Transverse Vibration of Cracked Graded Rayleigh Beam with Axial Motion

Abstract

  The paper presents the transverse vibration of an open edge crack graded Rayleigh beam with axial motion. The vibration equation was obtained relying on Hamilton's precept and resolved by the approach of Galerkin's. The power-law is adopted to represent the gradient of properties of the material composing the beam along the direction of the thickness. Cracks were modeled as rotational massless spring. The effects of axial velocity, material property change index, location, and depth of cracking on the vibration characteristics are observed. Also, the corresponding mode shapes are found for cracked moving graded Rayleigh beam with simply supported, and fixed-fixed end supports. The results clear up that the natural frequencies drop due to the rise in the axial velocity, the crack depth, and the material property index