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research-article  
Shmuel Katz and Sefi Givli
J. Appl. Mech   doi: 10.1115/1.4036018
Attributed to its significance in a wide range of practical applications, the postbuckling behavior of a beam with lateral constraints has drawn much attention in the last few decades. Despite the fact that, in reality, the lateral constraints are often flexible or deformable, vast majority of studies have considered fixed and rigid lateral constraints. In this paper, we make a step towards bridging this gap by studying the postbuckling behavior of a planar beam that is laterally constrained by a deformable wall. Unfortunately, the interaction with a compliant wall prevents derivation of closed-form analytical solutions. Nevertheless, careful examination of the governing equations of a simplified model reveals general properties of the solution and let us identify key features that govern the behavior. Specifically, we construct universal “solution maps” that do not depend on the mode number and enable simple and easy prediction of the contact conditions and of the mode-switching force (the force at which the system undergoes instantaneous transition from one equilibrium configuration (or mode) to another). The predictions of the mathematical model are validated against finite-element simulations.
TOPICS: Simulation, Equilibrium (Physics), Engineering simulation, Finite element analysis
Technical Brief  
W. Fan and W. D. Zhu
J. Appl. Mech   doi: 10.1115/1.4035857
A round elevator traveling cable is modeled using a singularity-free beam formulation. Equilibria of the traveling cable with different elevator car positions are studied. Natural frequencies and corresponding mode shapes of the traveling cable are calculated and they are in excellent agreement with those calculated by ABAQUS. In-plane natural frequencies of the traveling cable do not change much with the car position compared with its out-of-plane ones. Dynamic responses of the traveling cable are calculated and they are in good agreement with those from commercial multibody dynamics software RecurDyn. Effects of vertical motion of the car on free responses of the traveling cable and those of in-plane and out-of-plane building sways on forced responses are investigated.
TOPICS: Cables, Elevators, Mode shapes, Computer software, Dynamic response, Multibody dynamics

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