Abstract

Tapered rotating circular disc provides advantages of preferred stress state compared to the uniform-thickness circular disc rotating at the same speed. Hence, linearly-tapered circular disc and circular disc with hyperbolic profile along radial direction, often known as Stodola’s disc, are increasingly being used in many engineering applications such as in automobiles, turbomachinery, steam turbines, flywheels, and space structures. It is important to study the in-plane dynamics and out-of-plane dynamics of such circular discs as they play a vital role in causing vibration and noise. Design of circular disc for such applications also requires the knowledge of three-dimensional bending vibration characteristics of the disc. The present thesis aims at developing a generalized formulation and then to investigate the three-dimensional in-plane and out-of-plane vibration characteristics of uniform-thickness circular annular disc, linearly-tapered circular annular disc, and Stodola’s disc with clamped-free boundary condition.
The trigonometric functions in circumferential coordinate are employed in all the three displacement components in Rayleigh-Ritz method to calculate the natural frequencies. The numerical approach based on Rayleigh-Ritz method with finite-element-like modification has been developed to study the free vibration behaviour of the tapered circular discs made of isotropic and orthotropic materials and of clamped-free boundary condition. Numerical and symbolic computations have been performed using MATLAB and MAPLE software. The results for natural frequencies have been validated using Finite Element Method using ANSYS and results from previous literature wherever available. A comprehensive parametric study is conducted to study the effects of various design parameters.