A Closed-Form Solution for Harvesting Energy from the High-Order Sandwich Beam Subjected to Dynamic Loading

This study presents a closed-form solution for the dynamic response of a sandwich beam subjected to arbitrary impact loading, with a particular focus on energy harvesting from an attached piezoelectric layer. A thin piezoelectric patch is bonded to the bottom surface of the beam to convert mechanical vibrations into electrical energy. The governing equations of motion are derived using Hamilton’s principle, considering a non-symmetric sandwich cross-section and incorporating higher-order shear deformation effects. The state–space method is employed to obtain the exact dynamic response of the beam under impact excitation. The differential equations governing the output voltage and harvested power are solved analytically based on the derived response. The natural frequencies and dynamic responses are validated against classical beam theory, highlighting the significance of shear deformation. Numerical examples are provided to evaluate the generated voltage and energy harvesting efficiency. The results demonstrate the strong potential for energy harvesting from sandwich beam vibrations and elucidate the influence of impact loading conditions, distributed load amplitude, and the geometric dimensions of the beam on the harvested output.