Journal of Computational and Applied Mathematics, 2015
ABSTRACT This work presents a mathematical approach based on the point collocation technique to c... more ABSTRACT This work presents a mathematical approach based on the point collocation technique to compute the transmission loss of perforated dissipative silencers with transversal temperature gradients and mean flow. Three-dimensional wave propagation is considered in silencer geometries with arbitrary, but axially uniform, cross section. To reduce the computational requirements of a full multidimensional finite element calculation, a method is developed combining axial and transversal solutions of the wave equation. First, the finite element method is employed in a two-dimensional problem to extract the eigenvalues and associated eigenvectors for the silencer cross section. Mean flow as well as transversal temperature gradients and the corresponding thermal-induced material heterogeneities are included in the model. In addition, an axially uniform temperature field is taken into account, its value being the inlet/outlet average. A point collocation technique is then used to match the acoustic fields (pressure and axial acoustic velocity) at the geometric discontinuities between the silencer chamber and the inlet and outlet pipes. Transmission loss predictions are compared favorably with a general three-dimensional finite element approach, offering a reduction in the computational effort.
ABSTRACT A finite element approach is proposed for the acoustic analysis of automotive silencers ... more ABSTRACT A finite element approach is proposed for the acoustic analysis of automotive silencers including a perforated duct with uniform axial mean flow and an outer chamber with heterogeneous absorbent material. This material can be characterized by means of its equivalent acoustic properties, considered coordinate-dependent via the introduction of a heterogeneous bulk density, and the corresponding material airflow resistivity variations. An approach has been implemented to solve the pressure wave equation for a nonmoving heterogeneous medium, associated with the problem of sound propagation in the outer chamber. On the other hand, the governing equation in the central duct has been solved in terms of the acoustic velocity potential considering the presence of a moving medium. The coupling between both regions and the corresponding acoustic fields has been carried out by means of a perforated duct and its acoustic impedance, adapted here to include absorbent material heterogeneities and mean flow effects simultaneously. It has been found that bulk density heterogeneities have a considerable influence on the silencer transmission loss.
An analytical description of the acoustic performance of mufflers with elliptical cross-section h... more An analytical description of the acoustic performance of mufflers with elliptical cross-section has been obtained via the point source method and truncated modal superposition. First, the problem of natural frequencies and mode shapes has been addressed considering the Helmholtz equation in an elliptical domain, whose solution can be expressed by means of Mathieu functions. Then, the frequency response functions of the muffler have been evaluated, so that its acoustic performance is completely defined. The results obtained compare well with those obtained from finite element calculations, and with experimental measurements.
Acoustic transfer matrices are commonly found in the finite element modelling of devices associat... more Acoustic transfer matrices are commonly found in the finite element modelling of devices associated with the exhaust system of internal combustion engines. These matrices provide a relationship between the acoustic fields (usually pressure and velocity) associated with the nodes located at both sides of a particular region. For example, the acoustic behaviour of catalytic converters can be properly predicted if the monolith is replaced by a transfer matrix. In this case, only one-dimensional acoustic behaviour is allowed for the capillary ducts, while three-dimensional acoustic waves can still be present in the inlet/outlet and tapered ducts. In the previous problem, the finite element meshes considered in the bibliography are conforming at the connected interfaces, therefore leading to a straightforward evaluation of the coupling integrals. From a practical point of view, however, and to gain flexibility for the discretization, it is worth developing a procedure for connecting acou...
Railway vehicles running with wheel tread defects are known to cause abnormally high forces betwe... more Railway vehicles running with wheel tread defects are known to cause abnormally high forces between wheel and rail which reduce the life of track and vehicle components. Hertzian wheel-rail contact model is used by most of the vehicle-track dynamic interaction models at present. However, for wheel tread defects like shells or fresh wheel flats the assumptions of Hertzian contact theory are slightly inadequate. A methodology to calculate the coupled dynamic response between a railway vehicle and a track taking into account non-Hertzian contact models is presented. The overall system is modeled using a substructuring method where components with linear properties (vehicle, rails and sleepers) are connected with non-linear elements (wheel-rail contact, railpads and ballast). Numerical methods are used to pre-calculate contact elastic properties which are introduced into the whole system like a non-linear relationship between wheel and rail displacements in the contact point. Results ob...
Journal of Computational and Applied Mathematics, 2015
ABSTRACT This work presents a mathematical approach based on the point collocation technique to c... more ABSTRACT This work presents a mathematical approach based on the point collocation technique to compute the transmission loss of perforated dissipative silencers with transversal temperature gradients and mean flow. Three-dimensional wave propagation is considered in silencer geometries with arbitrary, but axially uniform, cross section. To reduce the computational requirements of a full multidimensional finite element calculation, a method is developed combining axial and transversal solutions of the wave equation. First, the finite element method is employed in a two-dimensional problem to extract the eigenvalues and associated eigenvectors for the silencer cross section. Mean flow as well as transversal temperature gradients and the corresponding thermal-induced material heterogeneities are included in the model. In addition, an axially uniform temperature field is taken into account, its value being the inlet/outlet average. A point collocation technique is then used to match the acoustic fields (pressure and axial acoustic velocity) at the geometric discontinuities between the silencer chamber and the inlet and outlet pipes. Transmission loss predictions are compared favorably with a general three-dimensional finite element approach, offering a reduction in the computational effort.
ABSTRACT A finite element approach is proposed for the acoustic analysis of automotive silencers ... more ABSTRACT A finite element approach is proposed for the acoustic analysis of automotive silencers including a perforated duct with uniform axial mean flow and an outer chamber with heterogeneous absorbent material. This material can be characterized by means of its equivalent acoustic properties, considered coordinate-dependent via the introduction of a heterogeneous bulk density, and the corresponding material airflow resistivity variations. An approach has been implemented to solve the pressure wave equation for a nonmoving heterogeneous medium, associated with the problem of sound propagation in the outer chamber. On the other hand, the governing equation in the central duct has been solved in terms of the acoustic velocity potential considering the presence of a moving medium. The coupling between both regions and the corresponding acoustic fields has been carried out by means of a perforated duct and its acoustic impedance, adapted here to include absorbent material heterogeneities and mean flow effects simultaneously. It has been found that bulk density heterogeneities have a considerable influence on the silencer transmission loss.
ABSTRACT This article presents a technique for modelling the dynamic response of rotating flexibl... more ABSTRACT This article presents a technique for modelling the dynamic response of rotating flexible solids with internal modal damping. The method is applicable to solids with geometry of revolution that rotate around their main axis at constant spinning velocity. The model makes use of an Eulerian modal coordinate system which adopts the vibration modes in a non-rotating frame as basis functions. Due to the coordinate system, the technique is particularly suitable for studying the dynamic interaction between rotating solids and non-rotating structures and permits to obtain Frequency Response Functions. The current investigation presents the development of the proposed technique from a previous Lagrangian model, and consequently the mathematical relationships between the two coordinate sets are found. The approach has been adopted to study the dynamics of a simply supported cylinder including damping in order to obtain the receptance function and the modal properties of the rotating solid.
Journal of Computational and Applied Mathematics, 2015
ABSTRACT This work presents a mathematical approach based on the point collocation technique to c... more ABSTRACT This work presents a mathematical approach based on the point collocation technique to compute the transmission loss of perforated dissipative silencers with transversal temperature gradients and mean flow. Three-dimensional wave propagation is considered in silencer geometries with arbitrary, but axially uniform, cross section. To reduce the computational requirements of a full multidimensional finite element calculation, a method is developed combining axial and transversal solutions of the wave equation. First, the finite element method is employed in a two-dimensional problem to extract the eigenvalues and associated eigenvectors for the silencer cross section. Mean flow as well as transversal temperature gradients and the corresponding thermal-induced material heterogeneities are included in the model. In addition, an axially uniform temperature field is taken into account, its value being the inlet/outlet average. A point collocation technique is then used to match the acoustic fields (pressure and axial acoustic velocity) at the geometric discontinuities between the silencer chamber and the inlet and outlet pipes. Transmission loss predictions are compared favorably with a general three-dimensional finite element approach, offering a reduction in the computational effort.
ABSTRACT A finite element approach is proposed for the acoustic analysis of automotive silencers ... more ABSTRACT A finite element approach is proposed for the acoustic analysis of automotive silencers including a perforated duct with uniform axial mean flow and an outer chamber with heterogeneous absorbent material. This material can be characterized by means of its equivalent acoustic properties, considered coordinate-dependent via the introduction of a heterogeneous bulk density, and the corresponding material airflow resistivity variations. An approach has been implemented to solve the pressure wave equation for a nonmoving heterogeneous medium, associated with the problem of sound propagation in the outer chamber. On the other hand, the governing equation in the central duct has been solved in terms of the acoustic velocity potential considering the presence of a moving medium. The coupling between both regions and the corresponding acoustic fields has been carried out by means of a perforated duct and its acoustic impedance, adapted here to include absorbent material heterogeneities and mean flow effects simultaneously. It has been found that bulk density heterogeneities have a considerable influence on the silencer transmission loss.
An analytical description of the acoustic performance of mufflers with elliptical cross-section h... more An analytical description of the acoustic performance of mufflers with elliptical cross-section has been obtained via the point source method and truncated modal superposition. First, the problem of natural frequencies and mode shapes has been addressed considering the Helmholtz equation in an elliptical domain, whose solution can be expressed by means of Mathieu functions. Then, the frequency response functions of the muffler have been evaluated, so that its acoustic performance is completely defined. The results obtained compare well with those obtained from finite element calculations, and with experimental measurements.
Acoustic transfer matrices are commonly found in the finite element modelling of devices associat... more Acoustic transfer matrices are commonly found in the finite element modelling of devices associated with the exhaust system of internal combustion engines. These matrices provide a relationship between the acoustic fields (usually pressure and velocity) associated with the nodes located at both sides of a particular region. For example, the acoustic behaviour of catalytic converters can be properly predicted if the monolith is replaced by a transfer matrix. In this case, only one-dimensional acoustic behaviour is allowed for the capillary ducts, while three-dimensional acoustic waves can still be present in the inlet/outlet and tapered ducts. In the previous problem, the finite element meshes considered in the bibliography are conforming at the connected interfaces, therefore leading to a straightforward evaluation of the coupling integrals. From a practical point of view, however, and to gain flexibility for the discretization, it is worth developing a procedure for connecting acou...
Railway vehicles running with wheel tread defects are known to cause abnormally high forces betwe... more Railway vehicles running with wheel tread defects are known to cause abnormally high forces between wheel and rail which reduce the life of track and vehicle components. Hertzian wheel-rail contact model is used by most of the vehicle-track dynamic interaction models at present. However, for wheel tread defects like shells or fresh wheel flats the assumptions of Hertzian contact theory are slightly inadequate. A methodology to calculate the coupled dynamic response between a railway vehicle and a track taking into account non-Hertzian contact models is presented. The overall system is modeled using a substructuring method where components with linear properties (vehicle, rails and sleepers) are connected with non-linear elements (wheel-rail contact, railpads and ballast). Numerical methods are used to pre-calculate contact elastic properties which are introduced into the whole system like a non-linear relationship between wheel and rail displacements in the contact point. Results ob...
Journal of Computational and Applied Mathematics, 2015
ABSTRACT This work presents a mathematical approach based on the point collocation technique to c... more ABSTRACT This work presents a mathematical approach based on the point collocation technique to compute the transmission loss of perforated dissipative silencers with transversal temperature gradients and mean flow. Three-dimensional wave propagation is considered in silencer geometries with arbitrary, but axially uniform, cross section. To reduce the computational requirements of a full multidimensional finite element calculation, a method is developed combining axial and transversal solutions of the wave equation. First, the finite element method is employed in a two-dimensional problem to extract the eigenvalues and associated eigenvectors for the silencer cross section. Mean flow as well as transversal temperature gradients and the corresponding thermal-induced material heterogeneities are included in the model. In addition, an axially uniform temperature field is taken into account, its value being the inlet/outlet average. A point collocation technique is then used to match the acoustic fields (pressure and axial acoustic velocity) at the geometric discontinuities between the silencer chamber and the inlet and outlet pipes. Transmission loss predictions are compared favorably with a general three-dimensional finite element approach, offering a reduction in the computational effort.
ABSTRACT A finite element approach is proposed for the acoustic analysis of automotive silencers ... more ABSTRACT A finite element approach is proposed for the acoustic analysis of automotive silencers including a perforated duct with uniform axial mean flow and an outer chamber with heterogeneous absorbent material. This material can be characterized by means of its equivalent acoustic properties, considered coordinate-dependent via the introduction of a heterogeneous bulk density, and the corresponding material airflow resistivity variations. An approach has been implemented to solve the pressure wave equation for a nonmoving heterogeneous medium, associated with the problem of sound propagation in the outer chamber. On the other hand, the governing equation in the central duct has been solved in terms of the acoustic velocity potential considering the presence of a moving medium. The coupling between both regions and the corresponding acoustic fields has been carried out by means of a perforated duct and its acoustic impedance, adapted here to include absorbent material heterogeneities and mean flow effects simultaneously. It has been found that bulk density heterogeneities have a considerable influence on the silencer transmission loss.
ABSTRACT This article presents a technique for modelling the dynamic response of rotating flexibl... more ABSTRACT This article presents a technique for modelling the dynamic response of rotating flexible solids with internal modal damping. The method is applicable to solids with geometry of revolution that rotate around their main axis at constant spinning velocity. The model makes use of an Eulerian modal coordinate system which adopts the vibration modes in a non-rotating frame as basis functions. Due to the coordinate system, the technique is particularly suitable for studying the dynamic interaction between rotating solids and non-rotating structures and permits to obtain Frequency Response Functions. The current investigation presents the development of the proposed technique from a previous Lagrangian model, and consequently the mathematical relationships between the two coordinate sets are found. The approach has been adopted to study the dynamics of a simply supported cylinder including damping in order to obtain the receptance function and the modal properties of the rotating solid.
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