Nonlinear vibration analysis of the viscoelastic composite nanoplate with three directionally imperfect porous FG core

In this study, the nonlinear vibration analysis of the composite nanoplate is studied. The composite nanoplate is fabricated by the functional graded (FG) core and lipid face sheets. The material properties in the FG core vary in three directions. The Kelvin-Voigt model is used to study the viscoelastic effect of the lipid layers. By using the Von-Karman assumptions, the nonlinear differential equation of the vibration analysis of the composite nanoplate is obtained. The foundation of the system is modeled by the nonlinear Pasternak foundation. The Bubnov-Galerkin method and the multiple scale method are used to solve the nonlinear differential equation of the composite nanoplate. The free and force vibration analysis of the composite nanoplate are studied. A comparison between the presented results and the reported results is done and good achievement is obtained. The reported results are verified by the results which are obtained by the Runge-Kutta method. The effects of different parameters on the nonlinear vibration frequencies, the primary, the super harmonic and subharmonic resonance cases are investigated. This work will be useful to design the nanosensors with high biocompatibility.