skip to main content


The NSF Public Access Repository (NSF-PAR) system and access will be unavailable from 10:00 PM ET on Friday, December 8 until 2:00 AM ET on Saturday, December 9 due to maintenance. We apologize for the inconvenience.

Title: Designing and Characterizing Negative Stiffness Devices for Apparent Weakening and Vertical Isolation
Nonlinear systems leveraging the effects of negative stiffness can exhibit beneficial qualities for passive seismic mitigation in structures. Such systems can be achieved by placing nonlinear devices displaying negative stiffness in parallel with linear positive stiffness systems such as a structure or spring. This thesis presents research into two such systems: (i) a device which causes apparent weakening in a structure subjected to horizontal ground motions and (ii) an isolation system to protect building contents from vertical seismic effects. Apparent weakening is the softening of a structure’s apparent stiffness by adding negative stiffness to the overall system via negative stiffness devices. Apparent weakening is an elastic effect that has the benefit of reducing the peak accelerations and base shears induced in a structure due to a seismic event without reducing the main structural strength. The smooth negative stiffness device (SNSD) presented in this thesis consists of cables, pulleys, and extension springs. A nonlinear mathematical model of the load-deflection behavior of the SNSD was developed and used to determine the optimal geometry for such a device. A prototype device was designed and fabricated for installation in a bench-scale experimental structure, which was characterized through static and dynamic tests. A numerical study was also conducted on two other SNSD configurations designed to achieve different load-deflection relations for use in an inelastic model building subject to a suite of historic and synthetic ground motions. In both the experimental prototype and the numerical study, the SNSDs successfully produced apparent weakening, effectively reducing accelerations and base shears of the structures. The buckled-strut vertical isolation system (BSVIS) presented in this thesis combines the non-linear behavior of a laterally-loaded buckled strut with a linear spring. The lateral load-deflection relation for a buckled strut, which is nonlinear and displays negative stiffness, was investigated for various conditions to two- and three-term approximations of the deflected shape of a strut. This relation and the linear positive effect of a spring were superimposed to give the load-deflection relation of a BSVIS. An experimental prototype was fabricated and subjected to static tests. These tests confirmed the validity of the model and the effectiveness of adding a spring in parallel with a buckled strut to achieve isolation-level stiffness. Based on the theoretical and experimental findings, a design guide is proposed for the engineering of a BSVIS to protect a payload from vertical seismic content.  more » « less
Award ID(s):
Author(s) / Creator(s):
Date Published:
Journal Name:
The University of Oklahoma Libraries
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Seismic isolation systems for buildings are generally selected to achieve higher seismic performance objectives, such as continued operation or immediate occupancy following a design earthquake event. However, recent large scale tests have suggested that these objectives may be compromised if the shaking includes large vertical acceleration components that are damaging to the nonstructural components and contents. Some research has been conducted to develop three dimensional isolation systems that can isolate the structure from both the horizontal and vertical components of ground motion. In several cases, systems have been proposed without much justification of the target design parameters. Rocking has been noted as a potential concern for structures with 3D isolation systems, and complex systems have been proposed to control the rocking. In this study, the fundamental dynamic response of structures with 3D isolation systems is explored. Target horizontal and vertical spectra for a representative strong motion site were developed based on NEHRP recommendations, and horizontal and vertical ground motions were selected that best fit the target spectra when the same amplitude scale factor was applied to all three motion components. Using a simple model of a rigid block resting on linear isolation bearings, the following aspects are evaluated for a wide range of horizontal and vertical isolation periods: response modes and severity of rocking, horizontal and vertical displacement demands in the isolation bearings, and attenuation of both horizontal and vertical accelerations in the structure relative to the ground acceleration. Preliminary results point to a number of useful observations. For example, rocking appears to be an issue only if the horizontal and vertical isolation periods are closely spaced. Helical spring isolation systems that have been applied to a few structures have this characteristic. However, if the horizontal isolation period is large relative to the vertical isolation period, troublesome rocking can be avoided. In addition, other researchers have proposed systems with vertical isolation periods on the order of 2 seconds, which require large displacement and damping capacity. However, preliminary results suggest that vertical isolation periods as low as 0.5 seconds will be effective in attenuating the vertical acceleration. Limiting the vertical isolation period will make design of a 3D isolation system more feasible with respect to vertical displacement capacity and avoiding rocking. 
    more » « less
  2. null (Ed.)
    This research presents an experimental program executed to understand the strength and stiffness properties of hollow built-up glass compression members that are intended for use in the modular construction of all glass, compression-dominant, shell-type structures. The proposed compression-dominant geometric form has been developed using the methods of form finding and three-dimensional graphical statics. This research takes the first steps towards a new construction methodology for glass structures where individual hollow glass units (HGU) are assembled using an interlocking system to form large, compression-dominant, shell-type structures, thereby exploiting the high compression strength of glass. In this study, an individual HGU has an elongated hexagonal prism shape and consists of two deck plates, two long side plates, and four short side plates, as is shown in Figure 1. Connections between glass plates are made using a two-sided transparent structural adhesive tape. The test matrix includes four HGUs, two each fabricated with 1 mm and 2 mm thick adhesive tape. All samples are dimensioned 64 cm on the long axis of symmetry, 51 cm on the short axis of symmetry, and are 10 cm in width. Glass plates are all 10 mm thick annealed float glass with geometric fabrication done using 5-axis abrasive water jet cutting. HGU assembly is accomplished using 3D printed truing clips and results in a rigid three-dimensional glass frame. Testing was done with the HGU oriented such that load was introduced on the short side edges of the two deck plates, resulting in an asymmetric load-support condition. A soft interface material was used between the HGU and steel plates of the hydraulic actuator and support for the purpose of avoiding premature cracking from local stress concentrations on the glass edges at the load and support locations. Force was applied in displacement control at 0.25 mm/minute with a full array of displacement and strain sensors. Test results for load vs. center deck plate transverse deflection are shown in Figure 2. All samples failed explosively by flexural buckling with no premature cracking on the load and support edges of the deck plates. Strain and deformation data clearly show the presence of second-order behavior resulting from bending deformation perpendicular to the plane of the deck plates. In general, linear axial behavior transitions to nonlinear second-order behavior, with increasing rates in deflection and strain growth, ultimately ending in glass fracture on the tension surfaces of the buckled deck plates. The failure resulted in near-complete disintegration of the deck plates, but with no observable cracking in any side plates and a secure connection on all adhesive tape. Results of the experimental program clearly demonstrate the feasibility of using HGUs for modular construction of compression dominant all-glass shell-type structures. This method of construction can significantly reduce the self-weight of the structure, and it will inspire the use of sustainable materials in the construction of efficient structures. 
    more » « less
  3. Elastic actuation can improve human-robot interaction and energy efficiency for wearable robots. Previous work showed that the energy consumption of series elastic actuators can be a convex function of the series spring compliance. This function is useful to optimally select the series spring compliance that reduces the motor energy consumption. However, series springs have limited influence on the motor torque, which is a major source of the energy losses due to the associated Joule heating. Springs in parallel to the motor can significantly modify the motor torque and therefore reduce Joule heating, but it is unknown how to design springs that globally minimize energy consumption for a given motion of the load. In this work, we introduce the stiffness design of linear and nonlinear parallel elastic actuators via convex optimization. We show that the energy consumption of parallel elastic actuators is a convex function of the spring stiffness and compare the energy savings with that of optimal series elastic actuators. We analyze robustness of the solution in simulation by adding uncertainty of 20% of the RMS load kinematics and kinetics for the ankle, knee, and hip movements for level-ground human walking. When the winding Joule heating losses are dominant with respect to the viscous losses, our optimal PEA designs outperform SEA designs by further reducing the motor energy consumption up to 63%. Comparing to the linear PEA designs, our nonlinear PEA designs further reduced the motor energy consumption up to 31%. From our convex formulation, our global optimal nonlinear parallel elastic actuator designs give two different elongation-torque curves for positive and negative elongation, suggesting a clutching mechanism for the final implementation. In addition, the different torque-elongation profiles for positive and negative elongation for nonlinear parallel elastic actuators can cause sensitivity of the energy consumption to changes in the nominal load trajectory. 
    more » « less
  4. This study presents a comprehensive design methodology for a magnetorheological-based damper device for a three-dimensional building isolation. The device acts as a suspension system itself by combining the liquid stiffness and controllable magnetorheological damping features in one unit. The bi-linear liquid stiffness feature enhances resistance to global rocking/overturning of the structural system by increasing the stiffness in the rebound mode compared to the compression mode. In the field, the system is combined with the conventional elastomeric bearings widely employed to mitigate the lateral seismic motions. During a seismic event, the system is subjected to dynamic vertical shaking and large lateral forces. The theoretical and simulation modeling to overcome this major challenge and achieve other system requirements are presented. In addition, a comprehensive optimization program is developed to achieve all design requirements. The modeling procedure is verified with experimental results. Also, the effectiveness of Displacement/Velocity-based control for a single degree-of-freedom system subjected to sinusoidal loading is evaluated. 
    more » « less
  5. Modern seismic resistant design has been focusing on development of cost effective structural systems which experience minimal damage during an earthquake. Unbonded post-tensioned precast concrete walls provide a suitable solution due to their self-centering behavior and their ability to undergo large nonlinear deformation with minimal damage. Several experimental and analytical investigation focusing on lateral load resisting behavior of unbonded post-tensioned precast walls has been carried out in the past two decades. These investigations have primarily focused on lateral load resistance, self-centering capacity, energy dissipation and extent of damage in confined concrete region of the wall system. Past experimental results have shown that self-centering capacity of the wall system decreases at higher lateral drifts. Particularly, rocking walls with higher energy dissipation capacity, sustain considerable residual displacement. This residual displacement in the wall system may affect the ability of the entire structure to re-center. Though increasing initial prestressing force helps in reducing residual drift, it also subjects concrete to increased axial compressive stress which may lead to premature strength degradation of confined concrete in rocking corners. Accurate prediction of expected concrete strains in confined regions during increasing drift cycle is critical in design of such wall systems. Simplified design procedures available in literature assume different values for plastic hinge length to estimate critical concrete strain values. The results from the experimental tests available in literature were analyzed, to understand the effects of energy dissipating elements on residual drift and to examine the accuracy of simplified design procedures in predicting critical concrete strain. Based on the findings, recommendations are made on design of energy dissipating elements and plastic hinge length for unbonded post-tensioned precast rocking walls. 
    more » « less