A new 2-D model of a thin annular disk using a modified assumption - Qian, Yichen (IEEE transactions on ultrasonics, ferroelectrics, and frequency control, 2010)
The work describes an improved 2-D model for a thin annulus by using a modified assumption with regard to coupled vibration. With this approach, the impedance spectrum and displacements due to radial modes, both in radial and thickness direction of a thin ring, are obtained. Bending displacement is investigated by finite element analysis (FEA) and matches our model. The bending in the thickness direction is coupled to radial modes and shows several node circles in the high radial overtone frequency range. The model is validated by FEA with excellent agreement between the new theory and FEA results