Invariance of eigenfrequencies under geometric transformation in plate structures

Geometric transformation is applied here to the problem of flexural waves in thin plates. Differently from problems governed by the Helmholtz equation, the equation of motion does not retain its form. A physical interpretation is given which involves a non homogenous anisotropic plate with axial stresses. Boundary conditions are not satisfied anymore after transformation, but some possible constraints can be applied on the transformation law in order to cancel differences at the boundary of the transformed domain. As a comparison tool, we propose the eigenfrequency analysis of rectangular plates and we show the correctness of the proposed approach for different transformations and boundary conditions.