Abstract <p>A new vibration damping device is proposed, designed as a band-rope system with a single-acting hydraulic cylinder or a torsion bar. The device is a vibration damper and can be used on domes, rectangular frames, locators, and other infrastructure exposed to dynamic loads from seismic impacts. The methods of determining the modules of external force impacts on the protected nodes through a band-rope system are described to select the parameters of the dampers and generate internal forces to counteract vibratory motion for a torsion damper and a single-acting hydraulic cylinder damper. The formulas derived by analytical calculations make it possible to determine the effective torsion stiffness of the torsion bar and stiffness of the hydraulic cylinder spring or coefficient of resistance to the motion of the hydraulic cylinder fluid.</p>