The rapid evolution of Unmanned Aerial Vehicles (UAVs) in modern asymmetric conflict environments has driven the automation of heavy machine guns (HMGs) for low-cost, high-precision kinetic interception. However, converting legacy systems such as the DShK 12.7 mm into automated platforms remains challenging due to high-frequency recoil impulses that excite structural modes of mounting platforms, leading to severe muzzle dispersion. This work proposes a computational mechanics framework that formally decouples the internal ballistic system from external mounting dynamics through an equivalent reduced-order dynamic representation. The mounting platform is modeled as a stochastic boundary condition with uncertain dynamic stiffness and modal properties, allowing the weapon to be treated as an independent second-order oscillatory system. A longitudinal sliding mechanism with spring–damper characteristics optimized via frequency-domain transmissibility minimization converts peak recoil impulses into controlled kinetic and potential energy. A frequency-domain analysis of the transmissibility ratio (TR) is used as the primary design criterion, targeting an operational frequency ratio (r) between 2.0 and 3.0, to ensure operation within the isolation zone (TR < 1). By replacing rigid reinforcement with dynamic isolation, transmitted forces are rendered slow-varying, preventing excitation of platform natural modes. The proposed framework is fully computational, platform-independent, and generalizable across recoil-dominated automatic weapon systems and diverse mounting structures.