Isogeometric free vibration of the porous metal foam plates resting on an elastic foundation using a quasi-3D refined theory

This study investigates the free vibration behavior of porous metal foam plates using the Quasi-3D refined plate theory. We consider three types of pores across the plate thickness: uniform, symmetric, and asymmetric distributions. Besides, the metal foam plate is reinforced by a Winkler-Pasternak foundation. By employing the variational principle and Quasi-3D refined theory, we derive the weak form for free vibration analysis. The Quasi-3D theory is essential for analyzing plates, as it accurately captures transverse shear and normal deformations, which are vital for understanding the behavior of thick and moderately thick plates. Unlike simpler models, it provides a detailed representation of stress and strain distributions across the plate’s thickness, enabling precise modeling of complex structural behaviors. The natural frequency of the porous metal foam plates is determined by solving the explicit governing equation using the isogeometric approach. Additionally, we examine how the porous coefficient, porous distribution, and geometry impact the vibrational frequency of the porous metal foam plate.