Derivation of Friedman Equations

Treballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Any: 2014, Tutor: Eduard Salvador SoléIn this report we make a detailed derivation of Friedman Equations, which are the dy- namical equations of a homogeneous and isotropic universe. First, we derive them in the framework of the General Relativity keeping the relativistic expressions as a reference for the rest of the report. Then, using the Newtonian formalism and solving some fundamental problems, we reach some dy- namical equations for the universe and compare the results with the relativistic ones, focusing our attention on the meaning of the expressions and on the cosmological constant

An energy flow study of a double-deck tunnel under quasi-static and harmonic excitations

© 2016. This version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/This paper presents a comparison between the vibration energy flow radiated by a double-deck tunnel and the one radiated by a simple tunnel when both are excited by constant or by harmonic moving loads. For both cases, the radiated energy is computed using a three-dimensional semi-analytical model of the system. The total energy radiated upwards is presented for a wide range of load speeds, when a constant moving load is considered, and for a wide range of excitation frequencies, when the excitation is a harmonic moving load. Significant differences have been obtained, first, for constant loads moving at very high speeds and, second, for harmonic loads moving at typical speeds for underground trains.Peer ReviewedPostprint (author's final draft

Dynamic response of a double-deck circular tunnel embedded in a full-space

© 2016. This version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/A three-dimensional dynamic model for calculating the ground-borne vibrations generated by harmonic loads applied on the interior floor of a double-deck circular tunnel is developed. The response of the system is obtained coupling the interior floor subsystem and the tunnel-soil subsystem in the wavenumber-frequency domain. The interior floor is modeled as a thin plate of infinite length in the train circulation direction and the tunnel-soil system is described using the Pipe in Pipe model. Some numerical instabilities of the resulting expressions are overcome by using analytic approximations. The results show that the dynamic behavior of the interior floor clearly influences the magnitude of the coupling loads acting on the tunnel structure. The soil response to a harmonic load acting on the double-deck tunnel is compared to the one obtained for the case of a simple tunnel finding significant differences between them for the whole range of frequencies studied. The proposed model extends the prediction of train-induced vibrations using computationally efficient models to this type of tunnel structure.Peer ReviewedPostprint (author's final draft

A method based on 3D stiffness matrices in Cartesian coordinates for computation of 2.5D elastodynamic Green's functions of layered half-spaces

This article elaborates on an extension to the classical stiffness matrix method to obtain the Green's functions for two-and-a-half dimensional (2.5D) elastodynamic problems in homogeneous and horizontally layered half-spaces. Exact expressions for the three-dimensional (3D) stiffness matrix method for isotropic layered media in Cartesian coordinates are used to determine the stiffness matrices for a system of horizontal layers underlain by an elastic half–space. In the absence of interfaces, virtual interfaces are considered at the positions of external loads. The analytic continuation is used to find the displacements at any receiver point placed within a layer. The responses of a horizontally layered half-space subjected to a unit harmonic load obtained using the present method are compared with those calculated using a well-established methodology, achieving good agreementPostprint (author's final draft

Control of ground-borne underground railway-induced vibration from double-deck tunnel infrastructures by means of dynamic vibration absorbers

The aim of this study is to investigate the efficiency of Dynamic Vibration Absorbers (DVAs) as a vibration abatement solution for railway-induced vibrations in the framework of a doubledeck circular railway tunnel infrastructure. A previously developed semi-analytical model of the track-tunnel-ground system is employed to calculate the energy flow resulting from a train pass-by. A methodology for the coupling of a set of longitudinal distributions of DVAs over a railway system is presented as a general approach, as well as its specific application for the case of the double-deck tunnel model. In the basis of this model, a Genetic Algorithm (GA) is used to obtain the optimal parameters of the DVAs to minimize the vibration energy flow radiated upwards by the tunnel. The parameters of the DVAs set to be optimized are the natural frequency, the viscous damping and their positions. The results show that the DVAs would be an effective countermeasure to address railway induced ground-borne vibration as the total energy flowradiated upwards fromthe tunnel can be reduced by an amount between 5.3 dB and 6.6 dB with optimized DVAs depending on the type of the soil and the train speedPostprint (updated version

An efficient experimental methodology for the assessment of the dynamic behaviour of resilient elements

The assessment of the dynamic behaviour of resilient elements can be performed using the indirect method as described in the standard ISO 10846-3. This paper presents a methodology for control the error on the estimation of the frequency response functions (FRF) required for the application of the indirect method when sweep sine excitation is used. Based on a simulation process, this methodology allows for the design of the sweep sine excitation parameters, i.e., the sweep rate and the force amplitude, to control three types of errors associated to the experimentally obtained FRF in the presence of background noise: a general error of the FRF in a selected frequency range, and the errors associated to the amplitude and the frequency of the FRF resonance peak. The signal processing method used can be also tested with this methodology. The methodology has been tested in the characterisation of two different resilient elements: an elastomer and a coil spring. The simulated error estimations has been found to be in good agreement with the errors found in the measured FRF. Furthermore, it is found that for large signal-to-noise ratios, both sweep rate and force amplitude significantly affect the FRF estimation error, while, for small signal-to-noise ratios, only the force amplitude can control the error efficiently. The current methodology is specially interesting for laboratory test rigs highly used for the dynamic characterisation of resilient elements which are required to operate efficiently, since it can be used for minimising test times and providing quality assurance. Moreover, the application of this methodology would be specially relevant when characterisation is done in noisy environmentsPostprint (published version

A hybrid SBM-MFS methodology to deal with wave propagation

In this paper, a novel hybrid 2.5D SBM-MFS approach is formulated and developed in the frequency domain. This approach inherits the accuracy of MFS while keeping the robustness presented by the SBM. The MFS is employed to study the smooth portion of the boundary, while the complex segments are analysed through the SBM. For the sake of presenting the potential of the proposed hybrid approach, a square-shaped boundary excited by a unit point load is considered. The performance of the hybrid method is thoroughly assessed against 2.5D BEM, MFS, and SBM methods, in terms of convergence error analysis. Since the considered problem does not have a known analytical solution, the 2.5D FEM-BEM approach with a highly refined mesh is taken as the reference in the error analysis. The convergence error is calculated in terms of receptances at two circular distributions of evaluation points. In the hybrid method, 70 percent of the virtual sources are allocated on an auxiliary virtual boundary (MFS sources) while the remaining 30 percent are allocated on the physical boundary (SBM sources). The convergence plots obtained by four methods show that the accuracy of the hybrid method is significantly higher than the one of MFS and, in some cases, even higher than the one of BEM. While MFS requires a large number of nodes per wavelength to achieve acceptable results, the 2.5D SBM-MFS presents a high convergence rate, even for a small number of nodes per wavelength. The main benefit of the hybrid method is not solely its accuracy, compared with the BEM and SBM methods, but also its computational efficiency is another achievement. Moreover, in contrast to integration-based methods, such as BEM, the implementation of the new procedure is quite simple. It can be concluded that the hybrid 2.5D SBM–MFS is an adequate alternative prediction tool for elastodynamic problems.Peer ReviewedPostprint (published version

Collimated beam FMCW radar for vital sign patient monitoring

© 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes,creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.Patient monitoring of vital signals such as breathing rhythm and heart beat rate can be done remotely by the use of a radar system. This approach is advantageous since it does not require any contact with the patient. Obviously contactless monitoring results in a more comfortable situation for the patient, and in occasions it is almost mandatory as in the case of heavy burnt or newborn patients. Moreover, additional information such movement patterns are also available. A 120 GHz FMCW radar is described with special focus on the design, construction and testing of a specific reflector antenna for the system. The system is based on a commercial radar chipset that includes its own antennas. The challenge has been to design the optimum reflector and to build it and test it in a cost effective way. The reflector has been 3D printed and a near-field testing technique has been implemented to assess its performance. The results show that the system is able to measure the vital signs at distances beyond one meter.Postprint (author's final draft

VIBWAY: A user-friendly computational tool for the prediction of railway-induced ground-borne noise and vibration

This paper aims to introduce preliminary statement of methods of a computationally efficient and user-friendly toolbox, called VIBWAY, able to predict vibration and re-radiated noise levels in two situations. On the one hand, it can predict levels in existing buildings due to new lines or after the application of mitigation measures in existing operational railway infrastructures. Thus, it can be used to assess the performance of vibration countermeasures applied at the track, at the soil and/or at the building. On the other hand, it can predict levels in new buildings to be constructed close to an existing railway line from vibration measurements in the surface of the ground where the building will be constructed. The VIBWAY toolbox is based on a non-interface 2.5D FEM-SBM approach for the wave propagation on the soil, on semi-analytical approaches for the track and the building and on rigid multibody dynamics modelling of the train vehiclePostprint (published version

3D-Printed UHF-RFID Tag for Embedded Applications

This paper presents the design, manufacture and characterization of a novel 3D passive UHF-RFID tag for embedded applications. The prototype is fabricated using additive manufacturing techniques: 3D printing and copper electroplating. The design, manufacturing process and measurement set-up are presented and discussed in detail. We propose a biconical antenna design with spiral strips embedded in the cones to provide compactness without breaking the symmetry of the component and to improve bandwidth. The antenna is matched to a commercial UHF-RFID integrated circuit. We incorporate a packaging design that consists of a dielectric coating, to provide proper operation in different media or surrounding environments with changing electromagnetic properties. The good agreement between experimental results and Finite Element Method simulations allows us to validate the whole process. Finally, a compact capsule-type RFID tag is proposed and its performance in different media is reported