Document Type : Original Research Paper
Authors
1
Faculty of Mechanical & Energy Engineering, Shahid Beheshti University, A.C., Tehran, Iran
2
Faculty of Mechanical and Energy Engineering, Shahid Beheshti University, Tehran, Iran
10.22111/cnmst.2024.44828.1233
Abstract
This paper explores the lateral vibration behavior of a micro cantilever beam with an open edge crack under axial load using the modified strain gradient theory (MSGT). A concentrated mass, incorporating its rotational inertia, is positioned at the beam's free end. The open edge crack is represented using the Dirac delta function. By employing MSGT, Hamilton's principle, and the Dirac delta function, the governing equations for system motion and relevant boundary conditions are derived to examine the size-dependence effects. Analytical solutions for the first and second natural frequencies of the cracked cantilever beam are provided, and validated through finite element modeling. The study further investigates the impact of various system parameters, including material length scale parameters, crack depth, crack location, cantilever beam length, axial load, and the presence of the concentrated mass, on the natural frequencies. The findings demonstrate that the crack depth, crack location, and material length scale parameters considerably influence the lateral vibration characteristics of the system. Notably, increasing the values of l_i/h from 0 to 0.25 leads to an approximate 40% rise in the natural frequency.
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