Mathematical modeling for predicting electrical energy harvested using piezoelectric composite materials for smart system applications

In the contemporary quest for sustainable energy, the potential of piezoelectric energy harvesters to convert mechanical vibrations into electrical energy has become increasingly important. This study focuses on piezoelectric composites, in particular a BaTiO₃/PLA (Barium Titanate/ Polylactic Acid) system with different volume percentages of BaTiO₃ ceramic particles (20%, 40% and 60%), with the aim of optimizing energy conversion efficiency. A mathematical model is introduced, encompassing material attributes, mechanical loading frequencies and electrical energy outputs. The central role of mathematical modeling in predicting harvested energy is highlighted, offering insights beyond experimental limitations. The model, which is functionally dependent on the properties of the ceramic and polymer, enables the systematic exploration of various compositions and the identification of optimal material ratios. Experimental validation of the model for different strains (0.4%, 0.8% and 1%) and compositions of BaTiO₃/PLA reaffirms its reliability. Notably, the highest power harvest observed is around 4.5 μW under a strain of 1% with a BaTiO₃ composition of 60%. With these specific numerical values, this approach merges materials science and energy technology, propelling the advancement of efficient piezoelectric materials for renewable energy applications.