Chaos in one-dimensional structural mechanics
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REVIEW
Chaos in one-dimensional structural mechanics Giuseppe Rega · Valeria Settimi Stefano Lenci
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Received: 13 May 2020 / Accepted: 25 July 2020 © Springer Nature B.V. 2020
Abstract Notwithstanding the presence of some books summarizing specific research bodies on structural systems, reviews on nonlinear dynamics and chaos in mechanical systems and structures are quite few. This paper aims at giving a first contribution in this direction, focusing on chaos in one-dimensional structural mechanics, and reviewing fundamental studies and main outcomes obtained for macromechanical systems and applications in classical areas of mechanical, aeronautical and civil engineering. Research material is presented according to a tentatively comprehensive perspective, by suitably framing the overviewed complex dynamic phenomena of a given class of structures within the underlying continuous/reduced modelling context and the regular phenomena from which they ensue. This is a demanding perspective, which also entails leaving a number of important topics aside. Chaos in cable, beam/arch, and coupled cablebeam structures is reviewed, as highlighted in both engineering-oriented studies and theoretically driven G. Rega · V. Settimi (B) Department of Structural and Geotechnical Engineering, Sapienza University of Rome, 00194 Rome, Italy e-mail: [email protected] G. Rega e-mail: [email protected] S. Lenci Department of Civil and Building Engineering and Architecture, Polytechnic University of Marche, 60131 Ancona, Italy e-mail: [email protected]
ones, paying attention also to some relevant applications. Keywords Nonlinear dynamics · Chaos · Structural mechanics · Cables · Beams · Coupled cable-beams
Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . 2 Cable structures . . . . . . . . . . . . . . . . . . . . . 2.1 Shallow cables: archetypal single-mode model . . . 2.2 Taut strings: multimode models . . . . . . . . . . . 2.3 Shallow cables: multimode models . . . . . . . . . 2.4 Experimental cable-mass suspension . . . . . . . . 2.5 Arbitrarily sagged and inclined cables: multimode models . . . . . . . . . . . . . . . . . . . . . . . . 3 Beam structures . . . . . . . . . . . . . . . . . . . . . 3.1 Buckled beam: early theoretical achievements and experimental evidences . . . . . . . . . . . . . . . 3.2 Beams and shallow arches: archetypal single-mode models . . . . . . . . . . . . . . . . . . . . . . . 3.3 Beams: two-mode models . . . . . . . . . . . . . 3.4 Shallow/non-shallow arches: internally resonant twomode models . . . . . . . . . . . . . . . . . . . . 3.5 Multimode models . . . . . . . . . . . . . . . . . 3.6 Finite difference/finite element approaches . . . . . 3.7 A few special topics . . . . . . . . . . . . . . . . . 3.8 Spatial chaos . . . . . . . . . . . . . . . . . . . . 4 Cable-beam coupled structures . . . . . . . . . . . . . 4.1 Single-dof models . . . . . . . . . . . . . . . . . . 4.2 Multi-dof models . . . . . . . . . . . . . . . . . . 5 Conclusions . . . . . . . . . . . . . . .
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