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Structural Engineering and Mechanics
  Volume 74, Number 1, April10 2020, pages 33-54

Free vibration and harmonic response of cracked frames using a single variable shear deformation theory
Baran Bozyigit and Yusuf Yesilce and Magd Abdel Wahab

    The aim of this study is to calculate natural frequencies and harmonic responses of cracked frames with general boundary conditions by using transfer matrix method (TMM). The TMM is a straightforward technique to obtain harmonic responses and natural frequencies of frame structures as the method is based on constructing a relationship between state vectors of two ends of structure by a chain multiplication procedure. A single variable shear deformation theory (SVSDT) is applied, as well as, Timoshenko beam theory (TBT) and Euler-Bernoulli beam theory (EBT) for comparison purposes. Firstly, free vibration analysis of intact and cracked frames are performed for different crack ratios using TMM. The crack is modelled by means of a linear rotational spring that divides frame members into segments. The results are verified by experimental data and finite element method (FEM) solutions. The harmonic response curves that represent resonant and anti-resonant frequencies directly are plotted for various crack lengths. It is seen that the TMM can be used effectively for harmonic response analysis of cracked frames as well as natural frequencies calculation. The results imply that the SVSDT is an efficient alternative for investigation of cracked frame vibrations especially with thick frame members. Moreover, EBT results can easily be obtained by ignoring shear deformation related terms from governing equation of motion of SVSDT.
Key Words
    cracked frame; free vibration; harmonic response; single variable shear deformation theory; transfer matrix method
Baran Bozyigit and Yusuf Yesilce:Department of Civil Engineering, Dokuz Eylul University, Buca, Izmir, Turkey
Magd Abdel Wahab:
1 Division of Computational Mechanics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
2 Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam

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