UBC Theses and Dissertations
Linear and nonlinear vibration response of thin rotating disks MohammadHasani Khorasany, Ramin
Spinning disks have substantial applications in today’s industries (e.g., saw mill industries). Developing a greater understanding the dynamics of spinning disks is a central topic for this thesis. Specifically, this thesis investigates the linear and nonlinear vibrations of spinning disks. In some of the spinning disk applications, the disks may experience a rigid body translational degree of freedom. Having this degree of freedom can change the stability characteristics of spinning disks. Using analytical techniques and a two-mode approximation, the stability characteristics of elastically guided spinning disks having a rigid body translational degree of freedom are thus studied. The effect of axisymmetric non-flatness on the frequency behaviour of spinning disks is also studied. The equations of motion are based on Von Karman plate theory. Assuming that the shape of initial runout is in the form of mode shapes with zero nodal diameters, the equations of motion are then discretized. Neglecting higher order terms, the equations are linearized and the effects of different levels of initial runout on the dynamics of spinning disks are thus studied. Using experimental measurements, the effects of large deformations on the frequency behaviour and amplitude of response for the spinning disks are investigated. Disks with different thicknesses are used in this study. The disks were under the application of a space fixed external force which can produce different levels of nonlinearity. By measuring the disk displacement and conducting FFT analyses, the frequencies were measured for different levels of initial deflection. In order to see how the geometrical nonlinear terms affect the frequency behaviour of spinning disks, the nonlinear governing equations are discretized and then solved to find the equilibrium solutions. By assuming a small perturbation around the equilibrium solution, the nonlinear equations of motion are linearized. Using the linearized form of the equations of motion, the effect of large deformations of the frequency characteristics of spinning disks is analyzed. The analytical results are then compared with the experimentally obtained results.
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