Purpose <p>Large amplitude vibrations of a multilayered nanocomposite arch enriched by graphene nanoplatelets (GNPs) are investigated in this article.</p> Method <p>The linear and nonlinear vibrational frequencies are analytically formulated for the nanocomposite arch on an elastic nonlinear support. The influence of temperature variation through the arch’s thickness is also investigated. Thermomechanical properties of the multilayered nanocomposite arch are evaluated by employing the Halpin-Tsai model of mixtures. The kinematic nonlinearity is included into the formulation within the framework of the von Kármán assumption. The kinematic relationships are valid for each layer on the basis of Reddy’s third-order shear deformation model. The equations of motion are formulated by implementing the Hamilton’s principle. A perturbation-based solution method is implemented to formulate the analytical expressions for the small- and largeamplitude vibrations. The obtained results present a comprehensive insight into the linear and nonlinear vibrations of laminated composite shallow arches in thermal field.</p> Results <p>Results of this examination illustrate the effects of arch’s slenderness ratio, temperature variation, arch’s curvature ratio, weight fraction and distribution pattern of GNPs, and also foundation stiffness on the frequencies of the nanocomposite arch.</p> Conclusion <p>It is seen that temperature change, radius of the arch, weight fraction of GNPs, Pattents of GNPs, stiffness of foundations are all important factors on frequencies of the composite arch.</p>