105 research outputs found
Vibroacoustics of timber-frame structures excited by structure-borne sound sources
This thesis investigates the measurement and prediction of machinery noise in timber-frame buildings. To quantify the structure-borne sound power input from multi-point sources, simplified approaches were assessed that reduce the required data for out-of-plane force excitation. This identified approaches that give estimates within ±5 dB from 20 Hz to 2000 Hz. To investigative the importance of out-of-plane moment excitation, inverse methods were used to determine the power input; these were affected by noise but processing was used to overcome this shortcoming. A series of experimental investigations were carried out on a timber-frame structure undergoing mechanical point excitation. The driving-point mobility showed orthotropic plate characteristics at low frequencies, ribbed-plate characteristics in a narrow frequency band and infinite plate characteristics in mid- and high-frequency ranges. The moment mobility above or in-between studs was similar to infinite beam or plate theory with interpolation between these theories where necessary. The experimental work indicated the potential to use Statistical Energy Analysis (SEA) to predict sound transmission. The first experimental finding was that above the mass-spring-mass resonance frequency, the vibrational response of the wall leaves was uncorrelated. The second was a significant decrease in vibration across the wall from the excitation point, with structural intensity showing a decrease in net power flow across successive timber studs. The third was that tongue and groove connections between chipboard sheets significantly reduce the vibration transmission above 500 Hz. This led to different SEA models being used to model a timber-frame wall undergoing mechanical point excitation. A 41-subsystem model was found to be necessary to reproduce the measured vibration levels on both leaves within 10 dB. As there is a significant decrease in vibration with distance in the mid- and high-frequency range, the region close to the excitation point is particularly important and the SEA model has better accuracy in this region. An alternative engineering approach to the prediction of machinery noise in timber-frame buildings was introduced and validated that used measured transmission functions between the injected power and the spatial-average sound pressure level in a receiving room. A field survey and case studies indicate this is a feasible and practical approach
A Mathematical Analysis of the Strip-Element Method for the Computation of Dispersion Curves of Guided Waves in Anisotropic Layered Media
Dispersion curves of elastic guided waves in plates can be efficiently computed by the StripElement Method. This method is based on a finite-element discretization in the thickness direction of the plate and leads to an eigenvalue problem relating frequencies to wavenumbers of the wave modes. In this paper we present a rigorous mathematical background of the Strip-Element Method for anisotropic media including a thorough analysis of the corresponding infinite-dimensional eigenvalue problem as well as a proof of the existence of eigenvalues
Local Analysis of Inverse Problems: H\"{o}lder Stability and Iterative Reconstruction
We consider a class of inverse problems defined by a nonlinear map from
parameter or model functions to the data. We assume that solutions exist. The
space of model functions is a Banach space which is smooth and uniformly
convex; however, the data space can be an arbitrary Banach space. We study
sequences of parameter functions generated by a nonlinear Landweber iteration
and conditions under which these strongly converge, locally, to the solutions
within an appropriate distance. We express the conditions for convergence in
terms of H\"{o}lder stability of the inverse maps, which ties naturally to the
analysis of inverse problems
Measurement of transmission functions in lightweight buildings for the prediction of structure-borne sound transmission from machinery
This paper develops and assesses protocols for the measurement of transmission functions in lightweight buildings. A transmission function is defined that relates the spatial-average sound pressure level in a room to the structure-borne sound power injected into a wall or floor. The intention is to facilitate the prediction of structureborne sound transmission from machinery to receiving rooms. Errors in the measurement of the power input can be reduced by using a pair of accelerometers on either side of the excitation point rather than a single accelerometer on one side. Laboratory measurements on a timber-frame wall indicate that steady-state excitation using an electrodynamic shaker and transient excitation with a force hammer can be considered as equivalent. Measured transmission functions from a laboratory test construction below 500 Hz are found not to be significantly affected by the choice of excitation position being directly above a stud or in a bay. Laboratory and field results on different timber-frame walls indicate that with transient excitation using a force hammer, the transmission function is measurable in vertically-, horizontally- and diagonally-adjacent receiving rooms over the frequency range from 20 to 1 kHz. The approach has been applied in field measurements which indicate that there is potential to create databases of average transmission functions as a simplified prediction tool for sound pressure levels from service equipment in buildings
Preasymptotic Convergence of Randomized Kaczmarz Method
Kaczmarz method is one popular iterative method for solving inverse problems,
especially in computed tomography. Recently, it was established that a
randomized version of the method enjoys an exponential convergence for
well-posed problems, and the convergence rate is determined by a variant of the
condition number. In this work, we analyze the preasymptotic convergence
behavior of the randomized Kaczmarz method, and show that the low-frequency
error (with respect to the right singular vectors) decays faster during first
iterations than the high-frequency error. Under the assumption that the inverse
solution is smooth (e.g., sourcewise representation), the result explains the
fast empirical convergence behavior, thereby shedding new insights into the
excellent performance of the randomized Kaczmarz method in practice. Further,
we propose a simple strategy to stabilize the asymptotic convergence of the
iteration by means of variance reduction. We provide extensive numerical
experiments to confirm the analysis and to elucidate the behavior of the
algorithms.Comment: 20 page
Electron Dephasing in Mesoscopic Metal Wires
The low-temperature behavior of the electron phase coherence time,
, in mesoscopic metal wires has been a subject of controversy
recently. Whereas theory predicts that in narrow wires should
increase as as the temperature is lowered, many samples exhibit
a saturation of below about 1 K. We review here the experiments
we have performed recently to address this issue. In particular we emphasize
that in sufficiently pure Ag and Au samples we observe no saturation of
down to our base temperature of 40 mK. In addition, the measured
magnitude of is in excellent quantitative agreement with the
prediction of the perturbative theory of Altshuler, Aronov and Khmelnitskii. We
discuss possible explanations why saturation of is observed in
many other samples measured in our laboratory and elsewhere, and answer the
criticisms raised recently by Mohanty and Webb regarding our work.Comment: 14 pages, 3 figures; to appear in proceedings of conference
"Fundamental Problems of Mesoscopic Physics", Granada, Spain, 6-11 September,
200
Optimal Convergence Rates for Tikhonov Regularization in Besov Scales
In this paper we deal with linear inverse problems and convergence rates for
Tikhonov regularization. We consider regularization in a scale of Banach
spaces, namely the scale of Besov spaces. We show that regularization in Banach
scales differs from regularization in Hilbert scales in the sense that it is
possible that stronger source conditions may lead to weaker convergence rates
and vive versa. Moreover, we present optimal source conditions for
regularization in Besov scales
Greedy Solution of Ill-Posed Problems: Error Bounds and Exact Inversion
The orthogonal matching pursuit (OMP) is an algorithm to solve sparse
approximation problems. Sufficient conditions for exact recovery are known with
and without noise. In this paper we investigate the applicability of the OMP
for the solution of ill-posed inverse problems in general and in particular for
two deconvolution examples from mass spectrometry and digital holography
respectively.
In sparse approximation problems one often has to deal with the problem of
redundancy of a dictionary, i.e. the atoms are not linearly independent.
However, one expects them to be approximatively orthogonal and this is
quantified by the so-called incoherence. This idea cannot be transfered to
ill-posed inverse problems since here the atoms are typically far from
orthogonal: The ill-posedness of the operator causes that the correlation of
two distinct atoms probably gets huge, i.e. that two atoms can look much alike.
Therefore one needs conditions which take the structure of the problem into
account and work without the concept of coherence. In this paper we develop
results for exact recovery of the support of noisy signals. In the two examples
in mass spectrometry and digital holography we show that our results lead to
practically relevant estimates such that one may check a priori if the
experimental setup guarantees exact deconvolution with OMP. Especially in the
example from digital holography our analysis may be regarded as a first step to
calculate the resolution power of droplet holography
Gradual caldera collapse at Bárdarbunga volcano, Iceland, regulated by lateral magma outflow
Large volcanic eruptions on Earth commonly occur with a collapse of the roof of a crustal magma reservoir, forming a caldera. Only a few such collapses occur per century, and the lack of detailed observations has obscured insight into the mechanical interplay between collapse and eruption.We usemultiparameter geophysical and geochemical data to show that the 110-squarekilometer and 65-meter-deep collapse of Bárdarbunga caldera in 2014-2015 was initiated through withdrawal of magma, and lateral migration through a 48-kilometers-long dike, from a 12-kilometers deep reservoir. Interaction between the pressure exerted by the subsiding reservoir roof and the physical properties of the subsurface flow path explain the gradual, nearexponential decline of both collapse rate and the intensity of the 180-day-long eruption
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