Thermo-mechanical forced vibration of FG-GOEAM plates supported by viscoelastic substrates with elastic edge restraints

Functionally graded graphene origami-enabled auxetic metamaterial (FG-GOEAM) plates offer high stiffness, low weight, and tunable mechanical properties. However, their thermo-mechanical forced vibration under viscoelastic substrate (VS) and elastic edge restraint (EER) remains insufficiently investigated. This study develops a quasi-three-dimensional (quasi-3D) finite element formulation for the forced vibration analysis of FG-GOEAM plates. A six-unknown quasi-3D plate theory with mixed Q4 Lagrange–Hermite interpolation is employed to account for transverse shear deformation and thickness stretching. The VS is modeled using a three-parameter Winkler–Pasternak foundation, while EERs are represented by distributed boundary springs. The formulation is validated against benchmark solutions, followed by parametric studies of GOri weight fraction, distribution pattern, folding degree, temperature, foundation stiffness, and edge restraint stiffness. The results show that foundation and edge restraint stiffnesses suppress forced vibration, whereas GOri configuration and folding degree significantly affect the dynamic response.