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Multiple-scale analysis

About: Multiple-scale analysis is a research topic. Over the lifetime, 1360 publications have been published within this topic receiving 27530 citations.


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TL;DR: In this paper, a low-dimensional model of a top-tensioned riser under excitations from vortices and time-varying tension is proposed, where the van der Pol wake oscillator is used to simulate the loading caused by the vortex shedding.
Abstract: A low-dimensional model of a top-tensioned riser under excitations from vortices and time-varying tension is proposed, where the van der Pol wake oscillator is used to simulate the loading caused by the vortex shedding. The governing partial differential equations describing the fluid–structure interactions are formulated and multi-mode approximations are obtained using the Galerkin projection method. The one mode approximation is applied in this study and two different resonances are investigated by employing the method of multiple scales. They are the 1:1 internal resonance between the structure and wake oscillator (also known as ‘lock-in’ phenomenon) and the combined 1:1 internal and 1:2 parametric resonances. Bifurcations under the varying nondimensional shedding frequency for different mass–damping parameters are investigated and the results of multiple-scale analysis are compared with direct numerical simulations. Analytical responses are calculated using the continuation method and their stability is determined by examining the eigenvalues of the corresponding characteristic equations. Effects of the system parameters including the amplitude of the tension variation, vortex shedding frequency and mass–damping parameter on the system bifurcations have been investigated. The analytical approach has allowed to probe bifurcations occurring in the system and to identify stable and unstable responses. It is shown that the combined resonances can induce large-amplitude vibration of the structure. Counter-intuitively, the amplitude of such responses increases rapidly as the amplitude of the tension variation grows. Comparisons between the analytical and numerical results confirm that the span of the system vibration can be accurately predicted analytically with respect to the obtained response amplitudes of responses. The proposed multi-mode approximation and presented findings of this study can be used to enhance design process of top tension risers.

25 citations

Journal ArticleDOI
TL;DR: In this article, the effect of time delays and control gains on the stability, amplitude, frequency-response behavior, peak amplitude, critical excitation amplitude, and compared the optimal values of the controllers gains, simulated and compared.
Abstract: The paper presents time-delayed feedback control to reduce the nonlinear resonant vibration of a piezoelectric elastic beam.a#13; Specially, we examine three single-input linear time-delayed feedback control methodologies: displacement, velocity anda#13; acceleration time-delayed feedback. Moreover, the multi-input time-delayed feedback control methodologies are discussed. Utilizinga#13; the method of multiple scales, the modulation equation and the first order approximations of the primary resonances are derived and the effect of time delay on the resonances is analyzed. Then the effect of time delays and control gains on the stability, amplitude,a#13; frequency-response behavior, peak amplitude, critical excitation amplitude are investigated. Optimal values of the controllers gainsa#13; and delay are obtained, simulated, and compared. The time-delayed feedback control acts as a vibration absorber at specific values of time delay. On the other hand, using using mixed delay feedback controllers demonstrates an excellent improvement in mitigating the first-mode vibration.

25 citations

Journal ArticleDOI
TL;DR: In this paper, a model of a magnetoelastic buckled beam subjected to an external axial periodic force in a periodic transversal magnetic field is investigated, and the model is described by a two-frequency parametric vibration system with self-excitation.

24 citations

Journal ArticleDOI
TL;DR: In this paper, the nonlinear vibration model of a moving strip between two mill with time-dependent tension was established, and approximate solutions were obtained using the method of multiple scales, and the stable regions and unstable regions for parametric resonance were determined with different cases.
Abstract: The strip with a time-dependent tension moves, namely a harmonically varying tension about a constant initial tension. The nonlinear vibration model of moving strip between two mills with time-dependent tension was established. Approximate solutions were obtained using the method of multiple scales. Depending on the variation of the tension, three distinct cases arise: frequency away from zero or two times the natural frequency, frequency close to zero, frequency close to two times the natural frequency. For frequency close to zero and away from zero and two times the natural frequency, the system is always stable. For frequency close to two times the natural frequency, the stability is analyzed respectively when the trivial solution exists and the nontrivial solution exists. Numerical simulation was made on some 1660 mm tandem rolling mill, and the stable regions and unstable regions for parametric resonance are determined with different cases. The rolling speed and the thickness of strip have strong influences on the stability of principle parametric resonances. But the distance between two mills has little influence on the stability of principle parametric resonances.

24 citations

Journal ArticleDOI
TL;DR: In this article, it is shown that natural vibrations, localized around the inclusion, are possible in a system consisting of an infinite string on an elastic foundation-concentrated inertial inclusion which moves at a constant, subcritical velocity.

24 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202320
202237
202150
202042
201972
201851