Some unexpected results in vibration of non-homogeneous beams on elastic foundation |
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| Institution: | 1. University of Michigan – Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai 200240, China;2. Department of Mechanical Engineering and Energy Processes, Southern Illinois University Carbondale, Carbondale, IL 62901, USA;3. Department of Mechanical Engineering, Virginia Tech, Blacksburg, VA 24061, USA;1. Laboratoire des Structures et Matériaux Avancés dans le Génie Civil et Travaux Publics, Université de Djellali Liabes, Sidi Bel Abbes, Algeria;2. Université Mustapha Stambouli of Mascara, Department of Civil Engineering, Mascara, Algeria;1. Department of Otolaryngology, University of Minnesota, 2001 6th St. SE, Lions Research Building, Room 210, Otopathology Laboratory, Minneapolis, MN 55455, USA;2. Department of Otorhinolaryngology Head and Neck Surgery, Universidade Federal de São Paulo (UNIFESP), Escola Paulista de Medicina, Rua dos Otonis, 700 - Piso Superior - Vila Clementino, São Paulo, SP 04025 002, Brazil |
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| Abstract: | A special class of inverse vibration problems is studied in this investigation. We pose the following problem: Find the spatial distribution of the material density and the elastic stiffness of an inhomgeneous beam on elastic formulation so that the vibration mode shape constitutes a preselected function, namely the static deflection of the associated homogeneous beam under some simple loading conditions. Four sets of boundary conditions are considered, in context of polynomial representation of the material density and stiffness. It turns out unexpectedly, that irrespective of the boundary condition, the natural frequency is given by the same analytical formula. |
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