Mode shape analysis of multiple cracked functionally graded beam-like structures by using dynamic stiffness method


  • Tran Van Lien National University of Civil Engineering, Hanoi, Vietnam
  • Ngo Trong Duc Design Consultant and Investment of Construction - Ministry of Defense, Vietnam
  • Nguyen Tien Khiem Institute of Mechanics, Vietnam Academy of Science and Technology, Hanoi, Vietnam



FGM, multiple cracked beam, modal analysis, dynamic stiffness method


Mode shapes of multiple cracked beam-like structures made of Functionally Graded Material (FGM) are analyzed by using the dynamic stiffness method. Governing equations in vibration theory of multiple cracked FGM beam are derived on the base of Timoshenko beam theory; power law variation of material; coupled spring model of crack and taking into account the actual position of neutral axis. A general solution of vibration in frequency domain is obtained and used for constructing dynamic stiffness matrix of the multiple cracked FGM Timoshenko beam element that provides an efficient method for modal analysis of multiple cracked FGM frame structures. The theoretical development is illustrated by numerical analysis of crack-induced change in mode shapes of multi-span continuous FGM beam.


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How to Cite

Lien, T. V., Duc, N. T., & Khiem, N. T. (2017). Mode shape analysis of multiple cracked functionally graded beam-like structures by using dynamic stiffness method. Vietnam Journal of Mechanics, 39(3), 215–228.



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