Vibrations of a Frame Structure with a Crack

Abstract

The study of the dynamic properties of frames is very important in structural design, as they are the cornerstone for many resistant structures. A crack on a structural member introduces a local flexibility which is a function of the crack depth. This new flexibility condition changes the dynamic behavior of the structure. The knowledge of the influence of the crack on the characteristic dynamic parameters of the frame makesit possible to determine both the position of the crack and its magnitude in damaged frames. In this paper, the crack is modeled by means of an elastically restrained hinge using Chondros’ formulation while the analytical analysis is based on variational calculus and the Euler-Bernoulli beam theory to describe the transversal displacements of the frame members. In the laboratory a device was built to measure experimentally the natural frequencies of steel frames. The first ten natural frequencies of in plane vibration of cracked L-frames are obtained, different locations and depths of the crack are considered. The experimentally measured frequencies are compared with the frequencies obtained from the proposed analytical solution, the finite element methodand with valuesreported in previous studies published on the subject by other authors.