In this thesis, a novel approach is developed for evaluating the deterministic and stochastic response of continuous systems coupled with discrete ones. Continuous systems are monodimensional beams with symmetric and asymmetric cross section as well as composite beams; discrete systems include a variety of attachments as masses, mass-spring subsystems, viscoelastic dampers and external constraints. The proposed approach is based on the theory of generalised functions to take into account discontinuities of response variables of beams. A generalization to two-dimensional frames is also developed. The proposed approach is applied to several cases of engineering interest, with a specific insight into vibration control applications using viscoelastic dampers. Focusing in random vibrations, a novel statistical linearization procedure is developed, where the response statistics of non-linear beams with non-linear external constraints and moderately-large displacements are obtained using the analytical constrained modes of an equivalent linear beam. In comparison to the standard response determination techniques, the proposed approach appears significantly more computationally efficient.

In questa tesi viene sviluppato un approccio innovativo per valutare la risposta dinamica, deterministica e stocastica, di sistemi continui accoppiati a sistemi discreti. Per sistemi continui si intendono travi con sezioni simmetriche e asimmetriche e travi in composito; per sistemi discreti si intendono una grande varietà di elementi come masse, sottosistemi massa molla, smorzatori viscoelastici e supporti esterni. L’approccio proposto si basa sulla teoria delle funzioni generalizzate per tenere conto delle discontinuità delle variabili di risposta delle travi. La formulazione viene estesa anche a telai bidimensionali. L’approccio proposto è applicato a molti casi di interesse ingegneristico, con una particolare attenzione al controllo delle vibrazioni utilizzando smorzatori viscoelastici. Per quanto riguarda la risposta stocastica viene sviluppata un’innovativa procedura di linearizzazione statistica, dove le statistiche delle variabili della risposta di travi non lineari con supporti esterni non lineari e che subisce grandi spostamenti sono ottenute utilizzando l’espressione analitica di modi vincolati di una trave lineare equivalente. In confronto alle tecniche presenti in letteratura, l’approccio proposto ha il vantaggio di essere molto più efficiente da un punto di vista computazionale.

A generalised function approach to the dynamic analysis of coupled continuous-discrete systems under deterministic and stochastic loads / Burlon, Andrea. - (2019 Apr 16).

A generalised function approach to the dynamic analysis of coupled continuous-discrete systems under deterministic and stochastic loads

Burlon, Andrea
2019-04-16

Abstract

In this thesis, a novel approach is developed for evaluating the deterministic and stochastic response of continuous systems coupled with discrete ones. Continuous systems are monodimensional beams with symmetric and asymmetric cross section as well as composite beams; discrete systems include a variety of attachments as masses, mass-spring subsystems, viscoelastic dampers and external constraints. The proposed approach is based on the theory of generalised functions to take into account discontinuities of response variables of beams. A generalization to two-dimensional frames is also developed. The proposed approach is applied to several cases of engineering interest, with a specific insight into vibration control applications using viscoelastic dampers. Focusing in random vibrations, a novel statistical linearization procedure is developed, where the response statistics of non-linear beams with non-linear external constraints and moderately-large displacements are obtained using the analytical constrained modes of an equivalent linear beam. In comparison to the standard response determination techniques, the proposed approach appears significantly more computationally efficient.
16-apr-2019
Settore ICAR/08 - SCIENZA DELLE COSTRUZIONI
FAILLA, Giuseppe
ARENA, Felice
ARENA, Felice
Doctoral Thesis
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12318/63618
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