ABSTRACT
The governing equation of Rayleigh beam is a single fourth-order differential equation in a single variable. In contrast, Timoshenko theory uses the coupled differential equations in two variables (harmonic vibrations). The Rayleigh beam theory also predicts the natural frequencies and mode shapes more accurately compared to the Euler-Bernoulli beam theory, without falling prey to the mathematical complexities of the Timoshenko beam theory. The finite element method is used to compute the natural frequencies of the non-uniform beams. Analytical expressions for the mass, bending stiffness and mass moment of inertia of such non-uniform beams are determined considering four specific cases. Furthermore, recent advancements in machining techniques- such as additive manufacturing and rapid prototyping - facilitate the manufacturing of beams with known breadth, height, and material property variation.
