Vibration Analysis of a Rectangular Thin Plate with Two Parallel Cracks

Abstract

The modeling of cracked plates is important to structural damage detection following the model-based approach. However, very little research has modeled plates with multiple cracks. In 2000, Khadem and Rezaee proposed a method for calculating the modal parameters of a plate with a single-crack parallel to one of the sides. The main purpose of this paper is to extend that work and develop a solution method for calculating the dynamic responses of a classically damped rectangular thin plate with two cracks. The basic idea is to treat the cracks as line springs with varying degrees of stiffness along their lines. When the plate is deflected or when it is vibrating, the slope of the plate is discontinuous at the two sides of the crack line. This change in slope varies along the crack as the crack depth is not uniform. In the governing equation, the cracks are considered as the continuity conditions along the crack line. It is assumed that each crack influences the stiffness only in its neighborhood, with that influence vanishing at a sufficient distance from the crack. By following this assumption, the natural frequencies of the cracked plate can be calculated using energy methods, and the time-domain response of the plate can then be calculated using the modal superposition method. The possibility of using the two-dimensional spatial wavelet transform in crack detection is also explored in this paper.