The present article investigates the dynamic characteristics of jute fiber-reinforced sandwich composite panels with periodic cores. The sandwich panel contains the jute fibers-reinforced polymer (JFRP) composites as face layers and the silicone rubber as the core layer. The tensile and flexural properties of JFRP composite material were examined using ASTM D3039 and ASTM D7264 standards. The finite element model was developed to obtain the dynamic properties of the composite sandwich panel with conventional and periodic cores. Furthermore, the influence of end condition, core to face layer thickness ratio, and face layer to core thickness ratio on the dynamic properties of the sandwich panels are presented. The numerical results indicate that the periodic core composite sandwich panel greatly influences the structural stiffness compared with a conventional composite sandwich panel.