J. António

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.

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.

Sound propagation around rigid barriers laterally confined by tall buildings

Abstract This paper focuses on the propagation of sound waves in the presence of acoustic barriers placed close to very tall buildings. The boundary element method (BEM) is used to model the acoustic barrier, while the presence of the tall buildings is taken into account by using the image source method. Different geometries are analyzed, representing the cases of a single building, two buildings forming a corner and three buildings defining a laterally confined space. The acoustic barrier is assumed to be non-absorbing, and all the buildings and the ground are modeled as infinite rigid plane surfaces. Calculations are performed in the frequency domain and time signals are then obtained by means of Inverse Fourier Transforms. The sound pressure loss provided by the acoustic barrier is computed, illustrating the importance of the lateral confinements.

Use of constant, linear and quadratic boundary elements in 3D wave diffraction analysis

The performance of the Boundary Element Method (BEM) depends on the size of the elements and the interpolation function used. However, improvements in accuracy and efficiency obtained with both expansion and grid refinement increases demand on the computational effort. This paper evaluates the performance of constant, linear and quadratic elements in the analysis of the three-dimensional scattering caused by a cylindrical cavity buried in an infinite homogeneous elastic medium subjected to a point load. A circular cylindrical cavity for which analytical solutions are known is used in the simulation analysis. First, the dominant BEM errors are identified in the frequency domain and related to the natural vibration modes of the inclusion. Comparisons of BEM errors are then made for different types of boundary elements, maintaining similar computational costs. Finally, the accuracy of the BEM solution is evaluated when the nodal points are moved inside linear and quadratic discontinuous elements.

A 2.5D TRACTION BOUNDARY ELEMENT METHOD FORMULATION APPLIED TO THE STUDY OF WAVE PROPAGATION IN A FLUID LAYER HOSTING A THIN RIGID BODY

This paper models three-dimensional wave propagation around two-dimensional rigid acoustic screens, with minimal thickness (approaching zero), and placed in a fluid layer. Rigid or free boundaries are prescribed for the flat fluid surfaces. The problem is computed using the Traction Boundary Element Method (TBEM), which is appropriate for modeling thin-body inclusions, overcoming the difficulty posed by the conventional direct Boundary Element Method (BEM). The problem is solved as a summation of two-dimensional problems for different wave numbers along the direction for which the geometry does not vary. The source in each problem is a spatially sinusoidal harmonic line load. The influence of the horizontal boundaries of the fluid medium on the final wave field is computed analytically using appropriate 2.5D Greens functions for each model developed. Thus, only the boundary of the rigid acoustic screen needs to be discretized by boundary elements. The computations are performed in the frequency domain and are subsequently inverse Fourier transformed to obtain time domain results. Complex frequencies are used to avoid aliasing phenomena in the time domain results.

3D seismic response of a limited valley via BEM using 2.5D analytical Green's functions for an infinite free-rigid layer

Abstract This paper presents analytical solutions for computing the 3D displacements in a flat solid elastic stratum bounded by a rigid base, when it is subjected to spatially sinusoidal harmonic line loads. These functions are also used as Greens functions in a boundary element method code that simulates the seismic wave propagation in a confined or semi-confined 2D valley, avoiding the discretization of the free and rigid horizontal boundaries. The models developed are then used to simulate wave propagation within a rigid stratum and valleys with different dimensions and geometries, when struck by a spatially sinusoidal harmonic vertical line load. Simulations are performed in the frequency domain, for varying spatial wave numbers in the axial direction of the valley. Time results are obtained by means of inverse Fourier transforms, to help understand how the geometry of the valley may affect the variation of the displacement field.

Green's functions for 2.5D elastodynamic problems in a free solid layer formation

This work presents analytical Greens functions for the steady state response of a homogeneous three-dimensional free solid layer formation (slab) subjected to a spatially sinusoidal harmonic line load, polarized along the horizontal, vertical and z directions. The equations presented here are not only themselves very interesting but are also useful for formulating three-dimensional elastodynamic problems in a slab-type formation, using integral transform methods and/or boundary elements. The final expressions are validated by comparing them with the results obtained by using the Boundary Element Method solution, for which both free surfaces of the slab are discretized with boundary elements.

Impact sound transmission provided by concrete layers incorporating cork granules

We report on the development of lightweight cement-based screeds containing cork granule waste. The reduction of transmitted impact noise provided by these screeds has been assessed by means of laboratory measurements in acoustic chambers at ITeCons (Instituto de Investigacao e Desenvolvimento Tecnologico em Ciencias da Construcao). The screed has been tested in two situations: over a heavyweight standard floor (reference laboratory floor) and as a resilient layer between the heavyweight standard floor and a floating concrete layer. Three different screeds were designed, with varying cement dosages. Thicknesses of 1.5, 3 and 4.5 cm were tested for each screed mixture. As the impact sound reduction of resilient materials is related to their dynamic stiffness, this was also measured in laboratory conditions. The results of dynamic stiffness were generally found to be related to the values of impact sound reduction when the cement/cork screed is used as floor covering. The results obtained show the potential of these composites in applications for reducing impact noise.

3D scattering by multiple cylindrical cavities buried in an elastic formation

This paper presents the three-dimensional scattering field obtained when multiple cylindrical circular cavities of infinite length buried in a homogeneous elastic medium, are subjected to dilatational point loads placed at some point in the medium. The solution is formulated using boundary elements for a wide range of frequencies and spatially harmonic line loads, which are then used to obtain time series by means of (fast) inverse Fourier transforms into space-time. The method and the expressions presented are implemented and validated by applying them to a cylindrical circular cavity buried in an infinite homogeneous elastic medium subjected to a dilatational point load, for which the solution is calculated in closed form. The boundary elements method is then used to evaluate the wave-field elicited by a dilatational point load source in the presence of a different number of cylindrical oval cavities. Simulation analyses using this idealized model are then applied to the study of wave propagation patterns in the vicinity of these inclusions. The amplitude of the wavefield in the frequency vs axial-wavenumber domain is presented, allowing the recognition, identification, and physical interpretation of the variation of the wavefield.