Vibration Analysis of Tapered Beam

Abstract

Beams are very common types of structural components and it can be classified according to their geometric configuration as uniform or taper and slender or thick. If practically analyzed, the non-uniform beams provide a better distribution of mass and strength than uniform beams and can meet special functional requirements in architecture, aeronautics, robotics, and other innovative engineering applications. Design of such structures is important to resist dynamic forces, such as wind and earthquakes. It requires the basic knowledge of natural frequencies and mode shapes of those structures. In this research work, the equation of motion of a double tapered cantilever Euler beam is derived to find out the natural frequencies of the structure. Finite element formulation has been done by using Weighted residual and Galerkin’s method. Natural frequencies and mode shapes are obtained for different taper ratios. The effect of taper ratio on natural frequencies and mode shapes are evaluated and compared.