Two perturbation formulations of the nonlinear dynamics of a cable excited by a boundary motion |
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| Institution: | 1. College of Civil Engineering, Hunan University, Changsha, China;2. Department of Structural and Geotechnical Engineering, Sapienza University of Rome, Rome, Italy;3. Key Laboratory for Damage Diagnosis of Engineering Structures of Hunan Province, Changsha, China;1. State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;2. Department of Mechanical Engineering, University of Alberta, Edmonton, AB T6G 1H9, Canada;1. School of Mathematical Sciences, East China Normal University, Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, Shanghai 200241, PR China;2. Department of Mathematics, Faculty of Science, Comilla University, Comilla 3506, Bangladesh;1. CIGIP, Universitat Politècnica de València, Camí de Vera S/N, 46022, València, Spain;2. Departamento de Matemáticas para la Economía y la Empresa, Universitat de València, Avenida de los Naranjos S/N, Spain;3. Centre for Quality and Change Management, Universitat Politècnica de València. Camí de Vera, s/n. 46022 València, Spain;1. Mechanical Engineering Department, Sharif University of Technology, Tehran, Iran;2. Mechanical Engineering Department, Iran University of Science and Technology, Tehran, Iran |
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| Abstract: | A nonlinear cable excited by an inclined boundary motion, termed as cable's moving boundary problem, is attacked by two different perturbation approaches, i.e., the boundary modulation formulation and the quasi-static drift formulation. The former transforms the boundary motion into a weak modulation on cable's high-order dynamics, while the latter introduces a hybrid mode expansion using an empirical drift shape function. In both formulations, the inclined boundary motion induces three different excitation effects, i.e., longitudinal direct, vertical boundary kinematic, and high-order parametric, all of which being characterized by the parametric modulation factors. Detailed comparative studies indicate that the modulation factors in the two formulations are exactly equivalent to each other only if a new drift shape function, well defined in the boundary modulation formulation, is used for the quasi-static drift formulation. In contrast, the empirical shape functions lead only to an approximate equivalence for intermediate/large boundary motion inclinations. Moreover, for small inclinations, the two formulations induce possible quantitative and qualitative differences. The approximate analytical framework is validated and shown to be computationally efficient, by comparison with the finite difference method. |
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