Optimal disks in vibration

The harmonic in-plane vibrations of axisymmetrical annular disks of non-uniform thickness are analysed and the problem of finding an optimal shape is given a classical mathematical formulation with differential equations and boundary conditions. It is then shown that there is no solution to this problem satisfying all conditions. The problem is then reformulated to become wellposed. In the case of non-axisymmetrical vibrations a method using successive iterations is presented and numerical solutions are obtained. © 1997 Elsevier Science Ltd