Non-Linear Response of Cable-Mass-Spring System in High-Rise Buildings under Stochastic Seismic Excitation

Abstract

In high-rise buildings earthquake ground motions induce bending deformation of the host structure. Large dynamic displacements at the top of the building can be observed which in turn lead to the excitation of the cables/ropes within lift installations. In this paper, the stochastic dynamics of a cable with a spring-damper and a mass system deployed in a tall cantilever structure under earthquake excitation is considered. The non-linear system is developed to describe lateral displacements of a vertical cable with a concentrated mass attached at its lower end. The system is moving slowly in the vertical direction. The horizontal displacements of the main mass are constrained by a spring-viscous damping element. The earthquake ground motions are modelled as a filtered Gaussian white noise stochastic process. The equivalent linearization technique is then used to replace the original non-linear system with a linear one with the coefficients determined by utilising the minimization of the mean-square error between both systems. Mean values, variances and covariances of particular random state variables have been obtained by using the numerical calculation. The received results were compared with the deterministic response of the system to the harmonic process and were verified against results obtained by Monte Carlo simulation.

Application of the forest classifier method for description of movements of an oscillator forced by a stochastic series of impulses

“…The theory of random dynamical systems is an interdisciplinary domain (Sobczyk, 1983;Iwankiewicz and Kotulski, 2009;Zembaty, 2009;Socha and Soong, 1991;Liu et al, 2023;Banks et al, 2023). It is applied in mechanics (Litak et al, 2008;Bozzoni et al, 2011;Hračov and Náprstek, 2017;Weber et al, 2021;Smolnicki et al, 2013;Rączka et al, 2013) where, like in the present paper, the idea of research refers to non-deterministic mechanics. The state of a system observed at any given moment does not univocally determine the states of the system at consecutive moments, which issues from the random character of stimulaton.…”

Modeling and Analysis of FBV Movements for Automotive Driveshafts in the PPR Region

“…The present work presents a perturbation approach, specifically the asymptotic method approach (AMA) [1], to investigate the principal parametric resonance (PPR) for the forced bending vibrating (FBV) movements of the elements of an automotive driveshaft (AD), with the AMA being a powerful tool for the investigation of vibrations induced by shocks, as mentioned by Webber in the literature [2]. To analyze the PPR region, a model for FBV movements of the AD elements was designed, with a specific multibody dynamic structure considering the following aspects: the geometric nonuniformity of the AD elements and the shock excitation induced by the road geometry.…”