Frequency equations for the in-plane vibration of orthotropic circular annular plate

Orthotropic circular annular plates have a lot of applications in engineering such as space structures and rotary machines. In this paper, frequency equations for the in-plane vibration of the orthotropic circular annular plate for general boundary conditions were derived. To obtain the frequency equation, first the equation of motion for the circular annular plate in the cylindrical coordinate is derived by using the stress-strain- displacement expressions. Helmholtz decomposition is used to uncouple the equations of motion. The wave equation is obtained by assumption a harmonic solution for the uncoupled equations. Using the separation of the variables leads to the general wave equation solution and the in-plane displacements in the r and θ directions. Finally, boundary conditions are exerted and the natural frequency is derived for general boundary conditions. The obtained results are validated by comparing with the previously reported and those from finite element analysis.