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The transfer matrix method for modal analysis of cracked multistep beam

The present study addresses the modal analysis of multistep beam with arbitrary number of cracks by using the transfer matrix method and modal testing technique. First, there is conducted general solution of free vibration problem for uniform beam element with arbitrary number of cracks that allows one to simplify the transfer matrix for cracked multistep beam. | Vietnam Journal of Science and Technology 55 (5) (2017) 598-611 DOI: 10.15625/2525-2518/55/5/9140 THE TRANSFER MATRIX METHOD FOR MODAL ANALYSIS OF CRACKED MULTISTEP BEAM Vu Thi An Ninh1, Luu Quynh Huong2, Tran Thanh Hai3, Nguyen Tien Khiem3, * 1 University of Transport and Communications, 3 Cau Giay, Dong Da, Hanoi 2 3 Thuy Loi University, Chua Boc, Dong Da, Hanoi Graduate University of Science and Technology, VAST, 18 Hoang Quoc Viet, Cau Giay, Hanoi * Email: ntkhiem@imech.vast.vn; khiemvch@gmail.com Received: 9 January 2017; Accepted for publication: 28 May 2017 ABSTRACT The present study addresses the modal analysis of multistep beam with arbitrary number of cracks by using the transfer matrix method and modal testing technique. First, there is conducted general solution of free vibration problem for uniform beam element with arbitrary number of cracks that allows one to simplify the transfer matrix for cracked multistep beam. The transferring beam state needs to undertake only at the steps of beam but not through crack positions. Such simplified the transfer matrix method makes straightforward to investigate effect of cracks mutually with cross-section step in beam on natural frequencies. It is revealed that step-down and step-up in beam could modify notably sensitivity of natural frequencies to crack so that the analysis provides useful indication for crack detection in multistep beam. The proposed theory was validated by an experimental case study. Keywords: stepped beam; cracked beam; modal analysis; transfer matrix method. 1. INTRODUCTION Stepped beam structures have found widespread application in engineering fields such as bridges, rotating machines, robotics and aerospace structures. In the engineering application, vibration of the structures is the problem of a great importance and it is studied in the enormous literature. Sato [1] studied an interesting problem that proposed to calculate natural frequency of beam with a groove in dependence on