Some unexpected results in vibration of non-homogeneous beams on elastic foundation

A special class of inverse vibration problems is studied in this investigat ion. We pose the Following problem: Find the spatial distribution of the ma terial density and the elastic stiffness of an inhomgeneous beam on elastic formulation so that the vibration mode shape constitutes a preselected Fun ction, namely the static deflection of the associated homogeneous beam unde r some simple loading conditions. Four sets of boundary conditions are cons idered, in context of polynomial representation of the material density and stiffness. It turns out unexpectedly, that irrespective of the boundary co ndition, the natural frequency is given by the same analytical formula. (C) 2001 Elsevier Science Ltd. All rights reserved.