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In this work, energy harvesting from a proposed three-mode T-shaped structure, composed of a vertical beam, two horizontal beams, a center mass, and tip masses, is investigated to expand the frequency bandwidth for energy harvesting, without compromising the power density due to the additional mass of the structure, as is the case with most multi-mode harvesters. The aim is to cleverly use and position the additional mass to help induce higher and more uniform strain levels throughout the piezoelectric patch, leading to greater power generation to help counteract the added mass. A numerical model was developed to analyze the structure, to obtain voltage and power frequency responses, taking into effect the load resistance modeling and the accurate evaluation of resonance peaks by estimating each mode damping ratio. The validity of the model was confirmed by comparisons with previous experiments involving other structures, which demonstrated strong agreement. The excitation load was strategically applied to induce maximum displacement of the center and tip masses relative to the fixed ends in each mode. The outcomes reveal that the T-shaped configuration exhibits the capacity to generate higher maximum strain and a more uniform strain distribution across the piezoelectric patch when compared to previous L-shaped and traditional cantilever harvesters' designs. These characteristics yielded a power density higher than that of the L-shaped structure by approximately 70% with only around 20% addition in structure mass. Additionally, the multi-mode T-shaped structure boasts a significantly broader harvesting bandwidth due to the additional mode, without compromising power density, as was the case with L-shaped structures. Furthermore, the positioning of the tip mass was systematically altered to assess its impact on the frequency bandwidth and power output of the horizontal and vertical beams in the three bending modes, demonstrating great robustness and tuning capabilities.