Exact Receptance Function of Cracked Beams and Its Application for Crack Detection

Abstract

The receptance function is very important which interrelates the harmonic excitation and the response of a structure in the frequency domain. This paper presents the exact receptance function of cracked beams. In this work, the “receptance curvature” is defined as the second derivative of the receptance. The influence of the crack on the receptance curvature is investigated. The results show that when there are cracks, the receptance curvature is influenced significantly at crack positions. This might be useful for the detection of cracks. In this paper, the derivation of exact receptance of the beam with general boundary conditions is presented, and the numerical simulations are provided.