Options
Equivalent linearization technique in non-linear stochastic dynamics of a cable-mass system with time-varying length
Publikationstyp
Journal Article
Date Issued
2019-10-25
Sprache
English
Author(s)
Institut
TORE-URI
Journal
Volume
71
Issue
4-5
Start Page
393
End Page
416
Citation
Archives of Mechanics 4-5 (71): 393-416 (2019-01-01)
Publisher DOI
Scopus ID
In this paper the transverse vibrations of a vertical cable carrying a concentrated mass at its lower end and moving slowly vertically within the host structure are considered. It is assumed that longitudinal inertia of the cable can be neglected, with the longitudinal motion of the concentrated mass coupled with the lateral motion of the cable. An expansion of the lateral displacement of a cable in terms of approximating functions is used. The excitation acting upon the cable-mass system is a base-motion excitation due to the sway motion of a host tall structure. Such a motion of a structure often results due to action of the wind, hence it may be adequately idealized as a narrow-band random process. The narrow-band process is represented as the output of a system of two linear filters to the input in a form of a Gaussian white noise process. The non-linear problem is dealt with by an equivalent linearization technique, where the original non-linear system is replaced with an equivalent linear one, whose coefficients are determined from the condition of minimization of a mean-square error between the non-linear and the linear systems. The mean value and variance of the transverse displacement of the cable as well as those of the longitudinal motion of the lumped mass are determined with the aid of an equivalent linear system and compared with the response of the original non-linear system subjected to the deterministic harmonic excitation.
Subjects
Cable-mass system
Equivalent linearization technique
Stochastic dynamics