Free Vibration Behavior of Cantilever Plate with Localized Stiffness Loss at the Clamped End

Abstract

Cracks and discontinuities present in the structure have a significant influence on the vibration properties of a component. The research work presented in this paper investigates the effect of a crack present at the fixed edge of the cantilever steel plate on the vibration frequency and mode of the steel plate. The analysis presented above adopts a combination of modeling techniques based on CPT and the numerical analysis technique based on FEM in the ANSYS APDL package and attempts to establish the amount of variation in the vibration properties of a plate with the rise of the  ratio of the crack. A detailed finite element analysis has been conducted with special attention to the modeling near the cracked area. The natural frequencies and modes have been analyzed for various values of the crack ratio and validated with theoretical values based on the frequency equations with an account for flexibility caused by the presence of cracks. Both theoretical and FE results show that with an increase in the value of the crack ratio, natural frequencies tend to reduce, especially for mode 1. Mode shapes show localization near the crack area, which indicates the effect of the crack on the system stiffness and vibration. The proposed equations derived by fitting the numerical results into the classical frequency equations offer a reliable means for determining the effect of the crack on the frequency shift without having to go to experimental methods. This research highlights the capabilities of a combined analytical and numerical approach to the prediction of the vibration response of cracked systems with a view to developing the area for complex damage configurations.