The dynamic response of a stationary truss structure made of Timoshenko beams excited by a moving... more The dynamic response of a stationary truss structure made of Timoshenko beams excited by a moving oscillator is studied in this paper. The frequencies and modes of the truss are first obtained by the finite element method and then the modes are cast in an analytical form within each element through the element shape functions. Each component beam of the stationary structure is meshed with an adaptable number of Timoshenko beam elements. During its horizontal travel and vertical vibration, the oscillator may separate from the vibrating truss and subsequently may reattach to it with impact. Both separation and reattachment with impact are studied. It is found through simulated examples that they produce a noticeable difference in the dynamic response and multiple separation and impact events are possible at high speeds.
This paper studies the latent roots and critical points of friction-induced vibration problems in... more This paper studies the latent roots and critical points of friction-induced vibration problems in which the stiffness matrix is asymmetric. The asymmetric terms are represented by a parameter or parameters related to the friction coefficient. As the parameter value increases, some latent roots of the asymmetric system change, and even become complex with positive real parts at a critical point, indicating flutter instability. A method is put forward for computing the latent roots and predicting the critical value of this parameter at the flutter instability boundary of the asymmetric system based on the receptance of the symmetric system. When measured receptances of the symmetric system (at those locations where friction forces would be acting in the corresponding asymmetric system) are available, the simulated numerical example shows that this method is efficient.
ABSTRACT This paper studies the vibration of a truss structure composed of a number of rigidly co... more ABSTRACT This paper studies the vibration of a truss structure composed of a number of rigidly connected Timoshenko beams. The excitation is provided by a moving oscillator of an unsprung mass that supports another mass through a spring (oscillator) and moves on top of the truss structure. Each component beam of the structure is meshed with a number of Timoshenko beam elements. The finite-element (FE) modes of the whole structure are first obtained for the nodes of the FE mesh and then they are converted into an analytical form that is constructed over all the elements of the top deck of the truss through the element shape functions, whereby the location of the moving oscillator is easily tracked and the displacement continuity and force equilibrium conditions at the contact point can be easily implemented. This numerical–analytical combined approach has the advantage of the versatility of the FE method in dealing with structures (trusses or frames in this paper) of arbitrary configurations and the special efficiency and convenience of the analytical method in dealing with moving loads. Vibration of the truss structure and vibration of the oscillator are studied through simulated examples. It is found that the dynamic response can be several times higher than the relevant static response at high speeds. It is also found that the dynamic contact force can be much higher than its static value and may become negative if the contact between the oscillator and the truss is assumed to be constantly maintained. Interestingly, suitably chosen parameter values can bring the dynamic response and the dynamic contact force close to their respective static values.
This article presents a technique for modelling the coupled dynamics of a railway vehicle and the... more This article presents a technique for modelling the coupled dynamics of a railway vehicle and the track. The method is especially useful for simulating the dynamics of high speed trains running on nonlinear tracks. The main hypothesis is a cyclic system: an infinite track on which there is an infinite set of identical vehicles spaced at a regular interval of distance. Thus the main problems of the finite-length track models (e.g. the waves that reflect at the end of the track and interact with the vehicle; and the time interval of integration must be shorter than the track length divided by the velocity) are avoided. The flexibility of the method can be observed from the case studies presented in the present work: a vehicle passing over a hanging sleeper, and the vehicle–track dynamics for different ballast compaction cases. The results show the influence of the hanging sleeper gap on the wheel–rail contact forces, and the bending moment at the sleeper for different ballast compaction cases.
The dynamic response of a stationary truss structure made of Timoshenko beams excited by a moving... more The dynamic response of a stationary truss structure made of Timoshenko beams excited by a moving oscillator is studied in this paper. The frequencies and modes of the truss are first obtained by the finite element method and then the modes are cast in an analytical form within each element through the element shape functions. Each component beam of the stationary structure is meshed with an adaptable number of Timoshenko beam elements. During its horizontal travel and vertical vibration, the oscillator may separate from the vibrating truss and subsequently may reattach to it with impact. Both separation and reattachment with impact are studied. It is found through simulated examples that they produce a noticeable difference in the dynamic response and multiple separation and impact events are possible at high speeds.
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 In this paper we propose a method of finding the initial equilibrium configuration of ca... more ABSTRACT In this paper we propose a method of finding the initial equilibrium configuration of cable structures discretized by finite elements applied to the shape-finding of the railway overhead system. Absolute nodal coordinate formulation finite elements, which allow for axial and bending deformation, are used for the contact and messenger wires. The other parts of the overhead system are discretized with non-linear bars or equivalent springs. The proposed method considers the constraints introduced during the assembly of the catenary, such as the position of droppers, cable tension, and height of the contact wire. The formulation is general and can be applied to different catenary configurations or transitions both in 2D and 3D with straight or curved track paths. A comparison of the results obtained for reference catenaries in the bibliography is also included.
... Paloma Vila1, Andrés Rovira1, Juan Fayos2 and Luis Baeza1* 1Dpto. ... Kaiser and K. Popp, Int... more ... Paloma Vila1, Andrés Rovira1, Juan Fayos2 and Luis Baeza1* 1Dpto. ... Kaiser and K. Popp, Interaction of elastic wheelsets and elastic rails: modelling and simulation, In Proceedings of 19th Symposium of the International Association for Vehicle System Dynamics, Milano (2005 ...
The dynamic response of a stationary truss structure made of Timoshenko beams excited by a moving... more The dynamic response of a stationary truss structure made of Timoshenko beams excited by a moving oscillator is studied in this paper. The frequencies and modes of the truss are first obtained by the finite element method and then the modes are cast in an analytical form within each element through the element shape functions. Each component beam of the stationary structure is meshed with an adaptable number of Timoshenko beam elements. During its horizontal travel and vertical vibration, the oscillator may separate from the vibrating truss and subsequently may reattach to it with impact. Both separation and reattachment with impact are studied. It is found through simulated examples that they produce a noticeable difference in the dynamic response and multiple separation and impact events are possible at high speeds.
This paper studies the latent roots and critical points of friction-induced vibration problems in... more This paper studies the latent roots and critical points of friction-induced vibration problems in which the stiffness matrix is asymmetric. The asymmetric terms are represented by a parameter or parameters related to the friction coefficient. As the parameter value increases, some latent roots of the asymmetric system change, and even become complex with positive real parts at a critical point, indicating flutter instability. A method is put forward for computing the latent roots and predicting the critical value of this parameter at the flutter instability boundary of the asymmetric system based on the receptance of the symmetric system. When measured receptances of the symmetric system (at those locations where friction forces would be acting in the corresponding asymmetric system) are available, the simulated numerical example shows that this method is efficient.
ABSTRACT This paper studies the vibration of a truss structure composed of a number of rigidly co... more ABSTRACT This paper studies the vibration of a truss structure composed of a number of rigidly connected Timoshenko beams. The excitation is provided by a moving oscillator of an unsprung mass that supports another mass through a spring (oscillator) and moves on top of the truss structure. Each component beam of the structure is meshed with a number of Timoshenko beam elements. The finite-element (FE) modes of the whole structure are first obtained for the nodes of the FE mesh and then they are converted into an analytical form that is constructed over all the elements of the top deck of the truss through the element shape functions, whereby the location of the moving oscillator is easily tracked and the displacement continuity and force equilibrium conditions at the contact point can be easily implemented. This numerical–analytical combined approach has the advantage of the versatility of the FE method in dealing with structures (trusses or frames in this paper) of arbitrary configurations and the special efficiency and convenience of the analytical method in dealing with moving loads. Vibration of the truss structure and vibration of the oscillator are studied through simulated examples. It is found that the dynamic response can be several times higher than the relevant static response at high speeds. It is also found that the dynamic contact force can be much higher than its static value and may become negative if the contact between the oscillator and the truss is assumed to be constantly maintained. Interestingly, suitably chosen parameter values can bring the dynamic response and the dynamic contact force close to their respective static values.
This article presents a technique for modelling the coupled dynamics of a railway vehicle and the... more This article presents a technique for modelling the coupled dynamics of a railway vehicle and the track. The method is especially useful for simulating the dynamics of high speed trains running on nonlinear tracks. The main hypothesis is a cyclic system: an infinite track on which there is an infinite set of identical vehicles spaced at a regular interval of distance. Thus the main problems of the finite-length track models (e.g. the waves that reflect at the end of the track and interact with the vehicle; and the time interval of integration must be shorter than the track length divided by the velocity) are avoided. The flexibility of the method can be observed from the case studies presented in the present work: a vehicle passing over a hanging sleeper, and the vehicle–track dynamics for different ballast compaction cases. The results show the influence of the hanging sleeper gap on the wheel–rail contact forces, and the bending moment at the sleeper for different ballast compaction cases.
The dynamic response of a stationary truss structure made of Timoshenko beams excited by a moving... more The dynamic response of a stationary truss structure made of Timoshenko beams excited by a moving oscillator is studied in this paper. The frequencies and modes of the truss are first obtained by the finite element method and then the modes are cast in an analytical form within each element through the element shape functions. Each component beam of the stationary structure is meshed with an adaptable number of Timoshenko beam elements. During its horizontal travel and vertical vibration, the oscillator may separate from the vibrating truss and subsequently may reattach to it with impact. Both separation and reattachment with impact are studied. It is found through simulated examples that they produce a noticeable difference in the dynamic response and multiple separation and impact events are possible at high speeds.
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 In this paper we propose a method of finding the initial equilibrium configuration of ca... more ABSTRACT In this paper we propose a method of finding the initial equilibrium configuration of cable structures discretized by finite elements applied to the shape-finding of the railway overhead system. Absolute nodal coordinate formulation finite elements, which allow for axial and bending deformation, are used for the contact and messenger wires. The other parts of the overhead system are discretized with non-linear bars or equivalent springs. The proposed method considers the constraints introduced during the assembly of the catenary, such as the position of droppers, cable tension, and height of the contact wire. The formulation is general and can be applied to different catenary configurations or transitions both in 2D and 3D with straight or curved track paths. A comparison of the results obtained for reference catenaries in the bibliography is also included.
... Paloma Vila1, Andrés Rovira1, Juan Fayos2 and Luis Baeza1* 1Dpto. ... Kaiser and K. Popp, Int... more ... Paloma Vila1, Andrés Rovira1, Juan Fayos2 and Luis Baeza1* 1Dpto. ... Kaiser and K. Popp, Interaction of elastic wheelsets and elastic rails: modelling and simulation, In Proceedings of 19th Symposium of the International Association for Vehicle System Dynamics, Milano (2005 ...
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Papers by Luis Baeza