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1. Experimental Evaluation of the Performance of a Nonlinear Dual-Mode Vibration Isolator/Absorber System

   Bin, P. ; Harvey, Jr. ( February 2021 , Proceedings of the 2021 International Modal Analysis Conference XXXIX)

   null (Ed.)

   Floor isolation systems (FISs) are used to mitigate earthquake-induced damage to sensitive building contents and equipment. Traditionally, the isolated floor and the primary building structure (PS) are analyzed independently, assuming the PS response is uncoupled from the FIS response. Dynamic coupling may be non-negligible when nonlinearities are present under large deflections at strong disturbance levels. This study investigates a multi-functional FIS that functions primarily as an isolator (i.e., attenuating total acceleration sustained by the isolated equipment) at low-to-moderate disturbance levels, and then passively adapt under strong disturbances to function as a nonlinear (vibro-impact) dynamic vibration absorbers to protect the PS (i.e., reducing inter-story drifts). The FIS, therefore, functions as a dual-model vibration isolator/absorber system, with displacement dependent response adaptation. A scale experimental model—consisting of a three-story frame and an isolated mass—is used to demonstrate and evaluate the design methodology via shake table tests. The properties of the 3D-printed rolling pendulum (RP) bearing, the seismic gap, and the impact mechanism are optimized to achieve the desired dual-mode performance. A suite of four ground motions with varying spectral qualities are used, and their amplitudes are scaled to represent various hazards—from service level earthquake (SLE), to design basis earthquake (DBE), and even maximum considered earthquake (MCE). The performance of the multi-functional FIS is established and is described in this paper. 

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2. Design and Assessment of Innovative Dual-Mode Rolling Isolation Systems

   https://doi.org/11244/321054  

   Hadikhan Tehrani, Mohammad ( August 2019 , The University of Oklahoma Libraries)

   null (Ed.)

   Loss of operation or devastating damage to buildings and industrial structures, as well as equipment housed in them, has been observed due to earthquake-induced vibrations. A common source of operational downtime is due to the performance reduction of vital equipment, which are sensitive to the total transmitted acceleration. A well-known method of protecting such equipment is seismic isolation of the equipment itself (or a group of equipment), as opposed to the entire structure due to the lower cost of implementation. The first objective of this dissertation is assessing a rolling isolation system (RIS) based on existing design guidelines for telecommunications equipment. A discrepancy is observed between the required response spectrum (RRS) and the one and only accelerogram recommended in the guideline. Several filters are developed to generate synthetic accelerograms that are compatible with the RRS. The generated accelerograms are used for probabilistic assessment of a RIS that is acceptable per the guideline. This assessment reveals large failure probability due to displacement demands in excess of the displacement capacity of the RIS. When the displacement demands on an isolation system are in excess of its capacity, impacts result in spikes in transmitted acceleration. Therefore, the second objective of this dissertation is to design impact prevention/mitigation mechanisms. A dual-mode system is proposed where the behavior changes when the displacement exceeds a predefined threshold. A new piecewise optimal control approach is developed and applied to find the best possible mechanism for the region beyond the threshold. By utilizing the designed curves obtained from the proposed optimal control procedure, a Kelvin-Voigt device is tuned for illustrative purposes. On the other hand, the preference for protecting equipment decreases as the earthquake intensity increases. In extreme seismic loading, the response mitigation of the primary structure (i.e., life safety and collapse prevention) is of greater concern than protecting isolated equipment. Therefore, the third objective of this dissertation is to develop an innovative dual-mode system that can behave as equipment isolation under low to moderate seismic loading and passively transition to behave as a vibration absorber for the primary structure under extreme seismic loading. To reduce the computational cost of simulating a large linear elastic structure with nonlinear attachments (i.e., equipment isolation with cubic hardening nonlinearity), a reduced order modeling method is introduced that can capture the behavior of such nonlinear coupled systems. The method is applied to study the feasibility of dual-mode vibration isolation/absorber. To this end, nonlinear transmissibility curves for the roof displacement and isolated mass total acceleration are developed from the steady-state responses of dual-mode systems using the harmonic balanced method. The final objective of this dissertation is to extend the reduced order modeling method developed for linear elastic structure with nonlinear attachment to inelastic structures (without attachments). The new inelastic model condensation (IMC) method uses the modal properties of the full structural model (in the elastic range) to construct a linear reduced order model in conjunction with a hysteresis model to capture the hysteretic inter-story restoring forces. The parameters of these hysteretic forces are easily tuned, in order to fit the inelastic behavior of the condensed structure to that of the full model under a variety of simple loading scenarios. The fidelity of structural models condensed in this way is demonstrated via simulation for different ground motion intensities on three different building structures with various heights. The simplicity, accuracy, and efficiency of this approach could significantly alleviate the computational burden of performance-based earthquake engineering. 

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3. Rolling-Type Isolation: An Experimental Characterization and Numerical Parametric Study

   https://doi.org/11244/53085  

   Casey, Corey ( December 2017 , The University of Oklahoma Libraries)

   null (Ed.)

   Building contents and nonstructural components are known to be vulnerable during seismic events. Of particular concern is computer and network equipment that is critical in the post-earthquake recovery process. A solution for mitigating the seismic hazard to such systems is rolling-type isolation systems (RISs), but the characterization of RISs with realistic loading conditions and system setups is not well documented. An experimental parametric case study was performed varying the mass eccentricity, the number of cabinets, and the damping to simulate in-service conditions. A series of free response tests was performed using an abrupt shake table displacement (pulse) along with forced response tests utilizing the VERTEQ-II Zone-4 waveform. An array or string potentiometers and accelerometers measured the longitudinal, transverse, and rotational responses of the systems. Supplementally damped systems were found to have increased rotations when a mass eccentricity was present. The increase in system size and mass reduced the overall rotations due to an increased restoring moment arm and higher mass moment of inertia. Increased damping decreased the displacement demand on the isolator but increased the overall accelerations slightly. However, the systems without the supplemental damping had such large displacements that impacts were experienced causing excessively high accelerations. Durability was an issue for lightly damped systems due to increased contact stress between the ball and concave rolling surface. A physics-based mathematical model was developed for the prediction of the response of multi-unit RIS arrays with mass eccentricity. The model was first calibrated to the experimental free response tests and then validated with the forced response tests. The validated model was then used to perform a numerical parametric case study. Configurations with one, two, four and eight cabinets were modeled, and the eccentricity was varied. The VERTEQ-II waveform was applied in both the front-to-back and side-to-side directions under varying ground motion scaling. Impacts are predicted at lower ground motion scaling with larger mass eccentricity due to the initiation of rotations. The ground motion scaling for which impacts occur is increased due to the systems higher resistance to rotations from increased number of isolated cabinets. Finally, capacity design curves for the impact point were determined, which can be used to establish the required configuration (number of cabinets and eccentricity) for a given ground motion intensity. 

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4. Friction-induced instability and vibration in a precision motion stage with a friction isolator

   https://doi.org/10.1177/1077546321999510  

   Wang, Jiamin ; Dong, Xin ; Barry, Oumar R ; Okwudire, Chinedum ( March 2021 , Journal of Vibration and Control)

   null (Ed.)

   Motion stages are widely used for precision positioning in manufacturing and metrology applications. However, they suffer from nonlinear premotion (i.e. “static”) friction, which adversely affects their speed and motion precision. In this article, a friction isolator is used as a simple and robust solution to mitigate the undesirable effects of premotion friction in precision motion stages. For the first time, a theoretical study is carried out to understand the dynamic phenomena associated with using a friction isolator on a motion stage. Theoretical analysis and numerical simulation are conducted to examine the dynamical effects of friction isolator on a proportional–integral–derivative-controlled motion stage under LuGre friction dynamics. The influence of friction isolator on the response and stability of the system is examined through theoretical and numerical analyses. Parametric analysis is also carried out to study the effects of friction isolator and friction parameters on the eigenvalue and stability characteristics. The numerical results validate the theoretical findings and demonstrate several other interesting nonlinear phenomena associated with the introduction of friction isolator. This motivates deeper nonlinear dynamical analyses of friction isolator for precision motion control. 

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5. A Statistical Hypothesis Testing Strategy for Adaptively Blending Particle Filters and Ensemble Kalman Filters for Data Assimilation

   https://doi.org/10.1175/MWR-D-22-0108.1  

   Kurosawa, Kenta ; Poterjoy, Jonathan ( January 2023 , Monthly Weather Review)

   Abstract Particle filters avoid parametric estimates for Bayesian posterior densities, which alleviates Gaussian assumptions in nonlinear regimes. These methods, however, are more sensitive to sampling errors than Gaussian-based techniques such as ensemble Kalman filters. A recent study by the authors introduced an iterative strategy for particle filters that match posterior moments—where iterations improve the filter’s ability to draw samples from non-Gaussian posterior densities. The iterations follow from a factorization of particle weights, providing a natural framework for combining particle filters with alternative filters to mitigate the impact of sampling errors. The current study introduces a novel approach to forming an adaptive hybrid data assimilation methodology, exploiting the theoretical strengths of nonparametric and parametric filters. At each data assimilation cycle, the iterative particle filter performs a sequence of updates while the prior sample distribution is non-Gaussian, then an ensemble Kalman filter provides the final adjustment when Gaussian distributions for marginal quantities are detected. The method employs the Shapiro–Wilk test to determine when to make the transition between filter algorithms, which has outstanding power for detecting departures from normality. Experiments using low-dimensional models demonstrate that the approach has a significant value, especially for nonhomogeneous observation networks and unknown model process errors. Moreover, hybrid factors are extended to consider marginals of more than one collocated variables using a test for multivariate normality. Findings from this study motivate the use of the proposed method for geophysical problems characterized by diverse observation networks and various dynamic instabilities, such as numerical weather prediction models. Significance Statement Data assimilation statistically processes observation errors and model forecast errors to provide optimal initial conditions for the forecast, playing a critical role in numerical weather forecasting. The ensemble Kalman filter, which has been widely adopted and developed in many operational centers, assumes Gaussianity of the prior distribution and solves a linear system of equations, leading to bias in strong nonlinear regimes. On the other hand, particle filters avoid many of those assumptions but are sensitive to sampling errors and are computationally expensive. We propose an adaptive hybrid strategy that combines their advantages and minimizes the disadvantages of the two methods. The hybrid particle filter–ensemble Kalman filter is achieved with the Shapiro–Wilk test to detect the Gaussianity of the ensemble members and determine the timing of the transition between these filter updates. Demonstrations in this study show that the proposed method is advantageous when observations are heterogeneous and when the model has an unknown bias. Furthermore, by extending the statistical hypothesis test to the test for multivariate normality, we consider marginals of more than one collocated variable. These results encourage further testing for real geophysical problems characterized by various dynamic instabilities, such as real numerical weather prediction models. 

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