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Natural frequencies and mode shapes of statically deformed inclined risers
Institution:1. Physical Sciences and Engineering Division, King Abdullah University of Science and Technology, Thuwal 23955-9600, Saudi Arabia;2. Department of Engineering Science and Mechanics, MC 0219, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA;3. Department of Mechanical Engineering, University of Jordan, Amman, Jordan;4. Department of Mechanical Engineering, State University of New York, Binghamton, NY 13902, USA;1. School of Civil Engineering and Architecture, Wuhan University of Technology, 430070, Wuhan, PR China;2. School of Civil, Environmental and Chemical Engineering, RMIT University, 3001, Melbourne, Australia;1. Department of Civil Engineering, Faculty of Engineering, Ariel University, Ariel 44837, Israel;2. School of Mechanical Engineering, Faculty of Engineering, Tel-Aviv University, Ramat Aviv 69978, Israel;1. Centro de Nanociencias y Nanotecnología, Universidad Nacional Autónoma de México, km. 107, Carretera Tijuana-Ensenada, 22860 Ensenada, B.C., Mexico;2. CINVESTAV Unidad Querétaro, Lib. Norponiente 2000, Real de Juriquilla, 76230 Querétaro, Qro., Mexico;1. State Key Laboratory of Ocean Engineering, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration, Shanghai 200240, China;2. Guangzhou Maritime University, Guangzhou 510725, China;1. Department of Mathematics, Northeast Forestry University, Harbin, 150040, PR China;2. Library, Northeast Forestry University, Harbin, 150040, PR China
Abstract:We investigate numerically the linear vibrations of inclined risers using the Galerkin approach. The riser is modeled as an Euler–Bernoulli beam accounting for the nonlinear mid-plane stretching and self-weight. After solving for the initial deflection of the riser due to self-weight, we use a Galerkin expansion employing 15 axially loaded beam mode shapes to solve the eigenvalue problem of the riser around the static equilibrium configuration. This yields the riser natural frequencies and corresponding exact mode shapes for various values of inclination angles and tension. The obtained results are validated against a boundary-layer analytical solution and are found to be in good agreement. This constitutes a basis to study the nonlinear forced vibrations of inclined risers.
Keywords:Inclined riser  Natural frequency  Mode shapes  Galerkin method
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