In-plane vibrations of an arch of variable cross section elastically restrained against rotation at one end and carrying a concentrated mass at the other |
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| Institution: | 1. Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, School of Mechanical Engineering, Tianjin University, Tianjin, 300350, China;2. The Joint Laboratory of Ocean Observing and Detection, Pilot National Laboratory for Marine Science and Technology, Qingdao, Shandong, 266237, China;1. Dokuz Eylul University, Department of Civil Engineering, Izmir, Turkey;2. University of Oxford, Department of Engineering Science, Oxford, United Kingdom;1. DICAR, Department of Civil Engineering and Architecture, Technical University of Bari, Bari 70125, Italy;2. College of Civil Engineering, Fuzhou University, Fuzhou 350108, China;3. DICATECH, Department of Civil Engineering, Environment, Territory, Building and Chemical, Technical University of Bari, Bari 70125, Italy;4. Department of Engineering and Geology, University of Chieti-Pescara “G. d''Annunzio”, Pescara 65127, Italy;1. Department of Mathematics, University of Patras, Rio 26504, Greece;2. School of Civil Engineering, National Technical University of Athens, Athens 15773, Greece |
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| Abstract: | This study deals with the determination of upper and lower bounds for the fundamental frequency of the structural system described in the title. The upper bound is determined by approximating the fundamental mode shape by means of a polynomial coordinate function in the angular coordinate, which includes an exponential optimization parameter. The fundamental frequency equation is generated by means of the Rayleigh-Ritz method, and the resulting upper bound is minimized with respect to the previously mentioned exponential parameter. The lower bound for the frequency coefficient is obtained by means of an extension of Dunkerley's method. |
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