Dynamic behaviour of a cracked shaft on elastic supports

Abstract

This is a simple but comprehensive study of the dynamic behavior of a shaft with a crack on elastic supports. The analysis is restricted to the single span shaft with uniform circular cross-section. The natural frequency and modes of vibration of a shaft having a transverse crack are investigated using the finite element method. The local flexibility due to the crack is evaluated using the theory of fracture mechanics. The effect of crack depth on the natural behavior is discussed. The results show that an increase in the depth of the of crack magnifies the response amplitude and decreases the natural frequencies. The effect of elastic supports on the dynamic behavior of the shaft is presented through computation. The range of maximum effect is given. -- The element stiffness matrix of a cracked shaft considering the longitudinal translation and axial rotation is first presented. This makes it possible to analysize the dynamic response of a practical shaft by FEM. A Fortran-77 program is developed which can be used to calculate the two and three dimensional vibration of a shaft containing more than one transverse crack, concentrated mass and elastic foundation. It can also be used in multi-span shaft with different cross-section and applied to some loads.