A Trefftz approach for medium-frequency vibrations of orthotropic structures

• A Trefftz method is used to simulate the vibration of orthotropic plates.
• The continuity of the solution is ensured through a dedicated weak formulation.
• The method is validated on two examples.

The Variational Theory of Complex Rays (VTCR) was developed in order to calculate the vibrational response of structures in the medium-frequency range. It leads to a numerical approximation of this response through the resolution of a small system of equations which, contrary to element-based methods, does not result from a refined spatial discretization. This strategy has already been validated for assemblies of isotropic plates. In this paper, we extend it to the case of orthotropic planar structure. The method is illustrated through various orthotropic plate vibration problems under several types of harmonic loading in the medium-frequency range.