Optimal support positions for a structure to maximize its fundamental natural frequency

A procedure and related theories are developed to find the loci of optimal support positions for a structure to maximize its fundamental eigenvalue by increasing the support stiffness. The concept of limit eigenvalue, which is the upper bound of fundamental eigenvalue achieved by adding supports, is introduced. A condition is derived on which the fundamental eigenvalue can be reached to its limit eigenvalue. A sensitivity formula of eigenvalues with respect to the change of support positions is also derived to set up an optimization problem and to obtain its optimal support positions. It is found that the loci of m supports start from the maximum displacement position of the structure's first eigenfunction and end at certain positions on the nodal line of its (m + 1)th eigenfunction if the fundamental eigenvalue can reach its limit eigenvalue. The suggested method is tested to find the loci for a beam and a plate structure. (C) 1998 Academic Press Limited.