This work focuses on determining the stochastic response properties, in the frequency domain, of a general class of nonlinear systems with polynomial nonlinearities. Specifically, the results are presented in terms of the stationary power spectral densities of the system's displacement and velocity. This is pursued by revisiting the conditional power spectrum concept, with the assumption that the response process is both ergodic and pseudo-harmonic and characterized by an amplitude, and a phase. A theoretical elucidation of an existing formula for the conditional spectrum is attempted. In particular, this concept is interpreted in conjunction with the time averaging approximation made in the definition of the stationary probability density function of a response amplitude quantity, associated with the original nonlinear system. It is shown that a proper definition of the stationary probability density of the response amplitude, along with a reasonable treatment of the distribution over...

A perspective on conditional spectrum-based determination of response statistics of nonlinear systems

Pomaro B.
;
2024

Abstract

This work focuses on determining the stochastic response properties, in the frequency domain, of a general class of nonlinear systems with polynomial nonlinearities. Specifically, the results are presented in terms of the stationary power spectral densities of the system's displacement and velocity. This is pursued by revisiting the conditional power spectrum concept, with the assumption that the response process is both ergodic and pseudo-harmonic and characterized by an amplitude, and a phase. A theoretical elucidation of an existing formula for the conditional spectrum is attempted. In particular, this concept is interpreted in conjunction with the time averaging approximation made in the definition of the stationary probability density function of a response amplitude quantity, associated with the original nonlinear system. It is shown that a proper definition of the stationary probability density of the response amplitude, along with a reasonable treatment of the distribution over...
File in questo prodotto:
File Dimensione Formato  
A perspective on conditional spectrum-based determination of response statistics of nonlinear systems.pdf

accesso aperto

Tipologia: Published (Publisher's Version of Record)
Licenza: Creative commons
Dimensione 4.35 MB
Formato Adobe PDF
4.35 MB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

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/11577/3537924
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
  • OpenAlex 0
social impact