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Matilda Equiluz
Dynamic-mode cantilever sensors are based on the principle of a one-side clamped beam being excited to oscillate at or close to its resonance frequency. An external interaction on the cantilever alters its oscillatory state, and this change can be detected and used for quantification of the external influence (e.g. a force or mass load). A very promising approach to significantly improve sensitivity without modifying the established laser-based oscillation transduction is the co-resonant coupling of a micro- and a nanocantilever. Thereby, each resonator is optimized for a specific purpose, i.e. the microcantilever for reliable oscillation detection and the nanocantilever for highest sensitivity through low rigidity and mass. To achieve the co-resonant state, the eigenfrequencies of micro- and nanocantilever need to be adjusted so that they differ by less than approximately 20%. This can either be realized by mass deposition or trimming of the nanocantilever, or by choice of dimensions. While the former is a manual and error-prone process, the latter would enable reproducible batch fabrication of coupled systems with predefined eigenfrequency matching states and therefore sensor properties. However, the approach is very challenging as it requires a precisely controlled fabrication process. Here, for the first time, such a process for batch fabrication of inherently geometrically eigenfrequency matched co-resonant cantilever structures is presented and characterized. It is based on conventional microfabrication techniques and the structures are made from 1 m thick low-stress silicon nitride. They comprise the microcantilever and high aspect ratio nanocantilever (width 2 m, thickness about 100 nm, lengths up to 80 m) which are successfully realized with only minimal bending. An average yield of \gt 80% of intact complete sensor structures per wafer is achieved. Desired geometric dimensions can be realized within 1% variation for length and width of the microcantilever and nanocantilever length, 10% and 20% for the nanocantilever width and thickness, respectively, resulting in an average variation of its eigenfrequency by 11%. Furthermore, the dynamic oscillation properties are verified by vibration experiments in a scanning electron microscope. The developed process allows for the first time the batch fabrication of co-resonantly coupled systems with predefined properties and controlled matching states. This is an important step and crucial foundation for a broader applicability of the co-resonant approach for sensitivity enhancement of dynamic-mode cantilever sensors.
Engineering seismology is a fusion of the scientific study of earthquakes (aka, seismology) and earthquake engineering. Although both disciplines focus on earthquakes, their fundamental approach is quite different. Seismologists usually train in Earth Science departments, while earthquake engineers train in schools of engineering. Although many of the physical laws used by these disciplines are the same, schools of engineering are typically distinct from science departments. Seismologists publish their research in different journals (e.g., Bulletin of the Seismological Society of America, or various journals of the American Geophysical Union) than earthquake engineers do (e.g., journals published by the American Society of Civil Engineers, or journals of the Earthquake Engineering Research Institute). More importantly, mistakes in earthquake engineering can have tragic consequences, while mistakes in seismology are viewed as opportunities for new understanding; earthquake engineers buy liability insurance and seismologists just change their minds.
My undergraduate training was in physics (Indiana Univ.) and my graduate training was in seismology (Caltech). My undergrad training in physics did not include continuum mechanics, a theory that is required to understand the fundamentals of seismology. Fortunately, Caltech had an exceptionally good group of continuum mechanicians who were part of the Division of Engineering and Applied Sciences. Caltech has a long-standing policy of encouraging inter-disciplinary collaboration. The insights that I learned from mentors in the engineering division profoundly changed the course of my research career.
I spent the first half of my career doing research in Seismology, but things changed in 1995 when Caltech appointed me to be a Professor of Engineering Seismology with a joint appointment in Civil Engineering and also in Geophysics. Suddenly, I was teaching engineering classes and attending Engineering professional meetings (new vocabulary and new colleagues). More importantly, I could clearly see fundamental inconsistencies between what engineers and seismologists thought that they knew about earthquakes.
I collected information from both disciplines to teach an engineering seismology class that was listed in both Geophysics and Civil Engineering (CE/Ge 181). Since there was no appropriate textbook, I developed a set of class notes. While many of the subjects can be found in other textbooks, there are also many subjects that my graduate students and I developed through years of research. In particular, Chapters 6, 7, and 8 contain important unpublished material about the physics of buildings and earthquakes. When I thought about the challenges of publishing this material in a peer-reviewed journal, I decided that it would be more practical to describe my thoughts in these class notes. I continued to add to and refine these notes for 25 years.
Although smaller earthquakes are far more numerous, large earthquakes (M > 7.5) account for most of the slip in plate tectonics. That is, the number of earthquakes generally decreases by a factor of ten for each unit increase in magnitude, but the energy of an individual earthquake increases by a factor of 32 with each unit increase in magnitude. If we assume that M 8.0 is the largest earthquake magnitude that an earthquake can have in California, then there is three times as much radiated energy in the M 7 to 8 earthquakes as there is in all other earthquakes smaller than M 7. Therefore, we see that although large earthquakes are infrequent, they are the major actors in plate tectonics; in this sense, large earthquakes are inevitable.
What will happen when one of these large magnitude earthquakes attacks one of our cities? Of course, the answer to this question depends on the particulars of the earthquake and the capacity of the buildings that are shaken. Even if we could anticipate the magnitude of our future earthquakes, it's still hard to say what shaking the buildings will experience; ground shaking can easily vary by a factor of ten times between sites that are equidistant from an earthquake. In order to deal with the large variability in observed shaking, it has become popular to construct probabilistic models of exceeding a given intensity of shaking (Probabilistic Seismic Hazard Analysis, PSHA). PSHA models are constructed using strong shaking recorded in the past four decades. One of the key questions is how well these records inform us about what will happen in future earthquakes. There are currently enough records to characterize motions that can occur in earthquakes up to about M 7. However, larger earthquakes are so infrequent that there are too few records to characterize the range of shaking that occurs in great earthquakes (e.g., the 1906 San Francisco earthquake). Therefore PSHA must extrapolate relationships between ground motion and earthquake magnitude to large magnitudes. As currently practiced, most of these extrapolations are based on log-normal statistical models (Gaussian distributions) that are commonly used in actuarial science. While this type of statistics may be appropriate for high-frequency ground shaking (peak ground acceleration), the statistics of low-frequency ground motions are best described with heavy-tailed power laws (sometimes referred to as a Pareto Distribution). Unfortunately, the current practice of extrapolating into the future using log-normal statistics may seriously underestimate the size of long-period ground motions that will occur in future earthquakes.
My research is in both earth sciences (understanding the physics of shaking) and in earthquake engineering (understanding the physics of yielding buildings). There seems to be an inconsistency between earth scientists and earthquake engineers about the significance of large magnitude earthquakes. Much of our work is aimed at a more complete understanding of the nature of ground shaking close to large earthquakes. That is, ground motions from large earthquakes are simulated by propagating waves through 3-dimensional earth structure models. The models produce realistic estimates of the large displacements (several meters in several seconds) that occur in great earthquakes. While accelerations that are associated with these large displacements may not be large enough to cause failure of strong, shear-wall structures (most of California's construction of 3 stories and less), they may cause severe deformations in flexible buildings (almost all buildings taller than 8 stories are flexible) that rely heavily on ductility for their performance in large earthquakes. This work is closely coordinated with Prof. John F. Hall.
We (Jing Yang) also investigated the potential performance of steel moment-resisting-frame buildings in large subduction zone earthquakes. We have simulated the deformations and damage that would have occurred to such buildings in the M 8.3 Tokachi-Oki earthquake (2003). Although there were no such buildings present on the island of Hokkaido during this earthquake, there were 275 strong motion records which we used as the basis of our study. In addition, we used this data as the basis of an empirical Greens function study of the potential effects of a giant (M>9) subduction earthquakes on high-rise buildings in the cities of Seattle, Portland, and Vancouver. Our simulations indicate that long-period shaking from a giant Cascadia earthquake will last for three to five minutes. Furthermore, long-period period (2 to 8 sec.) ground motions will be strongly amplified in the Seattle basin. Because the down-dip extent of rupture on the subduction zone is unknown, we simulated motions for three different cases: 1) the rupture is confined to the offshore part of the zone, 2) rupture extends about 20 km east of the coast, and 3) rupture extends to the eastern margin of the Olympic peninsula. Shaking from cases 2 and 3 is strong enough to induce large nonlinear deformations for building simulations in the Seattle basin. In many of the simulations, collapse is indicated. It seems clear that current design procedures for Seattle high-rises do not assure collapse prevention in the case of a giant Cascadia earthquake. This work is described in Jing Yang's Ph.D. dissertation (pdf).
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