The C1 Isogeometric analysis procedure for analysis of free vibration of GPLR-FG-TPMS nanoplates embedded in Pasternak foundation

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Abstract
The main goal of this study is to extend the isogeometric analysis (IGA) further to investigate the free vibration of graphene platelet (GPL)-reinforced functionally graded triply periodic minimal surface (FG-TPMS) nanoplates (so-called GPLR-FG-TPMS nanoplates) embedded in Pasternak foundation (PF). The computational model includes both nonlocal elasticity and strain gradient effects to account for the impact of small-size effects inherent in nanostructures. To achieve C1-continuity condition, an IGA framework based on HSDT is developed with 7-DOFs per a control point. The motion equation of the nanoplate is derived from Hamilton's principle. The calculation program is coded in Matlab environment and verified through comparative examples. From here, the influence of geometric parameters, material properties, and boundary conditions (BCs) on the frequency of nanoplates is investigated in detail. The results obtained are reference materials for further studies as well as in the calculation and design of GPLR-FG-TPMS structures in practice.

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