<p>This investigation presents the nonlinear vibration analysis of sandwich double curved shallow shell on elastic foundations in the thermal environment and subjected to electric, magnetic, and mechanical fields. The sandwich double curved shallow shell comprises a particle- and fiber-reinforced composite (PFRC) core and magneto-electro-elastic (MEE) face sheets. Analytical expressions of material properties for the particle- and fiber-reinforced composite are derived from the volume proportions of the polyester matrix, particles, and fibers. The coupling motion equations are derived using Reddy’s first-order shear deformation shell theory and the von Kármán geometric nonlinearity. Natural frequency, phase plane trajectory, and dynamic response of the sandwich double curved shallow shell are found using the Galerkin and Runge–Kutta methods. Numerical findings evaluate the effect of various factors encompassing dimensional attributes, fiber and particle volume fraction, temperature rise, electric and magnetic potentials, and elastic foundations coefficients on vibration characteristics of the sandwich double curved shallow shell.</p>