Near faults, recorded ground motions exhibit unique physical characteristics, different from those observed in far-field regions. These disparities are particularly evident in the configuration of accelerograms and their corresponding velocity- and displacement-based time-histories. The pulse structures observed in velocity time-histories characterized by an abrupt surge in the rate of energy release, especially in intensive ground motions with strong forward directivity effects, demand scrutiny. Many researchers have sought to develop closed-form formulas to accurately capture and explain these coherent pulses, as well as represent the medium- to high-amplitude frequency domains of strong ground motions. These closed-form formulas have been prepared to provide mathematical expressions that can effectively model the unique features of strong near-fault ground motions. Existing approaches typically rely on parametric formulations validated primarily through root-mean-square error minimization between modeled and recorded velocity time-histories. However, this paper presents a comprehensive analytical framework that implements systematic modeling and validation steps focused on capturing the essential physical characteristics of pulse-like near-fault ground motions critical for engineering applications. Adopting a set of closed-form formulas, this study replicates the key features of six strong near-fault earthquake records, with the methodology encompassing multiple validation criteria, including energy variation and displacement time-history profiles. The analytical models successfully captured at least 95% of the cumulative kinetic energy released during each record. These models demonstrate promising results in both rate of change and peak accuracy of displacement time-histories and effectively represent the main energetic frequency content throughout the analyzed time windows.