Computational and numerical analysis of a nonlinear mechanical system with bounded delay |
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Affiliation: | 1. Graduate Program in Modeling and Optimization, Federal University of Goiás, Campus Catalão Catalão-GO, CEP 75704-020, Brazil;2. Interdisciplinary Nucleus of Exact Sciences and Technological Innovation,Federal University of Pernambuco, Campus Agreste, Caruaru-PE CEP. 55002-971, Brazil;1. Faculty of Mathematics and Physics, Charles University in Prague, Sokolovská 83, Praha 8 – Karlín CZ 186 75, Czech Republic;2. Texas A&M University, Department of Mechanical Engineering, 3123 TAMU, College Station, TX 77843-3123, United States of America;1. Université Paris-Est, Laboratoire Navier (UMR 8205), CNRS, Ecole des Ponts ParisTech, IFSTTAR, F-77455 Marne La Vallée, France;2. Université Paris-Est, MAST, SDOA, IFSTTAR, F-77447 Marne La Vallée, France;1. Department of Applied Mathematics, Northwestern Polytechnical University, Xi׳an 710072, China;2. Department of Mechanics, State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou 310027, China;1. Department of Engineering Design, Indian Institute of Technology Madras, Chennai 600036, India;2. JK Tyre and Industries Ltd., RPSCOE for Tyre & Vehicle Mechanics, IIT Madras, Chennai 600036, India |
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Abstract: | Modern structures are increasingly resistant and complex. In many cases, such systems are modeled by numerical approximations methods, due to its complexities. In the study of vibration levels in the response of a system is important to consider issues like reliability and efficient design, since that such vibrations are undesirable phenomena that may cause damage, failure, and sometimes destruction of machines and structures. In this paper we investigated a modeling strategy of nonlinear system with damping, subject the time delayed. From models widely used in literature and with the help of numerical simulations a nonlinear damped system with two degree-of-freedom is analyzed. The system is constituted of a primary mass attached to the ground by a spring and damping with linear or nonlinear characteristics (primary system), and the secondary mass attached to the primary system by a spring and damping with linear or nonlinear characteristics (secondary system). It is well known that time delayed systems, due to its own nature, has singular behavior in its dynamics and that such singularities propagate over the time. Based on this, the main concerns of the present paper is to analyze the stability of a delayed system with two degree of freedom by means of the techniques development in [1] (Hu andWang, 2002). We also obtain the solution using the integration of equations of motions performing a Fourth Order Runge-Kutta Method. The behavior of a nonlinear main system with nonlinear secondary system will be investigated to many cases of resonances. In this case, various time delayed values are used to confirm its influence on the attenuation of vibrations, but, unfortunately, also the increase of nonlinearity (instable responses) of the system in question is observed. |
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Keywords: | Parametric resonances Bifurcations and instability Multiple scale methods Frequency-response methods Time delay Generalized Routh-Hurwitz criterion Nonlinear dynamic vibration absorber |
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