A novel composite structure composed of graphene origami reinforcement integrated with piezoelectric/piezomagnetic layers is defined in this paper. The Material composition is assumed as steel novel metamaterials. The proposed model can be used as a diving board in swimming. The vibrational-based formulation is extended using an advanced higher-order thickness-stretchable model. The governing motion equations are derived using Hamilton’s principle through the computation of strain and kinetic energies as well as external work. The constitutive relations are extended for the composite core in terms of volume fraction, folding degree, and thermal load using some modifier functions using Halpin-Tsai micromechanical models for modulus of elasticity, Poisson’s ratio, thermal expansion coefficient, and density. The natural frequency responses are derived using the analytical method in terms of characteristics of graphene origami such as thermal load, foldability parameter, and amount of reinforcement. Furthermore, an investigation on the impact of initial electro-magneto-mechanical loads is studied on the responses.
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