved by means of the rigid finite element method. The method enables us to model slender systems such as lines, cables and risers undergoing large base motions. The formulation allows elimination of large values of stiffness coefficients: shear, longitudinal and torsional (dependent on permissibility of the system analyzed). The analysis presented in the paper is concerned with the dynamics of a riser initially bent and undergoing heave excitation. Comparison of the results with those obtained using the finite difference and finite element methods shows good compatibility and indicates the correctness of the models obtained by means of the rigid finite element method. Numerical effectiveness of the method enables it to be applied in solving the dynamic optimization problem. The problem described is the compensation of the horizontal vibrations of the vessel or a platform by vertical displacements of the upper end of the riser. Bending moments which arise during the motion of a platform or a vessel can seriously influence and in some cases damage the structure. Thus the aim of the optimization is to ensure that the maximum bending moment at a given point does not exceed its static counterpart. The results of numerical simulations show that the systems enabling heave compensation can be used to minimize the difference between the bending moment caused by displacements of the platform or a vessel and the static moment.

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“…It was demonstrated that the stable response to the in-plane excitation at a certain vibration level was a whirling motion involving a phase lag of /2 between the modal co-ordinates. Recently, Benedettini et al [15] have investigated cable response phenomena of an elastic suspended cable subjected to both in-plane harmonically varying external loads per unit length and in-plane support-point motions. The focus was on a four-degree-of-freedom model containing two in-plane and two out-of-plane components, and both 2:1 resonance and harmonic resonance were studied based on a "rst order perturbation analysis of the discretized cable equations, i.e., 1:1 internal resonance and subharmonic external resonance of the order were considered.…”

Section: Introductionmentioning

confidence: 99%

Super and Combinatorial Harmonic Response of Flexible Elastic Cables With Small Sag

Nielsen

Kirkegaard

2002

Journal of Sound and Vibration

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The paper deals with the analysis of cables in stayed bridges and TV-towers, where the excitation is caused by harmonically varying in-plane motions of the upper support point with the amplitude ;. Such cables are characterized by a sag-to-chord-length ratio below 0)02, which means that the lowest circular eigenfrequencies for in-plane and out-of-plane eigenvibrations, and , are closely separated. The dynamic analysis is performed by a two-degree-of-freedom modal decomposition in the lowest in-plane and out-of-plane eigenmodes. Modal parameters are evaluated based on the eigenmodes for the parabolic approximation to the equilibrium suspension. Superharmonic components of the order n, supported by the parametric terms of the excitation and the non-linear coupling terms, are registered in the response for circular frequency K /n. At moderate ;, the cable response takes place entirely in the static equilibrium plane. At larger amplitudes the in-plane response becomes unstable and a coupled whirling superharmonic component occurs. In the paper a "rst order perturbation solution to the superharmonic response is performed based on the averaging method. For K(m/n), m(n, the geometrical non-linear restoring forces gives rise to a substantial combinatorial harmonic component with the circular frequency (n/m) . Both entirely in-plane and coupled in-plane and out-of-plane responses occur. Based on an initial frequency analysis of the response, an analytical model for these vibrations is formulated with emphasis on superharmonics of the order n"3 and combinatorial harmonics of the order (n, m)"(3,2). All analytical solutions have been veri"ed by direct numerical integration of the modal equations of motion.

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Non-linear oscillations of a four-degree-of-freedom model of a suspended cable under multiple internal resonance conditions

Cited by 146 publications

References 0 publications

Nonlinear normal modes of a self-excited system driven by parametric and external excitations

Nonlinear normal modes of a self-excited system driven by parametric and external excitations

Compensation of top horizontal displacements of a riser

Super and Combinatorial Harmonic Response of Flexible Elastic Cables With Small Sag

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