We model the dynamical behavior of a three dimensional (3-D) dissipative oscillator consisting of a m-block whose vertical fall occurs against a spring and which can also slide horizontally on a rigid truss rotating at an assigned angular speed ω(t). The bead’s z-vertical time law is obvious, whilst its x-motion along the horizontal arm is ruled by a linear differential equation we solve through the Hermite functions and the Kummer (1837) [1] confluent Hypergeometric Function (CHF) 1F1. After the rotation θ(t) has been computed, we know completely the m-motion in a cylindrical frame of reference so that some transients have then been analyzed. Finally, further effects as an inclined slide and a contact dry friction have been added to the problem, so that the motion differential equation becomes inhomogeneous: we resort to Lagrange method of variation of constants, helped by a Fourier–Bessel expansion, in order to manage the relevant intractable integrations.

Hypergeometric solutions to a three dimensional dissipative oscillator driven by aperiodic forces / Bocci, Alessio; Mingari Scarpello, Giovanni; Ritelli, Daniele*. - In: APPLIED MATHEMATICAL MODELLING. - ISSN 0307-904X. - ELETTRONICO. - 53:(2018), pp. 71-82. [10.1016/j.apm.2017.07.055]

Hypergeometric solutions to a three dimensional dissipative oscillator driven by aperiodic forces

Mingari Scarpello, Giovanni
Membro del Collaboration Group
;
Ritelli, Daniele
Membro del Collaboration Group
2018

Abstract

We model the dynamical behavior of a three dimensional (3-D) dissipative oscillator consisting of a m-block whose vertical fall occurs against a spring and which can also slide horizontally on a rigid truss rotating at an assigned angular speed ω(t). The bead’s z-vertical time law is obvious, whilst its x-motion along the horizontal arm is ruled by a linear differential equation we solve through the Hermite functions and the Kummer (1837) [1] confluent Hypergeometric Function (CHF) 1F1. After the rotation θ(t) has been computed, we know completely the m-motion in a cylindrical frame of reference so that some transients have then been analyzed. Finally, further effects as an inclined slide and a contact dry friction have been added to the problem, so that the motion differential equation becomes inhomogeneous: we resort to Lagrange method of variation of constants, helped by a Fourier–Bessel expansion, in order to manage the relevant intractable integrations.
2018
Hypergeometric solutions to a three dimensional dissipative oscillator driven by aperiodic forces / Bocci, Alessio; Mingari Scarpello, Giovanni; Ritelli, Daniele*. - In: APPLIED MATHEMATICAL MODELLING. - ISSN 0307-904X. - ELETTRONICO. - 53:(2018), pp. 71-82. [10.1016/j.apm.2017.07.055]
Bocci, Alessio; Mingari Scarpello, Giovanni; Ritelli, Daniele*
File in questo prodotto:
File Dimensione Formato  
BocciA_AMM_2018_postprint.pdf

Open Access dal 15/08/2019

Tipo: Postprint
Licenza: Licenza per Accesso Aperto. Creative Commons Attribuzione - Non commerciale - Non opere derivate (CCBYNCND)
Dimensione 738.52 kB
Formato Adobe PDF
738.52 kB Adobe PDF Visualizza/Apri

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: https://hdl.handle.net/11585/661506
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 1
social impact