Dynamics of imperfect inhomogeneous nanoplate with exponentially-varying properties resting on viscoelastic foundation

This article tries to investigate the dynamic deflection response of exponentially functionally graded material (EFGM) nanoplate considering the role of porosities when embedded in a visco-elastic foundation and subjected to moving load, for the first time. The effective material properties are found using an exponential model of the rule of mixture. Next, the governing equations for the nanoplates while resting on a visco-Winkler foundation are found based on the third-order shear deformation theory in conjunction with Eringen nonlocal elasticity by developing Hamilton's principle. To solve the time-dependent governing motion equations, a state-space method is developed to find the response of the structure including simply-supported edges under moving load. Through some examples, the validation of the approach is provided before investigating the roles of nonlocality, volume fraction index (exponential parameter), porosity index, visco-elastic foundation coefficients, and velocity and time span of moving load on the forced vibration of embedded E-FGM nano-size plate under moving load.

Automated summary

This article investigates the dynamic deflection response of exponentially functionally graded material (EFGM) nanoplate considering the role of porosities when embedded in a visco-elastic foundation and subjected to moving load, for the first time. The effective material properties are found using an exponential model of the rule of mixture. A state-space method is developed to solve the time-dependent governing motion equations and study the effects of various parameters on the forced vibration of the embedded nanoplate.