Abstract
In this paper the transverse vibrations of a vertical cable carrying at its lower end a concentrated mass and moving slowly vertically within the host structure are considered. It is assumed that longitudinal inertia of a 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 of vibrations of a cablemass system is a basemotion excitation due to the sway motion of a host tall structure. Such a motion of a structure is assumed to result from action of the wind, hence it may be adequately idealized as a narrowband random process. The narrowband process is represented as the output of a system of two linear filters to the input in form of a Gaussian white noise process. The nonlinear problem is dealt with by an equivalent linearization technique, where the original nonlinear system is replaced with an equivalent linear one, whose coefficients are determined from the condition of minimization of a meansquare error between the nonlinear and the linear system. The mean value and variance of the transverse displacement of the cable as well as those of a longitudinal motion of the lumped mass are determined with the aid of an equivalent linear system and compared with the response of the original nonlinear system subjected to the deterministic harmonic excitation.
Original language  English 

Pages (fromto)  393416 
Number of pages  24 
Journal  Archives of Mechanics 
Volume  71 
Issue number  45 
DOIs  
Publication status  Published  25 Oct 2019 
Keywords
 cablemass system
 stochastic dynamics
 equivalent linearization technique
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Prof Stefan Kaczmarczyk
 University of Northampton, Technology  Professor of Applied Mechanics
 Centre for Advanced and Smart Technologies
Person: Academic