Computational Models for the Vibration and Modal Analysis of Silica Nanoparticle-Reinforced Concrete Slabs with Elastic and Viscoelastic Foundation Effects

The integration of silica nanoparticles (NS) into cementitious composites has emerged as a promising strategy to refine the microstructure and enhance concrete performance. Beyond their chemical role in accelerating hydration and promoting additional C–S–H gel formation, silica nanoparticles act as physical fillers, reducing porosity and improving interfacial bonding within the matrix. These dual effects result in a denser and more resilient composite, whose mechanical and dynamic responses differ from those of conventional concrete. However, studies addressing the vibrational and modal behavior of nano-reinforced concretes, particularly under elastic and viscoelastic foundation conditions, remain limited. This study investigates the dynamic response of NS-reinforced concrete slabs using a refined quasi-3D plate deformation theory with five (05) unknowns. Different foundation configurations are considered to represent various soil interactions and assess structural integrity under diverse supports. The effective elastic properties of the nanocomposite are obtained through Eshelby’s homogenization model, while Hamilton’s principle is used to derive the governing equations of motion. Navier’s analytical solutions are applied to simply supported slabs. Quantitative results show that adding 30 wt% NS increases the Young’s modulus of concrete by about 26% with only ~1% change in density; for simply supported slender slabs, this results in geometry-dependent increases of up to 18% in the fundamental natural frequency. While the Winkler and Pasternak foundation parameters reduce this frequency, the damping parameter of the viscoelastic foundation enhances the dynamic response, yielding frequency increases of up to 28%, depending on slab geometry.