Résumé:
This study examines the influence of elastic foundations on the vibrational
characteristics of specific structures, particularly functionally graded material (FGM) plates.
The primary objective is to evaluate how the introduction of elastic foundations alters the
vibration modes of these complex structures. Additionally, the analysis of the effect of porosity
on the vibrational behavior of porosity-graded plates is studied. Three forms of porosity
distribution are used: uniform (FGU), asymmetric (FGA), and symmetric (FGS), to observe
their behavior on the foundations. Porosity is assumed to vary only across the thickness of the
plates. elastic foundations, acting as flexible supports, absorb and redistribute the vibrations
generated by the FGM plates, thus influencing their overall behavior in terms of resonance,
damping, and dynamic response. The plate is considered to be simply supported along its
perimeter, and the equations of motion are developed using the principle of energy
minimization, with solutions derived using the Navier technique. The results of this study
provide valuable insights for optimizing structures in terms of vibrational performance across
various application fields, such as aerospace, automotive, and other sectors where vibration
reduction and fatigue resistance are crucial.
In conclusion, this research enriches the understanding of the complex interactions between
material properties, structural geometry, and support conditions. It also explores the effect of
the porosity index, the length-to-thickness ratio (h/a), and the material index (p), paving the
way for potential innovations in the design of more efficient and resilient materials and
structures against vibrations
