Unveiling advanced modelling and analysis: the integrated system and formula for mass-spring-damper with hydraulic damper systems

In the midst of escalating seismic activity on a global scale, the imperative of devising ingenious structural solutions looms large, driven by the necessity to safeguard the security and soundness of constructed environments. This study delves into an inventive avenue for bolstering seismic resilience, by ingeniously merging hydraulic dampers (HD) into mass-spring-damper (MSD) systems through a configuration referred to as the integrated damper arrangement. This integration unfolds through the strategic placement of an HD at the centre of the spring of MSD system, optimizing the system's parameters via the dynamic optimizer Particle Swarm Optimization (PSO) method, emulating the PSO-derived output using MATLAB simulations and for best-of-best results assisted by Artificial neural network (ANN). In structure, building integrated systems work to protect the moments of tuned mass damper (TMD) system in their position and control the structural vibration to absorb the decapitated energy for proving stability. The central thrust of this research paper orbits around the ratio of both the systems that are combined and intricately integrated with their relevant parameters. This convergence of efforts culminates by ANN in peak displacement values of 0.7930 m and peak velocity reaching 1.7615 m per second. This study also establishes a seamlessly integrated system and a meticulously crafted analytical formula to govern this combined system, merging the worlds of structure and mechanics with precision in their application.