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• Low-velocity impact of sandwich beams with multilayer sandwich beams is analytically and numerically studied. • Analytical solutions for low-velocity impact of multilayer sandwich beams are developed. • Analytical solution captures the numerical results reasonably. • Impact position, foam strength and face-sheet thickness have significant effects on the dynamic response. The paper focuses on the dynamic response of multilayer sandwich beams with foam-filled trapezoidal corrugated and foam cores under low-velocity impact with heavy-mass using analytical and numerical methods. Based on the yield criterion for the multilayer sandwich structure, the circumscribing and inscribing loci of sandwich structure are obtained. Considering the interaction of bending and stretching, the analytical solution and "bound" solution for the dynamic response of multilayer sandwich beams with foam-filled trapezoidal corrugated and foam cores are developed. The numerical calculations are used to verify the analytical solutions, and all lie within the analytical "bound" predications. Then, the influences of impact position, foam strength and face-sheet thickness on the dynamic response of multilayer sandwich beams are discussed in detail by theoretical model. For a given deflection, the impact force decreases with impact position closer to the midspan, the impact force increases with the increase of foam strength and face-sheet thickness. The present analytical model can effectively predict the dynamic response of fully clamped multilayer sandwich beams with foam-filled trapezoidal corrugated and foam cores under low-velocity impact. [ABSTRACT FROM AUTHOR]