• Nguyen Tien Khiem Institute of Mechanics, Vietnam Academy of Science and Technology
  • An Ninh Thi Vu University of Transport and Communication
  • Hai Thanh Tran Institute of Mechanics, VAST



Timoshenko beam theory, multi-stepped beam, multi-cracked beam, natural frequencies, transfer matrix method


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


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Author Biographies

Nguyen Tien Khiem, Institute of Mechanics, Vietnam Academy of Science and Technology

Professor of VNU, Senior researcher of VAST, The President of Vietnam Association for Mechanics.

An Ninh Thi Vu, University of Transport and Communication

Ph.D, Lecturer in Theoretical Mechanics,

Hai Thanh Tran, Institute of Mechanics, VAST

Ph.D, Principal Researcher of VAST


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