6th ECCOMAS Conference on Smart Structures and Materials SMART2013 Politecnico di Torino, 24-26 June 2013 E. Carrera, F. Miglioretti and M. Petrolo (Editors) www.smart2013.com CRACK IDENTIFICATION IN FRAME STRUCTURES BY USING THE SPECTRAL ELEMENT METHOD AND WAVELET TRANSFORM NguyenTien Khiem * , TranVan Lien † , Duong The Hung †† and Trinh Anh Hao † * Institute of Mechanics Vietnam Academy of Science and Technology 264, Doi Can, Hanoi, Vietnam e-mail: ntkhiem@imech.ac.vn † Hanoi University of Civil Engineering 55, Giai Phong Road, Hanoi, Vietnam e-mail: LienTV_dhxd@yahoo.com and trinhanhhao@yahoo.com †† Thai Nguyen University of Technology Tan Thinh, Thai Nguyen, Vietnam e-mail: hungtd@tnut.edu.vn Key words: Crack Identification; Spectral Element Method; Wavelet Transform; Framed Structure. Summary. The problem of Structural Health Monitoring has recently attracted enormous attention of not only the structural engineers but also the researcher-mathematicians. However, most of the published works deal with the simple structures such as beam or plates. There are few papers devoted to study space frame structures that could be mostly investigated only by using the conventional finite element method. The present report deals firstly with a development of the spectral element method for modeling framed structure damaged to multiple cracks represented by equivalent springs. Then, the spectral element model of cracked frame is implemented to the problem of crack identification from structural vibration characteristics in conjunction with the wavelet transform. The theoretical development was illustrated and validated by numerical examples. 1 INTRODUCTION The problem of crack identification in structure has attracted a considerable attention of engineer-researchers for several recent decades due to its practical importance. A lot of procedures have been emerged to detect and quantify cracks in structures [1]. Among the numerous proposed methods the wavelet-based approach shows to be the most effective, especially for detecting the small local damage such as crack in structures [2-5]. The wavelet- based procedure for crack identification in structure consists mainly of the following steps: (1) Measuring or calculating the signal associated with response of the structure that has to be