The aerodynamic force acting on compact structures is often modeled as a quadratic function of the wind velocity, which fluctuates randomly due to the atmospheric turbulence. When a flexible structure is considered and the quasi-steady assumption is applied, the wind velocity is substituted by the wind-structure relative velocity and, even in case of linear structures, the composite aerodynamic-mechanical system is governed by a nonlinear differential equation characterized by a quadratic feedback term. This class of dynamical systems has been deeply investigated (with different levels of simplifications) applying several alternative mathematical approaches. In this paper we define a system approximation based on a 2nd-order Volterra series and obtain its statistical response in terms of cumulants. The response cumulants are calculated applying the Multiple Timescale Spectral Analysis leading to analytic or semi-analytic expressions. All the approximations are validated through Monte Carlo simulation within a wide parameter space. Then, the analytical structure of the obtained expressions is used to discuss, from a qualitative point of view, the behavior of the considered dynamical system.

Response of an oscillator to a random quadratic velocity-feedback loading

Carassale, Luigi
2015-01-01

Abstract

The aerodynamic force acting on compact structures is often modeled as a quadratic function of the wind velocity, which fluctuates randomly due to the atmospheric turbulence. When a flexible structure is considered and the quasi-steady assumption is applied, the wind velocity is substituted by the wind-structure relative velocity and, even in case of linear structures, the composite aerodynamic-mechanical system is governed by a nonlinear differential equation characterized by a quadratic feedback term. This class of dynamical systems has been deeply investigated (with different levels of simplifications) applying several alternative mathematical approaches. In this paper we define a system approximation based on a 2nd-order Volterra series and obtain its statistical response in terms of cumulants. The response cumulants are calculated applying the Multiple Timescale Spectral Analysis leading to analytic or semi-analytic expressions. All the approximations are validated through Monte Carlo simulation within a wide parameter space. Then, the analytical structure of the obtained expressions is used to discuss, from a qualitative point of view, the behavior of the considered dynamical system.
File in questo prodotto:
File Dimensione Formato  
Denoël, V.a_Response-of-an-oscillator-to-a-random-quadratic-velocityfeedback-loadingArticle_2015.pdf

accesso chiuso

Descrizione: Articolo
Tipologia: Documento in versione editoriale
Dimensione 1.94 MB
Formato Adobe PDF
1.94 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: https://hdl.handle.net/11567/898651
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 14
  • ???jsp.display-item.citation.isi??? 9
social impact