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Non-linear dynamic response of a cable system with a tuned mass damper to stochastic base excitation via equivalent linearization technique
Publikationstyp
Journal Article
Date Issued
2020-12
Sprache
English
Author(s)
Institut
TORE-URI
Journal
Volume
55
Issue
12
Start Page
2413
End Page
2422
Citation
Meccanica 55 (12): 2413–2422 (2020-12)
Publisher DOI
Scopus ID
Non-linear dynamic model of a cable–mass system with a transverse tuned mass damper is considered. The system is moving in a vertical host structure therefore the cable length varies slowly over time. Under the time-dependent external loads the sway of host structure with low frequencies and high amplitudes can be observed. That yields the base excitation which in turn results in the excitation of a cable system. The original model is governed by a system of non-linear partial differential equations with corresponding boundary conditions defined in a slowly time-variant space domain. To discretise the continuous model the Galerkin method is used. The assumption of the analysis is that the lateral displacements of the cable are coupled with its longitudinal elastic stretching. This brings the quadratic couplings between the longitudinal and transverse modes and cubic nonlinear terms due to the couplings between the transverse modes. To mitigate the dynamic response of the cable in the resonance region the tuned mass damper is applied. The stochastic base excitation, assumed as a narrow-band process mean-square equivalent to the harmonic process, is idealized with the aid of two linear filters: one second-order and one first-order. To determine the stochastic response the equivalent linearization technique is used. Mean values and variances of particular random state variable have been calculated numerically under various operational conditions. The stochastic results have been compared with the deterministic response to a harmonic process base excitation.
Subjects
Cable–mass system
Equivalent linearization technique
Stochastic dynamics
Tuned mass damper