A. Tadeu

Closed-form integration of singular terms for constant, linear and quadratic boundary elements. Part 1. SH wave propagation

One of the most important aspects in the application of boundary element techniques to wave propagation problems is the accurate representation of the singular terms at the points of application of the virtual loads. It is current practice to carry out this task by means of numerical quadrature. This paper presents an analytical evaluation of the singular integrals for constant, linear and quadratic boundary elements involving SH waves, the results of which are then used to model inclusions in a two-dimensional acoustic medium illuminated by dynamic anti-plane line sources. Finally, the BEM results are compared with the known analytical solutions for cylindrical inclusions.

Sound transmission through single, double and triple glazing. Experimental evaluation

Abstract Experimental results on sound insulation of glazed openings are reported in this work. The laboratory experiments were performed placing the text specimens between two relatively small rooms. The number of glass panels, their thickness, the air gap thickness between the panels and the type of fixing frame are the variables considered. The insulation conferred by the glazed opening is characterised, identifying the localisation of the dips of insulation in the frequency domain with those related to its own natural dynamic vibration modes and those related to the natural modes of vibration of the rooms. Since the full mathematical description of the acoustic insulation conferred by glazed panels is extremely complicated, simplified theoretical models are frequently used. In this work, the experimental insulation curves obtained are compared with those predicted by the simplified analytical models. This analysis shows that the predictive models, particularly when applied to multiple glazing windows, exhibit marked differences when compared with the experimental data.

Analytical evaluation of the acoustic insulation provided by double infinite walls

Abstract The acoustic insulation provided by infinite double panel walls, when subjected to spatially sinusoidal line pressure loads, is computed analytically. The methodology used extends earlier work by the authors on the definition of the acoustic insulation conferred by a single panel wall. It does not entail any simplification other than the assumption that the panels are of infinite extent. The full interaction between the fluid (air) and the solid layers is thus taken into account and the calculation does not involve limiting the thickness of any layer, as the Kirchhoff or Mindlin theories require. The problem is first formulated in the frequency domain. Time domain solutions are then obtained by means of inverse Fourier transforms using complex frequencies. The model is first used to compute the sound reduction provided by a double homogeneous brick wall, with identical panels, when illuminated by plane sound waves. The results are then compared with those provided by the simplified method proposed by London, which was later extended by Beranek (London–Beranek method). The limitations of the simplified London–Beranek model, namely, its applicability only to double walls with identical mass, subjected to plane waves, and its failure to account for the coincidence effect, are overcome by the method proposed. Time signatures are produced to illustrate the different sound transmission mechanisms. Several types of body and guided waves are originated, giving rise to a complex dynamic system with multiple reflections within the solid and fluid layers and the global resonance of the system. The effect of the cavity absorption is considered by attributing a complex density to the air filling the space between the two wall panels. Absorption attenuates the dips of insulation controlled by the cavity resonances. Several simulations are then performed for different combinations of wall and air layer thickness to assess the influence of this variable on the final acoustic insulation. The influence of the air cavity on sound reduction was found to be dependent on the frequency. At low frequencies a better performance was achieved for thicker air layers, while at higher frequencies a thinner air layer is preferable. The use of wall panels with different mass resulted in the wall performing better, particularly for high frequencies.

3D sound scattering by rigid barriers in the vicinity of tall buildings

The boundary element method (BEM) is used to evaluate the acoustic scattering of a threedimensional (3D) sound source by an infinitely long rigid barrier in the vicinity of tall buildings. The barrier is assumed to be non-absorbing and the buildings are modeled as an infinite barrier. The calculations are performed in the frequency domain and time signatures are obtained by means of inverse Fourier transforms. The 3D solution is obtained by means of Fourier transform in the direction in which the geometry does not vary. This requires solving a series of 2D problems with different spatial wavenumbers, kz. The wavenumber transform in discrete form is obtained by considering an infinite number of virtual point sources equally spaced along the z axis. Complex frequencies are used to minimize the influence of these neighboring fictitious sources. Different geometric models, with barriers of varying sizes, are used. The reduction of sound pressure in the vicinity of the buildings is evaluated and the creation of shadow zones by the barriers is analyzed and compared with results provided by a simplified method. # 2001 Elsevier Science Ltd. All rights reserved.

Numerical Simulation of Ground Rotations along 2D Topographical Profiles under the Incidence of Elastic Plane Waves

The surface displacement field along a topographical profile of an elastic half-space subjected to the incidence of elastic waves can be computed using different numerical methods. The method of fundamental solutions (MFS) is one of such tech- niques in which the diffracted field is constructed by means of a representation in terms of the Greens functions for discrete forces located outside the domain of inter- est. From the enforcement of boundary conditions, such forces can be computed; thus, the ground motion can be calculated. One important advantage of MFS over boundary integral techniques is that singularities are avoided. The computation of ground- motion rotations implies the application of the rotational operator to the displacement field. This can be done using either numerical derivatives or analytical expressions to compute the rotational Greens tensor. We validate the method using exact analytical solutions in terms of both displacement and rotation, which are known for simple geometries. To demonstrate the accuracy for generic geometries, we compare results against those obtained using the spectral-element method. We compute surface rota- tions for incoming plane waves (P, SV, and Rayleigh) near a topographical profile. We point out the effects of topography on rotational ground motion in both frequency and time domains. Online Material: Analysis of the dependence of rotational motion on incident plane-wave frequency.

Wave motion between two fluid-filled boreholes in an elastic medium

The boundary element method (BEM) is used to fully simulate the propagation of waves between two fluid-filled boreholes. The sources are placed in one of the boreholes while the receivers are placed in the other. This model is frequently used in cross-hole seismic prospecting techniques to assess the characteristics of the elastic medium between the two boreholes. This work studies the dependence of the wave propagation patterns on the distance between the source and the receiver, their location and orientation relative to the axis of a circular borehole and type of elastic formation (fast and slow formations). In addition, this BEM model is used to compute the influence of the deformed boreholes whose cross-section is not circular. Both the spectra responses and the time-domain responses are computed to elucidate the main physical features of the problem solved.

3-D wave propagation in fluid-filled irregular boreholes in elastic formations

Abstract Different seismic testing techniques rely on the propagation of acoustic waves in fluid-filled boreholes from sources placed within the borehole and in the solid media. The interpretation of the signals recorded relies on understanding how waves propagate in the borehole and its immediate vicinity. It is known that very complex wave patterns can arise, depending on the distance between the source and the receiver, and their placement and orientation relative to the axis of a circular borehole. The problem becomes more complex if the cross-section is not circular, conditions for which analytical solutions are not known. In this work, the Boundary Element Method (BEM) is used to evaluate the three-dimensional wave field elicited by monopole sources in the vicinity of a fluid-filled borehole. This model is used to assess the effects of the receiver position on the propagation of both axisymmetric and non-axisymmetric wave modes when different borehole cross-sections are used. Both frequency vs. axial-wave number responses and time-domain responses are calculated.

Mortars based in different binders with incorporation of phase-change materials: Physical and mechanical properties

In a society with a high growth rate and increased standards of comfort arises the need to minimise the currently high-energy consumption by taking advantage of renewable energy sources. The mortars with incorporation of phase-change materials (PCM) have the ability to regulate the temperature inside buildings, contributing to the thermal comfort and reduction in the use of heating and cooling equipment, using only the energy supplied by the sun. However, the incorporation of phase-change materials in mortars modifies its characteristics. The main purpose of this study was the production and characterisation in the fresh and hardened state of mortars with incorporation of different contents of PCM in mortars based in different binders. The binders studied were aerial lime, hydraulic lime, gypsum and cement. For each type of binder, different mortars were developed with different content of PCM. The proportion of PCM studied was 0, 20, 40 and 60% of the mass of the sand. It was possible to observe that the incorporation of PCM in mortars caused differences in properties such as workability, microstructure, compressive strength, flexural strength and adhesion.

Performance of the BEM solution in 3D acoustic wave scattering

Abstract A fixed cylindrical circular cavity and a cylindrical circular column of fluid of infinite length submerged in a homogeneous fluid medium, and subjected to a pressure point source, for which closed form solutions are known, are used to assess the performance of constant, linear and quadratic boundary elements in the analysis of acoustic scattering. This aim is accomplished by evaluating the error committed by the boundary element method (BEM) for a wide range of frequencies and wave numbers. First, the position of dominant BEM errors in the frequency versus spatial wave number domains are identified and related to the natural modes of vibration of the cylindrical circular inclusion. Then, the errors that occur by using constant, linear and quadratic elements are compared when the inclusion is modelled with the same number of nodes (i.e. maintaining computational cost). Finally, the importance of the position of the nodal points inside discontinuous boundary elements is analysed.

3D scattering of waves by a cylindrical irregular cavity of infinite length in a homogeneous elastic medium

Abstract The three-dimensional (3D) wave field scattered by an irregular, cylindrical cavity of infinite length contained in a homogeneous elastic medium illuminated by a dilatational point load is obtained. This model is used to evaluate the effect of the cross-sectional geometry of the cavity on the waves propagating in its vicinity. It particularly highlights the identification of the normal modes excited both in the frequency and time domain. The solution is formulated using the boundary element method for a wide range of frequencies and spatially harmonic line loads, which are then synthesized to obtain the time responses. The 3D solution is obtained as a summation of two-dimensional responses for different axial wavenumbers. The responses in the frequency vs. axial-wavenumber domains are presented, allowing the recognition, identification, and physical interpretation of the variation of the wave field when five irregular cross-sections are used, namely a circle, an oval, a thin oval, a kidney and a boomerang.