<p>This research investigates the nonlinear vibration of hybrid nanocomposite double curved shallow shell when subjected to electromagnetic fields and a uniformly distributed loading. The hybrid double curved shallow shell incorporates a three-phase nanocomposite material core with magneto-electro-elastic face sheets. This core comprises an epoxy matrix reinforced with graphene foams and carbon fibers with material properties determined using the rule of mixtures for the hybrid matrix and employing the Halpin–Tsai model for multiscale homogenization. The basic equations are formulated by combining first order shear deformation shell theory with Von Kármán geometric nonlinearity. The study uses the Galerkin method and Runge–Kutta technique to identify natural vibration frequency, phase-plane trajectories and dynamic responses of the hybrid double curved shallow shell. Numerical examples are provided to investigate the influences of various factors, including geometric parameters, elastic foundation stiffness, uniformly distributed loading, imperfection coefficients and electromagnetic potentials. The accuracy of the proposed formulation is validated through comparison with established benchmark solutions, exhibiting strong agreement. Numerical results indicate that the double-curved shell geometry exhibits superior dynamic stiffness with significantly higher natural frequencies and lower deflection amplitudes compared to flat plates and cylindrical panels, while the integration of elastic foundations effectively enhances structural stability. The results offer valuable insights for the precise design and fabrication of three-phase hybrid nanocomposite intelligent materials, contributing to the development of advanced smart materials for applications in aerospace, sensing systems, consumer electronics and biomedical technologies.</p> Graphical Abstract <p></p>