Title: Model Based Analysis of Shimmy in a Racing Bicycle
Authors: Nicolò Tomiati, Gianantonio Magnani, Bruno Scaglioni and Gianni Ferretti
Abstract:In this paper we are presenting a model of a racing bicycle, developed in Modelica language within the Dymola environment. The main purpose is to investigate the dynamic response of the bicycle and its modes of vibration, referring in particular to shimmy. This phenomenon occurs at high speeds and consists of sudden oscillations of the front assembly around the steering axis. Lateral accelerations on the horizontal tube of the frame can reach 5-10 g with a frequency that varies between 5-10 Hz. Even if it is quite uncommon, shimmy is a topic of great relevance, because it may be extremely dangerous for the rider. Thanks to this model, we can show that the main elements which contribute to the rise of the oscillations are the lateral compliance of the frame and the tyres’ deformation.
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Title: Object-oriented modelling of a flexible beam including geometric nonlinearities
Authors: Davide Invernizzi, Bruno Scaglioni, Gianni Ferretti and Paolo Albertelli
Abstract:In this paper, an efficient approach for the modelling and simulation of slender beams subject to heavy inertial loads is presented. The limitations imposed by a linear formulation of elasticity are overcome by a second order expansion of the displacement field, based on a geometrical exact beam model. In light of this, the nonlinearities of the elastic terms are shifted as inertial contributions, which yields an expression of the equations of motion in closed form. Thanks to the formulation in closed form, the proposed model is implemented in Modelica, with particular care to the suitability of the model with respect to the Modelica Multibody library. After describing the model formulation and implementation, the paper presents some simulation results, in order to validate the model with respect to benchmarks, widely adopted in literature.
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