Electrical analogous in viscoelasticity |
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| Institution: | 1. Università degli Studi di Palermo, Dipartimento di Energia, Ingegneria dell’Informazione e Modelli Matematici (DEIM), Viale delle Scienze Ed.9, I-90128 Palermo, Italy;2. Università degli Studi di Palermo, Dipartimento di Ingegneria Civile, Ambientale ed Aerospaziale, dei Materiali (DICAM), Viale delle Scienze Ed.8, I-90128 Palermo, Italy;3. Università degli Studi di Palermo, Dipartimento di Ingegneria Chimica, Gestionale, Informatica e Meccanica (DICGIM), Viale delle Scienze Ed.6, I-90128 Palermo, Italy;4. School of Control Science and Engineering, Shandong University, Jinan, Shandong 250061, PR China;1. Department of Mathematics, Anna University - Regional Centre, Coimbatore 641047, India;2. Department of Mathematics, Sungkyunkwan University, Suwon 440-746, South Korea;3. Department of Mathematics, Sri Ramakrishna Institute of Technology, Coimbatore 641010, India;1. MOE Key Lab for Intelligent Networks and Network Security, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China;2. College of Information Engineering, Tarim University, Alar, Xinjiang 843300, China;3. School of Science, Xi’an Polytechnic University, Xi’an, Shaanxi 710048, China;1. Grupo de Neurocomputación Biológica, Dpto. de Ingeniería Informática, Escuela Politécnica Superior, Universidad Autónoma de Madrid, 28049 Madrid, Spain;2. Instituto de Seguridad de la Información, Consejo Superior de Investigaciones Científicas, Serrano 144, 28006 Madrid, Spain;1. Department of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing, Jiangsu 210023, PR China;2. School of Automation, Southeast University, Nanjing, 210096, PR China;3. Institute of Information and Control Engineering Technology, Nanjing Normal University, Nanjing, Jiangsu 210042, PR China;4. College of Mechanical and Electronic Engineering, Nanjing Forestry University, Nanjing, Jiangsu 210042, PR China;1. College of Science, Shandong University of Science and Technology, Qingdao 266590, PR China;2. Shandong Key Laboratory of Robotics and Intelligent Technology, Qingdao 266590, PR China |
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| Abstract: | In this paper, electrical analogous models of fractional hereditary materials are introduced. Based on recent works by the authors, mechanical models of materials viscoelasticity behavior are firstly approached by using fractional mathematical operators. Viscoelastic models have elastic and viscous components which are obtained by combining springs and dashpots. Various arrangements of these elements can be used, and all of these viscoelastic models can be equivalently modeled as electrical circuits, where the spring and dashpot are analogous to the capacitance and resistance, respectively. The proposed models are validated by using modal analysis. Moreover, a comparison with numerical experiments based on finite difference time domain method shows that, for long time simulations, the correct time behavior can be obtained only with modal analysis. The use of electrical analogous in viscoelasticity can better reveal the real behavior of fractional hereditary materials. |
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| Keywords: | Fractional calculus Viscoelastic models Fractional capacitor Eigenvalues analysis |
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