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, $\tau_{\phi}$, in mesoscopic metal wires has been a subject of controversy recently. Whereas theory predicts that $\tau_{\phi}(T)$ in narrow wires should increase as $T^{-2/3}$ as the temperature $T$ is lowered, many samples exhibit a saturation of $\tau_{\phi}$ 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 $\tau_{\phi}$ down to our base temperature of 40 mK. In addition, the measured magnitude of $\tau_{\phi}$ is in excellent quantitative agreement with the prediction of the perturbative theory of Altshuler, Aronov and Khmelnitskii. We discuss possible explanations why saturation of $\tau_{\phi}$ 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