Mathematical modeling and parametric study of magnetic negative stiffness dampers

Abstract

This article presents mathematical modeling and parametric study of a type of magnetic negative stiffness dampers. A magnetic negative stiffness damper uses the interaction forces and movement of magnets inside a conductive pipe to achieve inverse force–deformation response and create frequency dependent damping. One advantage of magnetic negative stiffness dampers over other conventional dampers is that they do not add stiffness to the system and hence will not increase the force in the structural members to which the magnetic negative stiffness damper is attached. Using nonlinear regression analysis, simple formulas to describe the magnetic force and electromagnetic damping of a specific type of magnetic negative stiffness dampers are derived. A parametric study is then performed to show that maximum negative stiffness is obtained when the height-to-diameter (aspect) ratio of the magnets is in the range of 0.3–0.4, and for design applications upper bound values for the clear spacing-to-radius ratio and aspect ratio of the magnets are determined to be 3 and 2, respectively. The highest value of damping coefficient is found to correspond to a magnet aspect ratio of 1.6, and for design purpose the pipe wall thickness should be set equal to the height of the magnet. Based on a pushover analysis of three frames modeled as single-degree-of-freedom systems, it is found that the frame with the magnetic negative stiffness damper experiences lower base shear at the expense of a slightly higher residual drift. The effect of base shear reduction is more pronounced when the target displacement is small.