Effect of cracks on nonlinear flexural vibration of rotating Timoshenko functionally graded material beam having large amplitude motion

Abstract

This study investigates the stiffening effect due to rotation on the nonlinear vibrational characteristics for cracked Timoshenko beam for the first time. Fixed end of the beam is attached to a rotating hub. Functionally graded material is taken into consideration, in which the properties vary as a continuous function along the depth of the beam. An elastic mass-less rotational spring is assumed in the place of crack, which splits the beam into two different parts. The point on the neutral axis at the fixed end is assumed to be the center of rotation of the beam. Centrifugal force is considered to act towards the spanwise direction and along the neutral axis. An additional displacement due to rotation of the beam along with the centrifugal force is incorporated with the energy formulation. Timoshenko beam theory and classical Ritz method is employed to derive the governing equations. In order to solve the nonlinear governing equations, direct substitution iterative technique is used. Effects of various parameters such as rotating speeds, radius of hub, depth of crack, location of crack, and different functionally graded material properties on linear and nonlinear vibration characteristics are studied. Validity of the present methodology is assured by comparing the results with some of the results from the existing literatures.

Keywords

Rotating functionally graded material beam crack nonlinear vibration Ritz method

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