Publisher DOI: 10.24423/aom.3142
Title: Equivalent linearization technique in non-linear stochastic dynamics of a cable-mass system with time-varying length
Language: English
Authors: Weber, Hanna 
Iwankiewicz, Radoslaw Marek 
Kaczmarczyk, Stefan 
Keywords: Cable-mass system;Equivalent linearization technique;Stochastic dynamics
Issue Date: 25-Oct-2019
Source: Archives of Mechanics 4-5 (71): 393-416 (2019-01-01)
Journal or Series Name: Archives of mechanics 
Abstract (english): 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.
ISSN: 0373-2029
Institute: Mechanik und Meerestechnik M-13 
Type: (wissenschaftlicher) Artikel
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