<p>The research focuses on the influence of substrate geometric nonlinearity on the average output power of a hybrid galloping energy harvester with a vertically aligned D-shape-sectioned bluff body. Hamilton’s principle is applied to derive the geometrically-nonlinear-substrate-based model of the energy harvester. Then, a thorough comparison study is presented, between the established geometrically-nonlinear-substrate-based model for concurrent galloping and base excitation, and a geometrically-linear-substrate-based one in numerical simulation. The significant differences between the two models, not only discovered in energy harvesting but also in dynamic behaviors including single periodic vibrations, multi-periodic vibrations and even chaotic vibrations, are analyzed and inter-related. The present research will contribute to the application of substrate geometric nonlinearity in enhancing broadband concurrent energy harvesting for the investigated hybrid energy harvester.</p>