Thermovibrational convection in a water based metallic (Cu-water and Ag-water) or metallic oxide (Al2O3-water and TiO2-water) nanofluid saturated porous medium is addressed incorporating the Brinkman boundary correction. The nanofluid behaves more like a fluid rather than a conventional solid–fluid mixture and is studied through Khanafer–Vafai–Lightstone (KVL) model. A linear stability analysis is carried out through the Floquet theory to find the instability thresholds for convection onset in terms of critical Rayleigh number and critical wavenumber. The results corresponding to synchronous as well as subharmonic modes are obtained for the Darcy and Brinkman regimes. A rise in particle concentration is found to cause stabilizing response in general. However, it leaves an opposite effect in the Brinkman regime when the medium is filled with metallic nanofluid and is heated from above. Under this situation, the use of oblate-spheroidal particles in achieving optimal convective heat transfer enhancement is highlighted.