This is based an explicit expression of the natural frequencies in term of crack parameter derived in the form similar to the so-called Rayleigh quotient for vibrating beam. The obtained simple relationship between natural frequencies and crack parameters enables not only accurate calculating the natural frequencies but also to develop an efficient procedure for detecting multiple cracks from given natural frequencies. | Volume 36 Number 2 2 2014 Vietnam Journal of Mechanics, VAST, Vol. 36, No. 2 (2014), pp. 119 – 132 MULTIPLE CRACK IDENTIFICATION IN STEPPED BEAM BY MEASUREMENTS OF NATURAL FREQUENCIES Nguyen Tien Khiem1,∗, Duong The Hung2 , Vu Thi An Ninh3 of Mechanics, VAST, 18 Hoang Quoc Viet, Hanoi, Vietnam 2 Thai Nguyen University of Technology, Vietnam 3 Hanoi University of Transport and Communication, Vietnam 1 Institute ∗ E-mail: ntkhiem@ Received July 26, 2013 Abstract. A new approach is proposed for calculating natural frequencies and crack detection in a stepped cantilever beam with arbitrary number of cracks. This is based an explicit expression of the natural frequencies in term of crack parameter derived in the form similar to the so-called Rayleigh quotient for vibrating beam. The obtained simple relationship between natural frequencies and crack parameters enables not only accurate calculating the natural frequencies but also to develop an efficient procedure for detecting multiple cracks from given natural frequencies. The proposed technique called crack scanning method is illustrated and validated by numerical results. Keywords: Multi stepped beam, Rayleigh quotient, multi-crack detection, frequency based method, modal analysis. 1. INTRODUCTION Early detecting damage in engineering structures such as cracks is vitally important to prevent catastrophe that may lead to loss of either material or human lives. The task helps also to extend the structure lifetime by prompt maintenance and repair. A lot of methods have been proposed to detect cracks in structures and most of them are based on the crack-induced change in the dynamic characteristics of structure under consideration. This is because of the fact that crack in a structure member certainly modify the structure dynamic properties that can be usually obtained as results of the dynamic testing. The core of the vibration-based crack detection is the change in the structure modal parameters as
