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Mathematical model for elastic shear bending of trapezoidally corrugated plate with trough lines held straight including stiffness and stress analysis
Plate and acoustic finite elements simulation of window-room system coupled transient response to sonic booms, discussing equations of motion and cavity depth effect
A theoretical analysis is presented of the elastic shearing of a trapezoidally corrugated plate with discrete attachments at the ends of the corrugations. Numerical results on effective shear stiffness, stresses, and displacements are presented for selected geometries and end-attachment conditions. It is shown that the frame-like deformation of the cross-sections, which results from the absence of continuous end attachments, can lead to large transverse bending stresses and large reductions in shearing stiffness.
An analysis of the free vibration and transient response of laminates using a mixed shear flexible element is presented. The element is based on a refined theory that accounts for a parabolic distribution of the transverse shear stresses through each lamina and requires no shear correction coefficients. The mixed formulation of the theory treats the five displacement functions and six stress resultants independently so that they are nodal degrees of freedom in the finite element model. Sample problems using the element are analyzed and the results of free vibration and transient response are presented. Compared to the existing shear deformation plate theory the present refined theory gives more accurate results for frequencies, displacements and stresses.
The primary effort in this study during the past year has been directed along two separate lines: (1) expanding finite element models to include the entire Anatolian plate, the Aegean Sea and the Northeastern Mediterranean Sea, and (2) investigating the relationship between fault geometry and earthquake activity for the North Anatolian and similar strike-slip faults (e.g., San Andreas Fault). Both efforts are designed to provide an improved basis for interpreting the Crustal Dynamics measurements NASA has planned for this region. The initial phases of both investigations have been completed and the results are being prepared for publication. These investigations are described briefly.
The nature and dynamics of time-dependent deformation along major seismic zones including the influence of irregularities in fault geometry on the earthquake cycle, and the processes contributing to the state of stress and rates of strain in plate interior regions were studied. The principle findings of the research are discussed.
The long term objective of this project is to interpret NASA's Crustal Dynamics measurements (SLR) in the Eastern Mediterranean region in terms of relative plate motions and intraplate deformation. The approach is to combine realistic modeling studies with an analysis of available geophysical and geological observations to provide a framework for interpreting NASA's measurements. This semi-annual report concentrates on recent results regarding the tectonics of Anatolia and surrounding regions from ground based observations. Also briefly reported on is progress made in using GPS measurements to densify SLR observations in the Eastern Mediterranean.
The focus of the research was in two broad areas during the most recent 6 month period: the nature and dynamics of time-dependent deformation along major seismic zones, including the influence of irregularities in fault geometry on the earthquake cycles, and the processes contributing to the state of stress and rates of strain in plate interior regions. The principal findings of the research to date are described.
The long-term objective of this project is to interpret NASA's Crustal Dynamics measurements (SLR) in the Eastern Mediterranean region in terms of relative plate movements and intraplate deformation. The approach is to combine realistic modeling studies with analysis of available geophysical and geological observations to provide a framework for interpreting NASA's measurements. This semi-annual report concentrates on recent results regarding the tectonics of Anatolia and surrounding regions from ground based observations. Also reported on briefly is progress in the use of the Global Positioning System to densify SLR observations in the Eastern Mediterranean. Reference is made to the previous annual report for a discussion of modeling results.
During the past 6 months, efforts were concentrated on the following areas: (1) Continued development of realistic, finite element modeling of plate interactions and associated deformation in the Eastern Mediterranean; (2) Neotectonic field investigations of seismic faulting along the active fault systems in Turkey with emphasis on identifying seismic gaps along the North Anatolian fault; and (3) Establishment of a GPS regional monitoring network in the zone of ongoing continental collision in eastern Turkey (supported in part by NSF).
A geodetic network which spans the region between San Francisco and Lake Tahoe has been measured 5 times completely with triangulation in 1880, 1922, 1929, 1943, 1963. A resurvey with the Global Positioning System (GPS) in 1991 allows the formation of 1 coseismic and 4 interseismic epochs. The data from this network provide a unique opportunity to examine the temporal and spatial evolution of the strain field associated with the 1906 San Francisco earthquake in particular and with the Pacific-North American plate boundary in general. Calculations of strain rate from the network data lead to the following conclusions. (1) There is no resolvable (greater than 0.05 microradians/yr) strain in between Sutter Buttes and the Sierra Nevada. (2) Throughout the time since the 1906 earthquake, a region extending at least as far east as the westernmost Great Valley has been undergoing deformation related to Pac:Nam interaction and the associated earthquake cycle. (3) In the time and space of overlap, our results agree with those from the United States Geological Survey (USGS) trilateration data. Both data sets indicate that strain must be accumulating to the east of Vaca. (4) The San Andreas discrepancy cannot be accommodated in the Great Valley at the 1 sigma level of our results. It is possible to absorb it in that region at the 2 sigma level. (5) Strain rate is elevated in the years following the earthquake and decays slowly with time. It is possible that the rate in the Coast Ranges increases until around 1950 and then decays. With the exception of one epoch, strain rate in the Coast Ranges is consistently fault parallel, shows no sign changes, and is consistent with monotonic strain accumulation.
Recent progress in both the linear and nonlinear aspects of stability theory has highlighted the importance of the receptivity problem. One of the most unclear aspects of receptivity study is the receptivity of boundary-layer flow normal to vortical disturbances. Some experimental and theoretical results permit the proposition that quasi-steady outer-flow vortical disturbances may trigger by-pass transition. In present work such interaction is investigated for vorticity normal to a leading edge. The interest in these types of vortical disturbances arise from theoretical work, where it was shown that small sinusoidal variations of upstream velocity along the spanwise direction can produce significant variations in the boundary-layer profile. In the experimental part of this work, such non-uniform flow was created and the laminar-turbulent transition in this flow was investigated. The experiment was carried out in a low-turbulence direct-flow wind tunnel T-361 at the Central Aerohydrodynamic Institute (TsAGI). The non-uniform flow was produced by laminar or turbulent wakes behind a wire placed normal to the plate upstream of the leading edge. The theoretical part of the work is devoted to studying the unstable disturbance evolution in a boundary layer with strongly non-uniform velocity profiles similar to that produced by outer-flow vorticity. Specifically, the Tollmien-Schlichting wave development in the boundary layer flow with spanwise variations of velocity is investigated.
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Solidification within flowing medium imposing convective boundary condition on moving interface of solidifying layer
Analysis and numerical results are presented for the elastic shear stiffness of a corrugated shear web with a certain type of discrete attachments at the ends of the trough lines of the corrugations, namely point attachments to a rigid flange which interferes with the deformations of the end cross sections by preventing downward movement but permitting upward (lifting off) movement. The analysis is based on certain assumed modes of deformation of the cross sections in conjunction with the method of minimum total potential energy and the calculus of variations in order to obtain equations for the manner in which the assumed modes of deformation vary along the length of the corrugation. The numerical results are restricted to the case of equal-width crests and troughs but otherwise apply to a wide variety of geometries. They are in the form of graphs which give the overall shear stiffness as a fraction of the overall shear stiffness that could be obtained by having continuous attachment at the ends of the corrugations.
A particularly detailed set of observations in the vicinity of an intraplate, thrust earthquake (M 7.4) in Argentina, indicate a cyclic pattern of deformation very similar to that reported previously for interplate earthquakes. This deformation cycle, which may be characteristic of many seismically active areas, consists of: (1) steady strain accumulation, possibly punctuated by strain reversals; (2) coseismic strain release; (3) a period of continued strain release due to afterslip (persisting for perhaps a year or so); and (4) rapid postseismic strain accumulation which decreases exponentially and grades into steady strain accumulation. Deformation associated with three earthquakes in the U.S. (1940, M7.1 Imperial Valley California; 1964, M8.4 Alaska; 1959, M7.5 Hebgen Lake, Montana) are interpreted in light of this general earthquake cycle and are used to investigate the mechanics of strain release for these events. These examples indicate that large postseismic movements can occur for strike-slip, thrust, and normal fault events, and both viscoelastic relaxation and postseismic after-slip must be incorporated in models of earthquake related deformation. The mechanics of the strain release process revealed by these examples has implications for estimating earthquake repeat times from geodetic observations near active faults.
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