Analytical Study on Longitudinal Vibration of Viscoelastic Cracked Rod under Magnetic Field.

Rods are one of the most important members in engineering structures and due to the wide application in different mechanical equipments, vibration analysis of them have great importance. Uderstanding the longitudinal vibration of the rod in different support conditions and in the presence of crack is very useful. In this study, vibration analysis of cracked viscoelastic rod in magnetic field is studied. The crack is modeled as the local stiffness reduction of the structure. To consider the more realistic assumptions, in this study and for the first time, viscoelastic behavior is considered for crack. Newton's second law and structural damping are used to obtain the governing equations. Then boundary and inter-boundary conditions are applied at the crack location and characteristic equation of the system is derived. By solving the characteristic equation, the natural frequencies of the rod which in turn depends on boundary conditions and geometrical characteristics, including location and depth of crack, are obtained. To evaluate the accuracy and validity of the mention method, the results are compared with the literature. Finally, The effect of different parameters on the vibration characteristics of the rod is studied.