Effect of bidirectional thickness and porosity on the free vibration of cracked FG plates on elastic foundations

DOI: https://doi.org/10.55228/

Keywords

Elastic foundation, Free vibration, Voids, Cracked FG plate, Variable thickness

Abstract

This paper investigates the free vibration behavior of a rectangular plate resting on an elastic foundation. The plate is made of a functionally graded (FG) material with an exponential variation of properties, and its thickness varies along two in-plane directions. The mechanical model is formulated using the Mindlin plate theory and the finite element method, while the phase-field approach is employed to describe the crack state at the plate center. Model reliability is validated through comparison with published results. The effects of material volume fraction, porosity coefficient, crack length and inclination, thickness variation parameters, and foundation stiffness on the natural frequencies and mode shapes are examined. The results show that the elastic foundation, porosity, thickness variation, and crack length strongly affect the vibration response, whereas the crack inclination angle has a relatively minor influence

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