Design of heterogeneous clamped circular plates with specified fundamental natural frequency

The titled problem is solved by the aid of the semi-inverse formulation. At the first glance, a surprising demand is posed: Design a radially heterogeneous polar orthotropic circular plate whose fundamental mode shape coalesces with the static deflection of a homogeneous circular plate of the same radius and thickness under uniformly distributed load. Compatible polynomial variations of the radial and circumferential flexural rigidities are introduced. It turns out that these are infinite amount of polar orthotropic circular plates that solve the posed semi-inverse problem, depending on the free parameter represented by one of the coefficients in variation of flexural rigidities. This allows to provide an unique solution to the titled problem: there is a single plate that possesses the specified fundamental natural frequency.