Effect of magnetic negative stiffness damper on the seismic response of single-degree-of-freedom systems

Date of Award

June 2019

Degree Type


Degree Name

Doctor of Philosophy (PhD)


Civil and Environmental Engineering


Eric M. Lui


dynamic analysis under harmonic excitation, elastic seismic reposne analysis, inelastic seismic response analysis, magnetic negative stiffness damper, nonlinear static analysis, response spectra

Subject Categories



This dissertation focuses on the mathematical modeling of magnetic negative stiffness damper (MNSD) and the numerical evaluation of the dynamic response and seismic performance of single-degree-of-freedom (SDF) systems equipped with such a damper. MNSD is a special type of damper that uses the interaction forces and movement of magnets placed inside a conductive pipe to achieve inverse force-deformation response and create frequency dependent damping. By using MNSD, the demerit of most conventional dampers that tend to add stiffness to the system and hence increasing the force induced in the structural members to which the dampers are attached can be eliminated. If neodymium magnets are used, the device is very stable and durable since this type of permanent magnets are very resistant to demagnetization by external magnetic fields, and when operating under a temperature of 150C will not lose its magnetic strength for decades. By introducing negative stiffness while providing damping, good control of structural vibration can be achieved.

The basic elements of a MNSD consists of three permanent magnets housed in a cylindrical non-ferromagnetic conductive pipe (e.g. copper). Two of the magnets that are placed at the ends of the pipe are fixed in position while the third magnet in the middle can move. The negative stiffness effect is generated by magnetic interaction forces developed between the middle moving magnet and the two fixed magnets. Damping is created by eddy current when the moving middle magnet interacts with the conductive pipe.

To facilitate dynamic and seismic analyses of systems equipped with MNSD, a relatively simple mathematical model is proposed. This model incorporates all pertinent parameters that affects the response of MNSD such as magnet size and aspect ratio, magnetic field intensity, separation distance between the magnets, and wall thickness of the conductive pipe in the analysis. A study of these parameters show that higher magnetic interaction forces and negative stiffness can be obtained by increasing the magnet size or reducing the spacing between the moving and stationary magnets. Furthermore, for a given magnet an optimal height to diameter ratio of 1.6 is established.

By studying the responses of SDF systems equipped with either MNSD or viscous damper (VD) under a harmonic excitation, it can be shown that MNSD often outperforms VD on energy dissipation under low-frequency excitations, and on transmissibility under high-frequency excitations. In addition, the results obtained from a nonlinear static (push-over) analysis have shown that the peak forces of the hysteresis loops are lower for the MNSD system.

When SDF systems with MNSD are subjected to earthquake excitations, it is observed from the elastic response spectra that in the intermediate-period range (the so-called velocity sensitive region) of the spectral space, the response quantities are the most sensitive to damping, whereas the responses in short-period and long-period regions are essentially determined by the individual ground motion. Using a suite of 20 ground motion records, the mean and mean+1 elastic design spectra with different damping ratios are developed. These spectra can be used for the design of elastic MNSD systems.

By assuming an elastoplastic force-deformation relationship, inelastic response spectra of SDF MNSD systems are generated and the effect of yielding on ductility demand and peak deformation is studied. While the peak deformations of SDF systems equipped with MNSD or VD are comparable, the residual displacements experienced by systems with MNSD are generally smaller. Through the application of a yield strength reduction factor Ry, expressed as a function of system ductility μ, to the elastic design spectra, constant ductility inelastic design spectra are developed. These spectra can be used for the design of inelastic MNSD systems.

When the behavior of a wind turbine equipped with a tuned mass damper, a tuned liquid damper or a MNSD and modeled as an SDF system is compared, MNSD is shown to be the most effective in subduing wind induced vibration. A design example of a wind turbine equipped with MNSD that follows the guidelines provided in ASCE/SEI 7-16 (2016), ANSI/AISC 360-16 (2016) and IBC 2012 (2012) is then given.


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