Influence of symmetries and imperfections on the non-linear vibration modes of archetypal structural systems

Orlando, Diego; Gonçalves, Paulo B.; Rega, Giuseppe; Lenci, Stefano

doi:10.1016/j.ijnonlinmec.2012.10.004

Cited by 15 publications

(14 citation statements)

References 42 publications

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“…1, was proposed by Thompson and Gaspar [1] as an example of interactive buckling in the context of the catastrophe theory. The nonlinear static and dynamic behaviour of this model was recently explored by Orlando et al [2] and Gavassoni et al [3]. Their results show that the inherent symmetries and post-buckling solutions have a marked influence on the underlying potential function and, consequently, on the nonlinear dynamics of the system.…”

Section: Phenomenological Discrete Modelmentioning

confidence: 84%

Non-linear finite element analysis of the dynamics of a slender cable stayed tower

2018

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The aim of the present work is to investigate the static and dynamic nonlinear behaviour of a cable-stayed tower. A continuous structural model of a slender tower is discretized by the finite element method. First the buckling and post-buckling behaviour of the tower under axial load is explored, in order to understand the influence of the cable stiffness and lateral restrain on the load carrying capacity of the tower. Then, the linear vibration modes and frequencies are obtained. Due to the inherent symmetries of the tower, coincident buckling loads and vibration frequencies are obtained. This may lead to interactive buckling and internal resonance, increasing the effect of the geometric nonlinearities on the response. The results show that the tower exhibits a highly nonlinear response, which must be considered with care in the design stage.

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Section: Phenomenological Discrete Modelmentioning

confidence: 84%

Non-linear finite element analysis of the dynamics of a slender cable stayed tower

2018

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“…Similarly, in systems with impacts one solution can ensure correct operation of a machine, while others may lead to damage or destruction [5,4,14,28,15]. The same phenomena is present in multi-degree of freedom systems where interactions between modes and internal resonances play an important role [8,19,10,26].…”

Section: Introductionmentioning

confidence: 94%

Basin stability approach for quantifying responses of multistable systems with parameters mismatch

et al. 2016

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In this paper we propose a new method to detect and classify coexisting solutions in nonlinear systems. We focus on mechanical and structural systems where we usually avoid multistability for safety and reliability. We want to be sure that in the given range of parameters and initial conditions the expected solution is the only possible or at least has dominant basin of attraction. We propose an algorithm to estimate the probability of reaching the solution in given (accessible) ranges of initial conditions and parameters. We use a modified method of basin stability (Menck et al. in Nat Phys 9(2):89-92, 2013).In our investigation we examine three different systems: a Duffing oscillator with a tuned mass absorber, a bilinear impacting oscillator and a beam with attached rotating pendula. We present the results that prove the usefulness of the proposed algorithm and highlight its strengths in comparison with classical analysis of nonlinear systems (analytical solutions, path-following, basin of attraction ect.). We show that with relatively small computational effort (comparing to classical analysis) we can predict the behaviour of the system and select the ranges in parameter's space where the system behaves in a presumed way. The method can be used in all types of nonlinear complex systems.

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“…The immediate effect of a current acting in an angle α c with respect to the x axis is comparable to an initial imperfection (Orlando et al, 2013) because the current produces an initial static displacement, which for the numerical values in Table 1 …”

Section: Effect Of Ocean Currentsmentioning

confidence: 99%

“…However, this SDOF model is unable to capture the nonlinear coupling between different vibration modes and out-of-plane motions of the structure, which may lead to complex dynamic phenomena. This paper presents the derivation of the equations of motion of the compliant articulated tower under environmental loads using Augusti's model (Bazant and Cedolin, 2010;Pignataro et al, 2013;Orlando et al, 2013). The invariant-manifold approach proposed by Shaw and Pierre (1993) is then applied to the equations of motion, and the resulting equations are solved through an asymptotic expansion of the linear vibration modes of the linearized problem.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear vibration modes of an offshore articulated tower

2015

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Influence of symmetries and imperfections on the non-linear vibration modes of archetypal structural systems

Cited by 15 publications

References 42 publications

Non-linear finite element analysis of the dynamics of a slender cable stayed tower

Non-linear finite element analysis of the dynamics of a slender cable stayed tower

Basin stability approach for quantifying responses of multistable systems with parameters mismatch

Nonlinear vibration modes of an offshore articulated tower

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