The present paper addresses the problem for free vibration of multistep Timoshenko beams with arbitrary number of cracks, continuing the work accomplished in [28], where the problem was studied on the base of Euller-Bernoulli beam theory. First, the obtained general solution of uniform Timoshenko beam is employed to develop the TMM for modal analysis of multistep Timoshenko beam with multiple cracks. Then, effect of beam slenderness and stepped change in cross section on sensitivity of natural frequencies to cracks is thoroughly examined. | Modal analysis of multistep timoshenko beam with a number of cracks Vietnam Journal of Science and Technology 56 (6) (2018) 772-787 DOI: MODAL ANALYSIS OF MULTISTEP TIMOSHENKO BEAM WITH A NUMBER OF CRACKS Tran Thanh Hai1, Vu Thi An Ninh2, Nguyen Tien Khiem1, * 1 Graduate University of Science and Technology, VAST, 18 Hoang Quoc Viet, Ha Noi 2 University of Transport and Communications, 3 Cau Giay, Dong Da, Ha Noi * Email: ntkhiem@ Received: 2 May 2018; Accepted for publication: 15 October 2018 ABSTRACT Modal analysis of cracked multistep Timoshenko beam is accomplished by the Transfer Matrix Method (TMM) based on a closed-form solution for Timoshenko uniform beam element. Using the solution allows significantly simplifying application of the conventional TMM for multistep beam with multiple cracks. Such simplified transfer matrix method is employed for investigating effect of beam slenderness and stepped change in cross section on sensitivity of natural frequencies to cracks. It is demonstrated that the transfer matrix method based on the Timoshenko beam theory is usefully applicable for beam of arbitrary slenderness while the Euler-Bernoulli beam theory is appropriate only for slender one. Moreover, stepwise change in cross-section leads to a jump in natural frequency variation due to crack at the steps. Both the theoretical development and numerical computation accomplished for the cracked multistep beam have been validated by an experimental study. Keywords: Timoshenko beam theory; multi-stepped beam; multi-cracked beam; natural frequencies; transfer matrix method. Classification numbers: 1. INTRODUCTION Beam-like structures with stepwise changes in cross-section called stepped beams are widely used in the practice of construction and machinery engineering and can be used also as a proper approximation of nonuniform beams. Therefore, dynamics of stepped .
