<p>Integrating mechanical nanosensors with biological structures allows evaluating the mass, displacements, and forces in subcellular and cellular activities. On the other hand, studying bio-nanosensors is crucial for identifying biological, chemical, and physical structures. Therefore, the vibration analysis and critical damping behavior of Lipid/Graphene sandwich viscoelastic nanoplates must be studied. The current work investigates a bio-nanostructure referred to as sandwich viscoelastic nanoplates. The differential equations of bio-nanostructure embedded on the viscoelastic substrate have been derived based on the principle of Hamilton and solved numerically using a general differential quadrature method (GDQM) to predict the vibration behaviors of the bio-nanostructure. The differential quadrature method is utilized to extract the natural frequency and critical damping of the Lipid/ Graphene sandwich nanoplates with structural damping for the first time, and also examines the impact of the viscoelastic medium and the size effect (nonlocal parameter) on the vibration behavior of the bio-nanostructure. The findings of this study indicate that the frequencies of nanostructures decrease noticeably as the structural damping and the damping coefficients of the viscoelastic foundation increase. Moreover, by increasing the damping coefficient values of the viscoelastic foundation, the critical damping of Lipid/Graphene sandwich nanoplates (bifurcation curve) occurs at lower values of the nonlocal parameter. On the contrary, with the increase of structural damping, the critical damping of this bio-nanostructure occurs at higher nonlocal parameter values. These findings can be advantageous for the design and production of nanoscale equipment, including bio-nanosensors, resonators, and nano-devices, which require high precision and sensitivity.</p>