Analysis of the vibration of a cracked ferromagnetic rectangular plate in a transverse magnetic field

Abstract

The vibration of a cracked rectangular plate that is subject to an in-plane force and a transverse magnetic field and is simply supported at all its edges is considered. Based on the von Kármán plate theory, the equation of motion, including an in-plane force, a transverse magnetic field, and a damping coefficient, is derived. This study focused only on the first mode of natural frequency in the vibration. The nonlinear natural frequency is affected by the crack length and aspect ratio. These results are observed to be similar to those reported in the literature. The equations of vibration are reduced to an ordinary differential equation by assuming mode shape and using the Galerkin method. The natural frequency is determined using an ordinary different equation. Using the Runge–Kutta method, the amplitude–time, and velocity–amplitude relationships are determined. The effects of several vibrational parameters—such as the in-plane force, transverse magnetic field, damping coefficient, and crack length—on a cracked plate are considered and discussed in this study. The vibration of plate has been one of the interesting fields of research. Although vibration characteristics of cracked plate have extensively been performed, and have given rise to notable scientific achievements, the vibration of ferromagnetic crack plate is yet to be explored. The derivation in this study determines the vibration of a cracked rectangular plate in a magnetic field and is presented to bring out the effects of crack ratio on vibration.