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Steel and Composite Structures
  Volume 31, Number 5, June10 2019 , pages 489-502

Free and forced analysis of perforated beams
Alaa A. Abdelrahman, Mohamed A. Eltaher, Abdallah. M. Kabeel, Azza M. Abdraboh and Asmaa A. Hendi

    This article presents a unified mathematical model to investigate free and forced vibration responses of perforated thin and thick beams. Analytical models of the equivalent geometrical and material characteristics for regularly squared perforated beam are developed. Because of the shear deformation regime increasing in perforated structures, the investigation of dynamical behaviors of these structures becomes more complicated and effects of rotary inertia and shear deformation should be considered. So, both Euler-Bernoulli and Timoshenko beam theories are proposed for thin and short (thick) beams, respectively. Mathematical closed forms for the eigenvalues and the corresponding eigenvectors as well as the forced vibration time response are derived. The validity of the developed analytical procedure is verified by comparing the obtained results with both analytical and numerical analyses and good agreement is detected. Numerical studies are presented to illustrate effects of beam slenderness ratio, filling ratio, as well as the number of holes on the dynamic behavior of perforated beams. The obtained results and concluding remarks are helpful in mechanical design and industrial applications of large devices and small systems (MEMS) based on perforated structure.
Key Words
    resonant frequencies; forced Vibration, perforated beam; dynamical behavior; filling ratio; semi-analytical method
(1) Alaa A. Abdelrahman, Abdallah M. Kabeel:
Mechanical Design & Production Department, Faculty of Engineering, Zagazig University, P.O. Box 44519, Zagazig, Egypt;
(2) Mohamed A. Eltaher:
Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah, Saudi Arabia;
(3) Mohamed A. Eltaher:
Mechanical Design & Production Department, Faculty of Engineering, Zagazig University, P.O. Box 44519, Zagazig, Egypt;
(4) Azza M. Abdraboh:
Physics Department, Faculty of Science, Banha University, Banha, Egypt;
(5) Asmaa A. Hendi:
Physics Department, Faculty of Science, University of Jeddah,P.O.Box 80327, Jeddah, Saudi Arabia.

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