Efficient optimal frequency design of elastically supported distributed-parameter cantilevers

The purpose of this paper is to develop an efficient numerical method for finding the optimal bending stiffness distribution of an elastically supported distributed-parameter cantilever under a fundamental natural frequency constraint. The distributed-parameter cantilever is modeled by an FEM system and the bending stiffness distribution is approximated by a piecewise-linear function. A cubic displacement function is utilized in the FEM system. It is Shown that a semi-explicit expression, due to the present author, of the optimal bending stiffness distribution for a fixed-base model plays the key role in developing the efficient numerical method for an elastically supported model. A difficulty of solving nonlinear equations resulting from the effect of structural masses is overcome by combining the semi-explicit optimal design formula for a fixed-base model with a recursive technique for evaluating foundation displacements and solution stiffnesses. A numerical example of an elastically supported lower structure is presented in order to demonstrate the validity, efficiency and accuracy of this method. Copyright (C) 1996 Published by Elsevier Science Ltd.