Optimal tuned inerter negative stiffness damper design for adjacent structures

This study develops analytical solutions for optimal vibration control of adjacent structures using tuned inerter-negative-stiffness dampers (TINSD), providing closed-form expressions for TINSD parameters based on H₂-norm optimization that simultaneously address displacement, velocity and acceleration responses. The key contributions are explicit design formulas improving damping effectiveness by up to 8 times compared to conventional viscous dampers through combined inerter and negative stiffness effects, a practical parameter determination framework considering mass/frequency ratios and installation configurations, and extension to multi-modal control using multiple TINSD units to mitigate challenging higher-mode responses. Parametric studies examine key system parameter influences, while numerical validations using 20 earthquake records demonstrate effectiveness across structural configurations. The derived formulas offer practical engineering guidelines with theoretical rigor, providing direct design solutions with clear physical interpretation compared to existing numerical optimization methods. The multi-modal control strategy effectively addresses higher-mode responses where conventional methods often struggle, advancing vibration control design by combining theoretical completeness with practical applicability. These developments establish a systematic approach for adjacent structure vibration control through analytical optimization and multi-modal mitigation, demonstrating significant performance improvements while maintaining implementation feasibility for engineering practice.