The study explores the behaviour of systems under both free and forced vibrations of spherical sandwich panels supported by an elastic foundation exposed to various impact load profiles. The panels consist of multilayer composite face sheets formulated based on the first-order shear deformation theory, and a soft core characterized by a higher-order theory employing third-order in-plane and second-order transverse displacement fields. By calculating the mechanical energy components, and introducing a higher-order element with nine nodes and 15 degrees of freedom for each node, the element stiffness and mass matrices were determined. Boundary conditions are simulated through distributed virtual springs. A free vibration problem is evaluated to extract the structure’s natural frequencies and mode shapes. Using the Newmark method, time response of displacement, velocity, acceleration, and phase planes are calculated for various impact profiles, specifically for half-sine pulses. This comprehensive analysis of sandwich panels' dynamic response under various impact loads reveals that the load profile critically determines structural behavior, essentially governing the boundary between safe operation and potential failure. For example, sudden loads like rectangular pulse emerged as the most critical case, causing extreme discontinuous responses across all dynamic parameters, and gradual loads (Gaussian/exponential) proved optimal for sensitive applications by generating smooth, controlled structural responses and providing ideal performance for stability-critical systems.