Analysis of Longitudinal Dynamics in Viscoelastic Bars with Open Cracks Exposed to Magnetic Field

Abstract

Understanding the vibrational behavior of bars is crucial in engineering structures due to their extensive use in mechanical applications. Hence, exploring the longitudinal vibrations of rods under different support conditions, particularly in the presence of cracks, holds significant importance. This study examines the vibrations of a viscoelastic rod containing a crack exposed to a magnetic field. The crack is modeled as a reduction in local stiffness, with a novel approach introduced by treating the crack as viscoelastic. The motion equations are developed by utilizing Newton’s second law and considering structural damping. Boundary conditions and compatibility conditions at the crack location are used to extract the eigenvalue problem. Natural frequencies, influenced by boundary conditions and geometric properties such as crack position and depth, are determined from the solution. Validation of this method is performed by comparing results with existing literature, demonstrating satisfactory accuracy. Additionally, the effect of various parameters on the dynamic features of the rod is investigated.

Keywords

• axial dynamics
• viscoelastic rods
• cracks
• magnetic field
• structural damping
• natural frequencies
• boundary conditions