Free Vibration and Buckling Analysis of Tapered Beam with Open Transverse Crack

Abstract

Tapering beams are used in diversities for their economic, aesthetic and other considerations in architecture, aeronautics, robotics and other innovative engineering applications. More recently they have been the subject of numerous studies. Present study deals with the vibration and buckling behavior of linearly tapered beams with single open transverse cracks. The variety of natural frequency and buckling load with distinctive parameters including relative crack depth, position of cracks and the slope of the beam are analyzed using finite element methods (FEM). A Matlab code is developed for the computation of natural frequencies and buckling loads of the cracked beam. Crack in the beam is represented by a rotating spring in line with T. D. Chaudhari, S. K. Maiti (1999). Stiffness matrix of the cracked tapered beam element is obtained from the flexibility matrix of the intact beam and the additional flexibility matrix due to crack. Free vibration frequencies and buckling load of a cracked cantilever beam reduce with an increase in crack depth. And also frequencies reduce more with the crack located nearer to the fixed end than the free end. For an intact tapered beam the frequencies vary more for the depth ratio compared to breadth ratio. The free vibration frequencies of a single cracked beam also vary more for depth ratio compared to breadth ratio. The vibration results can also be utilized as a tool for structural health monitoring, testing of structural integrity, execution and safety.