This paper proposes an original and efficient approach to the moving load problem on Euler–Bernoulli beams, with Kelvin–Voigt viscoelastic translational supports and rotational joints, and in addition, equipped with Kelvin–Voigt viscoelastic tuned mass dampers (TMDs). While supports are taken as representative of external devices such as grounded dampers or in-span supports with flexibility and damping, the rotational joints may model rotational dampers or connections with flexibility and damping arising from imperfections or damage. The theory of generalised functions is used to treat the discontinuities of the response variables, which involves deriving exact complex eigenvalues and eigenfunctions from a characteristic equation built as determinant of a 4 × 4 matrix. Based on built pertinent orthogonality conditions for the deflection eigenfunctions, a closed-form analytical response is established in the time domain. The proposed solution holds for any number of TMDs and along-axis supports/joints. To show its applicability, accuracy and efficiency, in a numerical application a beam with multiple supports/joints is considered, subjected to a moving concentrated force and a series of concentrated forces, respectively. In two different configurations, the beam is equipped with one TMD and three TMDs, respectively.

On the moving load problem in beam structures equipped with tuned mass dampers

FAILLA, Giuseppe;
2017

Abstract

This paper proposes an original and efficient approach to the moving load problem on Euler–Bernoulli beams, with Kelvin–Voigt viscoelastic translational supports and rotational joints, and in addition, equipped with Kelvin–Voigt viscoelastic tuned mass dampers (TMDs). While supports are taken as representative of external devices such as grounded dampers or in-span supports with flexibility and damping, the rotational joints may model rotational dampers or connections with flexibility and damping arising from imperfections or damage. The theory of generalised functions is used to treat the discontinuities of the response variables, which involves deriving exact complex eigenvalues and eigenfunctions from a characteristic equation built as determinant of a 4 × 4 matrix. Based on built pertinent orthogonality conditions for the deflection eigenfunctions, a closed-form analytical response is established in the time domain. The proposed solution holds for any number of TMDs and along-axis supports/joints. To show its applicability, accuracy and efficiency, in a numerical application a beam with multiple supports/joints is considered, subjected to a moving concentrated force and a series of concentrated forces, respectively. In two different configurations, the beam is equipped with one TMD and three TMDs, respectively.
Euler–Bernoulli beam; Moving loads; Rotational joint; Translational support; Tuned mass damper
File in questo prodotto:
File Dimensione Formato  
Adam et al., 2017.pdf

non disponibili

Tipologia: Versione Editoriale (PDF)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 1.16 MB
Formato Adobe PDF
1.16 MB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.12318/665
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 17
  • ???jsp.display-item.citation.isi??? 15
social impact