On some regularities in dynamic response of cyclic periodic structures |
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| Institution: | 1. Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, Berlin 10623, Germany;2. Complex Systems Lab, Discipline of Physics, Indian Institute of Technology Indore, Simrol, Indore, Madhya Pradesh 453552 India;1. College of Hydraulic & Environmental Engineering, China Three Gorges University, Yichang, Hubei 443002, PR China;2. School of Aeronautics and Astronautics, Dalian University of Technology, Dalian, Liaoning 116024, PR China\n;3. Department of Civil Engineering, University of Siegen, D-57068, Nordrhein-Westfalen, Germany;2. Centre for Experimental and Constructive Mathematics, Simon Fraser University, Burnaby, BC, Canada;3. Escuela de Qumica, Universidad de Costa Rica, Ciudad Universitaria Rodrigo Facio, San Jose, Costa Rica;1. Department of Statistics and Operations Researches, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia;2. Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah, 11952, Saudi Arabia;3. College of Engineering, Majmaah University, Al-Majmaah 11952, Saudi Arabia;4. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam;1. Department of Economics, Quantitative Methods and Management, University of Milano Bicocca, Piazza Ateneo Nuovo 1, Milano, 20126, Italy;2. Department of Economics and Social Sciences, Catholic University, Via Emilia Parmense 84, Piacenza, 29100, Italy |
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| Abstract: | The paper deals with cyclic periodic structures modelling bladed disk assemblies of blades with friction elements for vibration damping. These elements placed between adjacent blades reduce the vibration amplitudes by means of dry friction resulting from centrifugal forces acting on the elements and relative displacements of the blades. However, the application of these friction elements results in an additional dynamical coupling which together with mistuning of some system parameters (e.g., blade eigenfrequency or contact parameters) may cause localization of vibration. In the present paper a linear approximation of such a system is investigated. The structure composed of cyclic periodic cells modelled each as a clamped-free beam interacting with each other by means of viscoelastic elements of complex stiffness is applied for dynamic system analysis. In case of free vibrations as well as in case of steady-state dynamic response to a harmonic pressure field, a perfect periodic structure and the structures with periodically mistuned parameters (blade eigenfrequencies and contact parameters) are studied. Some regularities in the dynamic response of the systems with mistuning have been noticed. Despite the fact that only a linear approximation has been used, the results and conclusions can be applied for models which describe the blade interaction in a nonlinear way. |
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