Oscillations in the combustion chamber of solid rocket motors (SRMs) are quite common and can significantly impact the safe operation of SRMs, potentially leading to mission failure. Therefore, it is crucial to investigate the unsteady combustion mechanisms of solid propellants at the microscale. This paper focuses on Nitrate Ester Plasticized Polyether (NEPE) propellant and examines its unsteady combustion behavior under oscillatory pressure disturbances. The proposed numerical framework introduces a refined chemical kinetic model that accounts for condensed-phase pyrolysis and complex interactions in the gas phase. Compared to our previous work, this section's novelty lies in the updated condensed phase kinetic model and the revised combustion parameters for the primary flame and final diffusion flame. In the governing equations section, we solve the low-mach number incompressible ideal gas equations to address the complex laminar reactive flow in the gas phase, while the solid phase is simplified by only solving the heat conduction equation. To model the oscillation environment, a sine wave pressure oscillation is incorporated into the gas phase. In the results and discussion section, we analyze the combustion response of Al-based NEPE propellant under various amplitudes and frequencies. Additionally, we thoroughly investigate the effects of heterogeneity and pressure oscillations on transient burning rate oscillations.