Nonlinear vibration and primary resonance analysis of porous FG/Lipid sandwich bionanoplates based on nonlocal strain gradient theory

Abstract

Mechanical nanosensors embedded within biological systems offer unique opportunities to assess variations in mass, displacements, and forces resulting from subcellular and cellular processes. On the other hand, these mechanical nanosensors establish a foundation for biological measurement devices capable of detecting individual molecules, owing to their exceptional size compatibility with molecular interactions. To enhance the performance of micro-/nanoscale biosensors, various organic layers, including biostructures like RNA, specific antibodies, and DNA, as well as lipid layers, are employed to identify a range of physical, chemical, and biological entities. This study investigates the nonlinear vibrations and primary resonance of a bionanostructure utilizing the first-order shear deformation plate theory (FSDT) in conjunction with the nonlocal strain gradient theory (NSGT). The sandwich nanoplates comprise a functionally graded core (FG) integrated with lipid bilayers on its upper and lower surfaces. The boundary condition is specified as immovable and simply supported, and this nanobiostructure is embedded in a nonlinear elastic foundation. The impact of porosity on both free and forced vibrations of functionally graded (FG) lipid sandwich nanoplates has been examined. The viscoelastic characteristics of the lipid layers were analyzed using the Kelvin–Voigt model. The Hamiltonian principle is utilized to formulate the nonlinear differential equations governing FG/Lipid sandwich nanoplates. The resulting partial differential equations are discretized through the application of the Galerkin method. Then perturbation techniques, including the multiple scale method and the Krylov–Bogoliubov–Mitropolski approach, are employed to analytically solve the system’s equations. A good agreement has been established by juxtaposing the present numerical outcomes with the results of earlier studies. The effects of several parameters, such as nonlocal and strain gradient indices, various foundation types, porosity volume fraction, excitation force magnitudes, different plate theories, and lipid viscoelastic properties, have been comprehensively examined. Drawing from the investigations and analyses conducted in this study, the findings on the nonlinear vibration characteristics of FG/Lipid sandwich nanoplates can be applied by researchers in the development of highly biocompatible nanobiosensors, nanodevices, and resonators.