Joshua A. Schultz

Lateral-Mode Vibration of Microcantilever-Based Sensors in Viscous Fluids Using Timoshenko Beam Theory

To more accurately model microcantilever resonant behavior in liquids and to improve lateral-mode sensor performance, a new model is developed to incorporate viscous fluid effects and Timoshenko beam effects (shear deformation, rotatory inertia). The model is motivated by studies showing that the most promising geometries for lateral-mode sensing are those for which Timoshenko effects are most pronounced. Analytical solutions for beam response due to harmonic tip force and electrothermal loadings are expressed in terms of total and bending displacements, which correspond to laser and piezoresistive readouts, respectively. The influence of shear deformation, rotatory inertia, fluid properties, and actuation/detection schemes on resonant frequencies (fres) and quality factors (Q) are examined, showing that Timoshenko beam effects may reduce fres and Q by up to 40% and 23%, respectively, but are negligible for width-tolength ratios of 1/10 and lower. Comparisons with measurements (in water) indicate that the model predicts the qualitative data trends, but underestimates the softening that occurs in stiffer specimens, indicating that support deformation becomes a factor. For thinner specimens, the model estimates Q quite well, but exceeds the observed values for thicker specimens, showing that the Stokes resistance model employed should be extended to include pressure effects for these geometries.

Timoshenko Beam Model for Lateral Vibration of Liquid-Phase Microcantilever-Based Sensors

Dynamic-mode microcantilever-based devices are potentially well suited to biological and chemical sensing applications. However, when these applications involve liquid-phase detection, fluid-induced dissipative forces can significantly impair device performance. Recent experimental and analytical research has shown that higher in-fluid quality factors (Q) are achieved by exciting microcantilevers in the lateral flexural mode. However, experimental results show that, for microcantilevers having larger width-to-length ratios, the behaviors predicted by current analytical models differ from measurements. To more accurately model microcantilever resonant behavior in viscous fluids and to improve understanding of lateral-mode sensor performance, a new analytical model is developed, incorporating both viscous fluid effects and “Timoshenko beam” effects (shear deformation and rotatory inertia). Beam response is examined for two harmonic load types that simulate current actuation methods: tip force and support rotation. Results are expressed in terms of total beam displacement and beam displacement due solely to bending deformation, which correspond to current detection methods used with microcantilever-based devices (optical and piezoresistive detection, respectively). The influences of the shear, rotatory inertia, and fluid parameters, as well as the load/detection scheme, are investigated. Results indicate that load/detection type can impact the measured resonant characteristics and, thus, sensor performance, especially at larger values of fluid resistance.

Harvesting of Ambient Floor Vibration Energy Utilizing Micro-Electrical Mechanical Devices

Recent advances in device fabrication and energy harvesting technology combined with an increasing need for sustainable energy generation have encouraged the development of the micro-electro-mechanical (MEMS) energy harvesting model for floor vibrations presented herein. By calibrating arrays of MEMS energy harvesters in resonance with floor vibrations, building occupants become sustainable energy sources. Optimization of these harvesters to frequency ranges of floor vibrations, subsequent synchronization of harvester location to occupant flow and improved electromechanical modeling may result in an efficient, passive power source for low-demand applications independent of external environmental conditions. A model of a floor-harvester system is developed, utilizing ambient floor vibration to excite MEMS energy harvesters via harmonic base translation. These devices then convert the mechanical vibrations to electrical power. Design considerations for piezoelectric-based energy harvesters inspired by MEMS-scale arrays are investigated. Single degree of freedom and distributed beam parameter electromechanical models are employed to predict performance, by optimization of resonant frequencies from measured low-level ambient vibrations. A simplified analytical expression for a frequency correction factor accounting for shear deformation and rotatory inertia effects is derived in terms of fundamental system parameters. Floor and energy harvesting device models are validated by comparison to experimental results and numerical modeling, respectively.

Experimental Investigation of Numerical Design Method for Point-Supported Glass

AbstractCalculating stresses in structural glass components is essential for design, but is especially complex for customized components like point-supported glass (PSG) balustrades. Stress concentrations are introduced at the discontinuities of the plates precisely where boundary conditions elicit maximum field stresses. Further complicating design, most published stress data for glass components are based on annealed, edge-supported glass experiments—with limited applicability to fully tempered (FT), PSG applications. This article presents experimental and numerical results for a typical application of FT glass as a PSG structural balustrade. Strain data from six FT, monolithic glass balusters loaded to both service and ultimate conditions indicates 55.2-MPa stresses at service load and 155-MPa stresses at failure. Additionally, a design algorithm is developed, using beam theory with stress concentration factors to establish preliminary thickness for use in an optimized numerical analysis to calculate s...

Parametric Studies of Point-Supported Laminated Glass for Simplified Design

To accurately determine the stresses, the design engineer typically relies on detailed finite element analysis (FEA). While the associated computational cost is often acceptable for complex geometries or atypical applications, it is often desirable to reduce dependence on FEA wherever possible. There exists in the literature some closed-form analytical solutions for glass composites (beams or plates), but these are typically limited to edge supported conditions and are often intractable for design purposes. As a result, it is desirable to obtain simplified methods for design of some of the most commonly encountered geometries, loads and materials for point-supported structural glass through numerical parametric studies. This research is two-fold in that it provides detailed parametric studies of point-supported laminated glass and compares the results to analytical and experimental results. First, existing specifications for design are evaluated to be used as a baseline for subsequent FEA but are found to give stress results that vary by up to 44%. Parametric studies of point-supported, fully-tempered, laminated glass specimens are performed for various thickness, number and location of point supports, panel geometry and loading. The results of the parametric studies are found to be within 2% of experimental results. The disparity between industry specified geometry and acceptable stresses prompts further research into development of reliable hand-calculations.

Timber Tower Research: Concrete Jointed Timber Frame

Tall buildings pose a challenge to the sustainability movement because they offer both positive and negative environmental impacts. Positive impacts include reducing urban sprawl, promoting alternative transportation, and allowing efficient energy use on a district scale. However, these benefits come with the cost of greater carbon emissions associated with both material production and building construction compared to a low-rise building. The goal of this research was to develop a structural system for tall buildings using mass-timber as the main structural material that reduces the carbon dioxide emissions associated with the structure. The structural system research was applied to a prototypical building based on an existing concrete benchmark for comparison. The selected concrete benchmark building is the Dewitt-Chestnut Apartments; a 120m tall, 42-story building in Chicago designed by Skidmore Owings and Merrill and built in 1966. This building was chosen as the benchmark because the geometry is a rectangular extrusion, the lease depths are consistent with contemporary residential buildings, and the concrete structural system is efficient in material usage providing a lower bound for comparison with the prototypical building. This paper discusses key design issues associated with tall mass-timber buildings along with potential solutions. Specific challenges include low structural weight and associated net uplift due to lateral loads, long term differential shortening, floor vibrations, and fire performance. It is believed that the system proposed in the research and discussed in the paper could mitigate many of these design issues. The proposed system, the “Concrete Jointed Timber Frame”, relies primarily on solid mass-timber for the main structural elements such as the floor panels, shear walls, and columns. The main structural mass-timber elements are connected by steel reinforcing through cast-in-place concrete at the connection joints. This system plays to the strengths of both materials and allows the designer to apply sound tall building engineering fundamentals. The result is believed to be an efficient structure that could compete with reinforced concrete and structural steel while reducing the associated carbon emissions by 60 to 75%.

Numerical Modeling of Steel-Framed Floors for Energy Harvesting Applications

Pedestrian movement on lightweight steel-framed floor systems can excite several vibration modes in the frequency range from 0 to 30 Hz. Although structural engineers are able to design floor systems that minimize annoying vibrations due to human activities, the frequency modes may be targeted for secondary applications such as low-demand energy harvesting. The techniques of modal analysis are useful in determining the parameters of these floor systems, with the goal of targeting resonant frequency modes for energy harvesting.

Response of Meso-Scale Energy Harvesters Coupled with Dynamic Floor Systems

Conversion of ambient vibrations to electrical power (energy scavenging, energy harvesting etc.) is an increasingly popular research area. However, many of these applications are focused at either the micro- (e.g., biosensors, wireless monitoring) or macro-scale (e.g., viscous dampers for buildings). This research focuses on a meso-scale application of energy harvesting of floor vibrations by numerical investigation and experimental validation of dynamic response of coupled linear floor-harvester systems. A refined methodology for numerical modeling of floor vibrations has been developed and validated against experimental tests of a composite steel-framed floor. The dynamic response of the floor is presented as a baseline for modeling of coupled harvester-floor systems. Using this baseline, the dynamic response of the coupled floor system is investigated for a range of design parameters and optimized for a mass/stiffness of 2.00%/5N combination resulting in acceleration exceedance of 0.1g for 31.7% of the total peaks. The optimization, limitations, and extensions of the numerical model and a modeling protocol is discussed as well as future work.

Evaluation of North American Vibration Standards for Mass-Timber Floors

Mass-timber is an emerging building technology created by using structural adhesives to laminate layers of dimensional lumber together to create large ‘timber’ panels. These panels can be used as structural building elements in floors and walls. However, due to relatively large stiffness-to-mass ratios and low inherent damping, optimized timber floors can be vibration controlled even at spans of 3 m. There are several current North American vibration standards that can be applied to timber floors. The goal of this research is twofold: (1) investigate floor performance under various North American vibration criteria for various boundary conditions and (2) address general methods of optimizing floor performance. The impact of support compliance for CLT floors is presented in span-to-depth and span-to-frequency charts intended to assist practitioners with preliminary floor design. The results indicate that existing evaluation methods provide wide-ranging and sometimes conflicting results. However, for all criteria surveyed, it is shown that increasing rotational restraint results in up to 35% thinner floor panels.