Abstract
The study's contribution is to examine, while taking into account pinned-pinned boundary conditions, the free vibration response of multi-cracks Euler-Bernoulli perfect FG beams structure on Pasternak-Winkler elastic foundations. The finite element approach is used to discretize the equations. The material properties are taken into account using a power-law form, and they differ in the thickness and width directions of the beam structure. The 2D FG beam's reduced cross section is used to calculate the stiffness of the cracked structure. On the other hand, the Pasternak-Winkler type foundation has a longitudinal distribution and makes the system stiffer. For convergence research, the numerical results are compared with the outcomes of earlier investigations in terms of dimensionless fundamental frequencies. Case studies were carried out to examine the effects on the natural frequencies of the beams structure of the power law index, multi-cracks, depths, location, and Pasternak-Winkler-elastic foundation. These studies demonstrate the benefits of the two-dimensional FG beam in the presence of cracks over the unidirectional FG and pure metallic beams.
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