Large displacement analysis of elastically constrained rotating disks with rigid body degrees of freedom

A central aspect of the linear vibration theory of rotating disks involves the concept of critical speeds. At such rotation speeds an axisymmetric disk can support a standing wave as recorded by a stationary observer. In such situations an applied space fixed constant force can give rise to a resonance in the disk. Such a response is of concern in industrial applications as diverse as circular saw blades and computer floppy disks. In such situations the magnitude of response may exceed the limits of linear theory. The present paper is concerned with the effects of large displacements upon the disk response in the neighborhood of such critical speeds. The effects of geometric nonlinearities and the influence of rigid body tilting and translation (caused by the boundary conditions) are considered. The equations of motion are based on Von Karman plate theory. The eigenfunctions of two self-adjoint eigenvalue problems, corresponding to the stress function and the transverse displacement, are determined and used as approximation functions in a numerically efficient Galerkin formulation. The coupled nonlinear ordinary differential equations of motion are solved using the Runge–Kutta method. Numerical results are presented for disks that are free to translate and rotate at their inner boundary and are constrained from lateral motion by space fixed linear springs. The effects of vibration magnitude on system response in the sub and super-critical speed regions are computed and the effects of large displacements on critical speed behavior and forced response are investigated. Experiments are conducted to verify the accuracy of the numerical results obtained in this paper. ► The effect of geometrical nonlinear terms on the amplitude of disk oscillations are studied. ► It is found that large deformations increases the nonlinear critical speeds of the spinning disks. ► A disk under the application of a force does not have zero frequency at the linear critical speed.