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This article analyzes the vibrational behavior of the double-layered micro-nanosphere to simulate the drug delivery mechanism in the biological structure under the influence of the temperature environment and the viscoelastic substrate for the polar lipid fraction E (PLFE) liposome isotropic material model. In order to obtain the micro-nano structural equations of the double-layer spherical shell, the displacement-strain relations of the shell have been expressed according to the first-order shear deformation theory and the non-local strain gradient theory. The partial differential equations of motion have been obtained by applying Hamilton’s principle. The system of linear couple equations have been solved using the Galerkin method. After validating the model with the results of the articles available in the literature to determine the accuracy of the presented model, numerical results are presented to investigate the effects of various parameters such as the radius of curvature ratio to length, damping coefficient, Kelvin-Voight damping coefficient, boundary conditions and temperature on vibration frequency response are provided and discussed. Results of the current research indicates that natural frequency decreases as the damping coefficient related to the viscous effect between the liposome bilayers increase. Results of the current research can be used as a benchmark for drug delivery applications.

Temperature-dependent vibrational behavior of bilayer doubly curved micro-nano liposome shell: Simulation of drug delivery mechanism