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, GiovanniMembro 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.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.