Normal oscillatory modes of rotating orthotropic disks

We present the governing equations of transverse vibrations for rotating cylindrically orthotropic disks and calculate their normal oscillatory modes. We use a collocation method to discretize the ordinary differential equation that determines the radial variation of the lateral displacement field in the linear regime. We then construct a nonlinear eigenvalue problem in the matrix form for given azimuthal wavenumbers and compute the eigenfrequencies and their conjugate mode shapes through solving a determinantal equation followed by evaluating the adjoint matrix of a singular linear map. We reveal some notable features of mode shapes in isotropic and orthotropic rotating disks and discuss on their eigenfrequency spectra as the material and geometric properties are varied.