A modal-spectral model for flanking transmissions

A model for the prediction of direct and indirect (flanking) sound transmissions is presented. It can be applied to geometries with extrusion symmetry. The structures are modelled with spectral finite elements. The acoustic domains are described by means of a modal expansion of the pressure field and must be cuboid-shaped. These reasonable simplifications in the geometry allow the use of more efficient numerical methods. Consequently the coupled vibroacoustic problem in structures such as junctions is efficiently solved. The vibration reduction index of T-junctions with acoustic excitation and with point force excitation is compared. The differences due to the excitation type obey quite general trends that could be taken into account by prediction formulas. However, they are smaller than other uncertainties not considered in practice. The model is also used to check if the sound transmissions of a fully vibroacoustic problem involving several flanking paths can be reproduced by superposition of independent paths. There exist some differences caused by the interaction between paths, which are more important at low frequencies.Peer ReviewedPostprint (author's final draft

Transmission Loss formulas for junctions taking into accountin-plane waves

In the transmission of vibrations through structural junctions at high frequencies,the distribution of energy between wave types con suffer important variations. It means, for example, that incoming energy concentrated in a bending wave(out-of-plane vibration) can be split in transmitted energy of other wave types:bending, quasi-longitudinal or transverse shear waves. The goal of the research is to provide simple formulas to include this phenomenon in a Statistical Energy Analysis (SEA) model through the Coupling Loss Factor (CLF) coefficients. A large number of simulations of a population of junctions is generated by means of a numerical model. Afterwards, this data is post-processed in order to obtain the Transmission Loss (TL) between the different wave types by means of a procedure that mimics the Experimental SEA (it is ESEA with some modifications because in the numerical simulations, the internal loss factor is imposed a priori). Each junction is characterised by means of a parameter that minimises the scattering of the TL data with respect to the approximation formula. Some application examples to building structures are shown.Postprint (published version

A boundary algebraic formulation for plane strain elastodynamic scattering

Solving of elastodynamic problems arises in many scientific fields such as wave propagation in the ground, non-destructive testing, vibration design of buildings, or vibroacoustics in general. An integral formulation based on boundary algebraic equations is presented here. This formulation leads to a numerical method with a discretised boundary. An important advantage of the method over the standard boundary element method (BEM) is that no contour (2D) or surface (3D) integral needs to be computed. This feature is helpful in order to obtain a discrete version of the combined field integral equations (designed to damp numerically the fictitious eigenfrequencies) without difficulties caused by the evaluation of hypersingular integrals. The key aspects are: (i) the approach deals with discrete equations from the very beginning; (ii) discrete (instead of continuous) tensor Green's functions are considered (the methodology to evaluate them is demonstrated); (iii) the boundary must be described by means of a regular square grid. In order to overcome the drawback of this third condition the boundary integral is coupled, if needed, with a thin layer of finite elements. This improves the description of curved geometries and reduces numerical errors. The properties of the method are demonstrated by means of numerical examples: the scattering of waves by objects and holes in an unbounded elastic medium, and an interior elastic problem.Peer ReviewedPostprint (author's final draft

Using spectral finite elements for parametric analysis of the vibration reduction index of heavy junctions oriented to flanking transmissions and EN-12354 prediction method

The vibration reduction index of heavy junctions is predicted by means of a model based on spectral finite elements. This is equivalent to a finite element method but faster and with smaller computational costs. This advantage is used in order to perform a parametric analysis of the vibration reduction index for several junction types: T-shaped, L-shaped and +-shaped. The influence of several parameters such as: damping, junction dimensions or the mass ratio on the vibration reduction index is observed. The study is focussed to provide data and guidelines oriented to the EN-12354 design method for flanking transmission in buildings.Peer ReviewedPostprint (author’s final draft

The block gauss-seidel method in sound transmission problems

Sound transmission through partitions can be modelled as an acoustic fluid-elastic structure interaction problem. The block Gauss-Seidel iterative method is used in order to solve the finite element linear system of equations. The blocks are defined in a natural way, respecting the fluid and structural domains. The convergence criterion (spectral radius of iteration matrix smaller than one) is analysed and interpreted in physical terms by means of simple one-dimensional problems. This analysis highlights the negative influence on the convergence of a strong degree of coupling between the acoustic domains. A selective coupling strategy has been developed and successfully applied to problems with strong coupling (i.e. sound transmission through double walls)

Catalogue of vibration reduction index formulas for heavy junctions based on numerical simulations

© (2017) S. Hirzel Verlag/European Acoustics Association. The definitive publisher-authenticated version is available online at http://www.ingentaconnect.com/contentone/dav/aaua/2017/00000103/00000004/art00011 and http//dx.doi.org/10.3813/AAA.919091. Readers must contact the publisher for reprint or permission to use the material in any form.The vibration reduction index (Kij) is a key parameter in the prediction of flanking transmissions according to the EN-12354 standard. Formulas for the evaluation of Kij in L, T and X junctions that depend on the mass ratio are available in the Annex E. Junctions of straight elements with different thickness or thin elastic layers are also included. However, other junction types that are important for building industry are not considered: H-shaped junctions, L or T junctions not forming a right angle, asymmetrical T-junctions , X-junctions where only one of the parts is different (thickness or material) from the other two/three. In the current research, expressions for these non-covered junctions are provided. They are obtained by means of numerical simulations based on the spectral finite element method. Kij is predicted for a large population of junctions, considering usual thicknesses and heavy material combinations (no lightweight frame systems have been considered). Statistical analysis is carried out to obtain relatively simple formulae that could be used in acoustic design projects without the need for time-consuming computations with finite element software.Peer ReviewedPostprint (author's final draft

Error estimation in vibroacoustic problems solved by means of finite elements

The vibroacoustic equations can be solved by means of the finite element method. A discretisation of the structure and the acoustic domains is required and highly influences the quality of the numerical solution. There exist meshing criteria (a priori error estimators) for the case of the Helmholtz equation but these studies have not focused their attention in the case of the vibroacoustic problem. The fluid structure interaction represents a new source of numerical errors and meshes in the interaction zone should be designed by not only taking into account the physical properties of the acoustic medium but also the mechanical properties of the structure. The goal of the work is to obtain an a priori error estimation criterion for the vibroacoustic problem and Illustrate its efficiency by means of numerical experiments.Peer ReviewedPostprint (published version

Eigenvalue and eigenmode synthesis in elastically coupled subsystems

A method to synthesize the modal characteristics of a system from the modal characteristics of its subsystems is proposed. The interest is focused on those systems with elastic links between the parts which is the main feature of the proposed method. An algebraic proof is provided for the case of arbitrary number of connections. The solution is a system of equations with a reduced number of degrees of freedom that correspond to the number of elastic links between the subsystems. In addition the method is also interpreted from a physical point of view (equilibrium of the interaction forces). An application to plates linked by means of springs shows how the global eigenfrequencies and eigenmodes are properly computed by means of the subsystems eigenfrequencies and eigenmodes.Peer ReviewedPostprint (author's final draft

DEPURADORA DE FIRGAS [Material gráfico]

Copia digital. Madrid : Ministerio de Educación, Cultura y Deporte, 201

An SEA-like model for double walls filled with absorbing materials

Modelling absorbing materials with statistical energy analysis (SEA) is an open issue. They are neither reverberant subsystems nor conservative couplings. The absorbing material layers located inside the cavities of double walls should be treated as non-conservative couplings between the wall leaves. However, the standard SEA formulation cannot take into account non-conservative couplings. In this work, an equivalent circuit analogy is used to deduce how to introduce these couplings in an SEA-like system. Besides, a technique for obtaining the SEA-like factors associated to a double wall filled with absorbing material is presented. These factors are computed from numerical simulations of the vibroacoustic leaf-absorbing material-leaf system and applied for solving larger problems with SEA.Peer ReviewedPostprint (published version