Free vibration analysis of multi-cracked micro beams based on Modified Couple Stress Theory

Document Type: Full Length Article


1 Assistant Professor, Mechanical & Energy Engineering, Shahid Beheshti University, A.C., Tehran, Iran

2 Ph.D. Candidate, Faculty of Mechanical & Energy Engineering, Shahid Beheshti University, A.C., Tehran, Iran



In this article, the size effect on the dynamic behavior of a simply supported multi-cracked microbeam is studied based on the Modified Couple Stress Theory (MCST).  At first, based on MCST, the equivalent torsional stiffness spring for every open edge crack at its location is calculated; in this regard, the Stress Intensity Factor (SIF) is also considered for all open edge cracks. Hamilton’s principle has been used in order to achieve the governing equations of motion of the system and associated boundary conditions are derived based on MCST. Then the natural frequencies of multi-cracked microbeam
are analytically determined. After that, the Numerical solutions have been presented for the microbeam with two open edge cracks. Finally, the variation of the first three natural frequencies of the system is investigated versus different values of the depth and the location of two cracks and the material length scale parameter. The obtained results express that the natural frequencies of the system increase by increasing the material length scale parameter and decrease by moving away from the simply supported of the beam and node points, in addition to increasing the number of cracks and cracks depth.


  • The size effect on vibration behavior of a multi-cracked microbeam is studied.
  • The governing equations are derived based on the Modified Couple Stress Theory.
  • The equivalent stiffness of the crack is calculated considering the SIF.
  • The natural frequencies of multi-cracked microbeam are determined analytically


Main Subjects

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