The fusion cross sections and barrier distributions of stable Zr isotope targets 90,92,94,96Zr with 30Si projectile nuclei are investigated theoretically via the Energy-dependent Woods-Saxon Potential (EDWSP) and Coupled Channel (CC) models. In our calculations, we have taken the bombarding energy range of the projectile-target interaction to be around the Coulomb barrier for all reactions. All theoretical accounts have been worked via the NRV Knowledge Base, the CCFULL code, and Wong's formula. We detailed interrogated the repercussions of phonon number in projectile and target nuclei on heavy-ion fusion cross sections and barrier distributions. Over this investigation, we presented that the EDWSP and CC models, and all computation bases operated to elucidate the fusion cross-section data and barrier distributions are decent. Our theoretical investigation proves the importance of inspecting heavy-ion fusion reactions with theory-based research and encourages new experimental investigations that are not yet included in the literature.