An analytical study on the static vertical stiffness of wire rope isolators

The vibrations caused by earthquake ground motions or the operations of heavy machineries can affect the functionality of equipment and cause damages to the hosting structures and surrounding equipment. A Wire rope isolator (WRI), which is a type of passive isolator known to be effective in isolating shocks and vibrations, can be used for vibration isolation of lightweight structures and equipment. The primary advantage of the WRI is that it can provide isolation in all three planes and in any orientation. The load-supporting capability of the WRI is identified from the static stiffness in the loading direction. Static stiffness mainly depends on the geometrical and material properties of the WRI. This study develops an analytical model for the static stiffness in the vertical direction by using Castigliano’s second theorem. The model is validated by using the experimental results obtained from a series of monotonic loading tests. The flexural rigidity of the wire ropes required in the model is obtained from the transverse bending test. Then, the analytical model is used to conduct a parametric analysis on the effects of wire rope diameter, width, height, and number of turns (loops) on vertical stiffness. The wire rope diameter influences stiffness more than the other geometric parameters. The developed model can be accurately used for the evaluation and design of WRIs.