Precision analysis and dynamic stability in the numerical solution of the two-dimensional wheel/rail tangential contact problem

This is an Accepted Manuscript of an article published by Taylor & Francis in Vehicle System Dynamics on 2018, available online: https://doi.org/10.1080/00423114.2018.1552365[EN] In this paper the two-dimensional contact problem is analysed through different mesh topologies and strategies for approaching equations, namely; the collocation method, Galerkin, and the polynomial approach. The two-dimensional asymptotic problem (linear theory) associated with very small creepage (or infinite friction coefficient) is taken as a reference in order to analyse the numerical methods, and its solution is tackled in three different ways, namely steady-state problem, dynamic stability problem, and non-steady state problem in the frequency domain. In addition, two elastic displacements derivatives calculation methods are explored: analytic and finite differences. The results of this work establish the calculation conditions that are necessary to guarantee dynamic stability and the absence of numerical singularities, as well as the parameters for using the method that allows for maximum precision at the minimum computational cost to be reached.The authors gratefully acknowledge the financial support of the Spanish Ministry of Economy, Industry and Competitiveness and the European Regional Development Fund (project TRA2017-84701-R), as well as the European Commission through the projects 'RUN2Rail - Innovative RUNning gear soluTiOns for new dependable, sustainable, intelligent and comfortable RAIL vehicles' (Horizon 2020 Shift2Rail JU call 2017, grant number 777564) and 'PIVOT - Performance Improvement for Vehicles On Track' (Horizon 2020 Shift2Rail JU call 2017, grant number 777629).Giménez, JG.; Alonso Pazos, A.; Baeza González, LM. (2018). Precision analysis and dynamic stability in the numerical solution of the two-dimensional wheel/rail tangential contact problem. Vehicle System Dynamics. 57(12):1822-1846. https://doi.org/10.1080/00423114.2018.1552365S182218465712Rodríguez-Tembleque, L., Abascal, R., & Aliabadi, M. H. (2012). Anisotropic wear framework for 3D contact and rolling problems. Computer Methods in Applied Mechanics and Engineering, 241-244, 1-19. doi:10.1016/j.cma.2012.05.025On the action of a locomotive driving wheel. (1926). Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 112(760), 151-157. doi:10.1098/rspa.1926.0100Kalker JJ. On the rolling contact of two elastic bodies in the presence of dry friction [PhD Thesis]. Delft University of Technology, 1973.KALKER, J. J. (1977). Variational Principles of Contact Elastostatics. IMA Journal of Applied Mathematics, 20(2), 199-219. doi:10.1093/imamat/20.2.199Kalker, J. J. (1990). Three-Dimensional Elastic Bodies in Rolling Contact. Solid Mechanics and Its Applications. doi:10.1007/978-94-015-7889-9Giner, J., Baeza, L., Vila, P., & Alonso, A. (2017). Study of the Falling Friction Effect on Rolling Contact Parameters. Tribology Letters, 65(1). doi:10.1007/s11249-016-0810-8KALKER, J. J. (1982). A Fast Algorithm for the Simplified Theory of Rolling Contact. Vehicle System Dynamics, 11(1), 1-13. doi:10.1080/00423118208968684Giménez, J., Alonso, A., & Gómez *, E. (2005). Introduction of a friction coefficient dependent on the slip in the FastSim algorithm. Vehicle System Dynamics, 43(4), 233-244. doi:10.1080/00423110412331282913Guiral, A., Alonso, A., Baeza, L., & Giménez, J. G. (2013). Non-steady state modelling of wheel–rail contact problem. Vehicle System Dynamics, 51(1), 91-108. doi:10.1080/00423114.2012.713499Baeza, L., Vila, P., Roda, A., & Fayos, J. (2008). Prediction of corrugation in rails using a non-stationary wheel-rail contact model. Wear, 265(9-10), 1156-1162. doi:10.1016/j.wear.2008.01.024Hu, G., & Wriggers, P. (2002). On the adaptive finite element method of steady-state rolling contact for hyperelasticity in finite deformations. Computer Methods in Applied Mechanics and Engineering, 191(13-14), 1333-1348. doi:10.1016/s0045-7825(01)00326-7KNOTHE, K., & GROSS-THEBING, A. (1986). Derivation of Frequency Dependent Creep Coefficients Based on an Elastic Half-Space Model. Vehicle System Dynamics, 15(3), 133-153. doi:10.1080/00423118608968848Galin LA. Contact Problems in the Theory of Elasticity, Department of Mathematics, School of Physical Sciences and Applied Mathematics, North Carolina State College, 1961

A linear non-Hertzian unsteady tangential wheel-rail contact model

[EN] The increase in computational capacity has considerably reduced the use of linear models for wheel/rail tangential contact, being currently replaced by theories that adopt non-linear formulations able to address the most complex conditions realistically. However, linear formulations are difficult to replace in certain applications such as acoustic problem modelling, in which case a linear formulation of the track-contact-vehicle system is needed. The vibration that appears in this type of problem covers a wide range of audible frequencies, so, in addition to linearity, these theories are required to be non-stationary. The literature in contact mechanics gives response to this problem through models that consider low creepage levels, but it remains to cover other conditions in which the mean creepage is not small, such as when a railway vehicle negotiates a curve. This work presents a new theory of unsteady linear tangential rolling contact for non-Hertzian areas that considers kinematics as the sum of a constant creepage resulting from large stationary forces (such as those that occur when the vehicle negotiates a curve with constant radius) and small variable creepage due to a high-frequency phenomenon (e.g. the dynamic interaction between the vehicle and the track). The model is based on the Variational Theory (i.e. the CONTACT method for tangential problems), from which a linear formulation with variable creepage is deduced. According to this formulation, the non-steady state contact problem can be solved for any shape of the wheel/rail contact region, requiring a much smaller computational effort than the general unsteady CONTACT approach. The results show a satisfactory agreement of the proposed model to the unsteady CONTACT version, hence confirming the soundness of the proposed contact model.The first and third authors acknowledge the financial support through the grants PID2020-118013RB-C21 (funded by MCIN/AEI/10.13039/501100011033) and PROMETEO/2021/046 (funded by Generalitat Valenciana).Baeza González, LM.; Bruni, S.; Giner Navarro, J.; Liu, B. (2023). A linear non-Hertzian unsteady tangential wheel-rail contact model. Tribology International. 181:1-10. https://doi.org/10.1016/j.triboint.2023.10834511018

Simulation of the evolution of rail corrugation using a rotating flexible wheelset model

[EN] This paper presents a simulation tool designed for predicting the wear pattern on the running surface of the rails and for studying the evolution of rail corrugation after thousands of wheelset passages. This simulation tool implements a cyclic track model, a rotating flexible wheelset model, a wheel-rail contact model and a wear model. The vehicle-track system is modelled by using a substructuring technique, by which the vehicle, the rails and the sleepers are treated independently of each other and are coupled by the forces transmitted through the wheel-rail contact and the railpad. The vehicle model takes only account of the wheelset since the sprung masses of the vehicle are not relevant in the frequency range analysed. The wheelset model considers the flexibility of the wheelset and the effects associated with rotation. By using the Campbell diagram, two cases have been identified in which the combined effect of two different modes may give rise to higher wheel-rail contact forces and wear. © 2011 Taylor & Francis.The authors gratefully acknowledge the support for this work provided by the Project TRA2010-15669 (Ministerio de Ciencia e Innovacion) and the valuable help of P. Torstensson from Chalmers University, who suggested the use of the Campbell diagram in this investigation.Vila Tortosa, MP.; Fayos Sancho, J.; Baeza González, LM. (2011). Simulation of the evolution of rail corrugation using a rotating flexible wheelset model. Vehicle System Dynamics. 49(11):1749-1769. https://doi.org/10.1080/00423114.2011.552619S17491769491

A fast version of 'CONTACT' for normal problem calculations

[EN] In its different versions, the CONTACT method developed by Prof. Kalker is the primary reference in wheel-rail contact mechanics. Despite adopting simplifications associated with the elastic behaviour of the solids and being a non-conformal contact theory, CONTACT provides precise solutions for most wheel-rail contact conditions, with lower computational and modelling costs than other numerical methods such as Finite Elements. Nevertheless, the computational cost of CONTACT is still too high for its implementation in dynamic simulation. The present work proposes a fast and accurate wheel-rail contact method for normal problems based on Kalker's CONTACT algorithm. Dissimilarly to CONTACT, the new method formulates the normal traction distribution through a suitable basis, which reduces the dimension of the problem. This method is able to faithfully reproduce the contact patch and the normal traction distribution, even when the yaw angle of the wheelset is non-zero. Results obtained with this method are compared with the ones calculated with CONTACT, and errors about 0.05% are obtained in normal contact forces, with a reduction on the computation cost between 30 and 60 times.Grant PRE2018-084067 funded by MCIN/AEI/10.13039/501100011033 and by the EU program "ESF Investing in your future". Grant PID2020-118013RB-C21 funded by MCIN/AEI/10.13039/501100011033. Grant PROMETEO/2021/046 funded by Generalitat Valenciana.Giner Navarro, J.; Gómez-Bosch, J.; Alonso, A.; Baeza González, LM. (2023). A fast version of 'CONTACT' for normal problem calculations. Wear. 530-531:1-12. https://doi.org/10.1016/j.wear.2023.205074112530-53

Development of a simulation tool for the dynamic analysis of railway vehicle - Track interaction

[EN] The importance of modelling and simulation in the field of railway systems has greatly increased in the last decades. Various commercial simulation packages have been developed and are used to analyse the dynamic performance of railway systems. However, although sometimes the user needs to analyse various non-standard solutions, the possibility to integrate further modifications into the structure of such software is quite limited. Therefore, in some cases, in particular for specific modelling and analysis tasks, a feasible option is to develop flexible and robust simulation tools capable of using different configurations by modifying the models performing the dynamic analysis. The paper presents the mathematical modelling background and the conceptual design of a new of a new computational tool for the dynamic simulation of railway vehicle systems. The formulations employed in the proposed mathematical model are based on the multibody techniques. The developed model uses a combined frame of references that allows the use of independent coordinates without the possibility to have singularity configurations depending on the rotation sequence. The simulation tool is designed in a flexible form that enables the study of different configurations of the railway vehicles, as well as various track combinations.Shaltout, R.; Ulianov, C.; Baeza González, LM. (2015). Development of a simulation tool for the dynamic analysis of railway vehicle - Track interaction. Transport Problems. 10:47-58. doi:10.21307/tp-2015-061S47581

PACDIN statement of methods

This is an Accepted Manuscript of an article published by Taylor & Francis in Vehicle System Dynamics on 2014 available online: https://doi.org/10.1080/00423114.2014.963126[EN] PAntograph-Catenary Dynamic Interaction (PACDIN) is a code developed by the vehicle technology research centre (CITV) of the Universitat Politecnica de Valencia in collaboration with the railway company Talgo S.L. The model of the catenary is a finite element model using absolute nodal coordinates. It is based on a general formulation that can be applied for analysing a wide range of catenary configurations, including stitch wire, transitions or non-straight path tracks. The formulation is fully non-linear and includes large deformations, dropper slackening and contact interaction. The model is linearised when deformations are small, as in the case of the benchmark dynamic analysis. The results of the PACDIN code show a good agreement with the average results of other benchmark codes.The authors wish to thank Generatitat Valenciana for the financial support received in the framework of the PROMETEO 2012/023 Programme.Tur Valiente, M.; Baeza González, LM.; Fuenmayor Fernández, F.; Garcia, E. (2014). PACDIN statement of methods. Vehicle System Dynamics. 53(3):402-411. https://doi.org/10.1080/00423114.2014.963126S402411533Shabana, A. A. (1998). Nonlinear Dynamics, 16(3), 293-306. doi:10.1023/a:1008072517368BERZERI, M., & SHABANA, A. A. (2000). DEVELOPMENT OF SIMPLE MODELS FOR THE ELASTIC FORCES IN THE ABSOLUTE NODAL CO-ORDINATE FORMULATION. Journal of Sound and Vibration, 235(4), 539-565. doi:10.1006/jsvi.1999.2935Gerstmayr, J., & Shabana, A. A. (2006). Analysis of Thin Beams and Cables Using the Absolute Nodal Co-ordinate Formulation. Nonlinear Dynamics, 45(1-2), 109-130. doi:10.1007/s11071-006-1856-1Tur, M., García, E., Baeza, L., & Fuenmayor, F. J. (2014). A 3D absolute nodal coordinate finite element model to compute the initial configuration of a railway catenary. Engineering Structures, 71, 234-243. doi:10.1016/j.engstruct.2014.04.015Collina, A., & Bruni, S. (2002). Numerical Simulation of Pantograph-Overhead Equipment Interaction. Vehicle System Dynamics, 38(4), 261-291. doi:10.1076/vesd.38.4.261.828

Rail corrugation growth accounting for the flexibility and rotation of the wheel set and the non-Hertzian and non-steady-state effects at contact patch

[EN] In this work, a simulation tool is developed to analyse the growth of rail corrugation consisting of several models connected in a feedback loop in order to account for both the short-term dynamic vehicle track interaction and the long-term damage. The time-domain vehicle track interaction model comprises a flexible rotating wheel set model, a cyclic track model based on a substructuring technique and a non-Hertzian and non-steady-state three-dimensional wheel rail contact model, based on the variational theory by Kalker. Wear calculation is performed with Archard s wear model by using the contact parameters obtained with the non-Hertzian and non-steady-state three-dimensional contact model. The aim of this paper is to analyse the influence of the excitation of two coinciding resonances of the flexible rotating wheel set on the rail corrugation growth in the frequency range from 20 to 1500 Hz, when contact conditions similar to those that can arise while a wheel set is negotiating a gentle curve are simulated. Numerical results show that rail corrugation grows only on the low rail for two cases in which two different modes of the rotating wheel set coincide in frequency. In the first case, identified by using the Campbell diagram, the excitation of both the backward wheel mode and the forward third bending mode of the wheel set model (B-F modes) promotes the growth of rail corrugation with a wavelength of 110mm for a vehicle velocity of 142 km/h. In the second case, the excitation of both the backward wheel mode and the backward third bending mode (B-B modes) gives rise to rail corrugation growth at a wavelength of 156 mm when the vehicle velocity is 198 km/h.The authors acknowledge the financial contribution by the Spanish Ministry of Economy and Competitiveness through the project TRA2010-15669.Vila Tortosa, MP.; Baeza González, LM.; Martínez Casas, J.; Carballeira, J. (2014). Rail corrugation growth accounting for the flexibility and rotation of the wheel set and the non-Hertzian and non-steady-state effects at contact patch. Vehicle System Dynamics. 52:92-108. https://doi.org/10.1080/00423114.2014.881513S9210852Grassie, S. L., & Kalousek, J. (1993). Rail Corrugation: Characteristics, Causes and Treatments. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 207(1), 57-68. doi:10.1243/pime_proc_1993_207_227_02Hempelmann, K., Hiss, F., Knothe, K., & Ripke, B. (1991). The formation of wear patterns on rail tread. Wear, 144(1-2), 179-195. doi:10.1016/0043-1648(91)90014-lHempelmann, K., & Knothe, K. (1996). An extended linear model for the prediction of short pitch corrugation. Wear, 191(1-2), 161-169. doi:10.1016/0043-1648(95)06747-7GRASSIE, S. L., & ELKINS, J. A. (1998). RAIL CORRUGATION ON NORTH AMERICAN TRANSIT SYSTEMS. Vehicle System Dynamics, 29(sup1), 5-17. doi:10.1080/00423119808969548Egana, J. I., Vinolas, J., & Seco, M. (2006). Investigation of the influence of rail pad stiffness on rail corrugation on a transit system. Wear, 261(2), 216-224. doi:10.1016/j.wear.2005.10.004Igeland, A. (1996). Railhead Corrugation Growth Explained by Dynamic Interaction between Track and Bogie Wheelsets. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 210(1), 11-20. doi:10.1243/pime_proc_1996_210_322_02Gómez, I., & Vadillo, E. G. (2003). A linear model to explain short pitch corrugation on rails. Wear, 255(7-12), 1127-1142. doi:10.1016/s0043-1648(03)00282-5Collette, C., Vanhonacker, P., Bastaits, R., & Levy, D. (2008). Comparison between time and frequency studies of a corrugated curve of RER Paris network. Wear, 265(9-10), 1249-1258. doi:10.1016/j.wear.2008.01.030Daniel, W. J. T., Horwood, R. J., Meehan, P. A., & Wheatley, N. (2008). Analysis of rail corrugation in cornering. Wear, 265(9-10), 1183-1192. doi:10.1016/j.wear.2008.02.030Fayos, J., Baeza, L., Denia, F. D., & Tarancón, J. E. (2007). An Eulerian coordinate-based method for analysing the structural vibrations of a solid of revolution rotating about its main axis. Journal of Sound and Vibration, 306(3-5), 618-635. doi:10.1016/j.jsv.2007.05.051Baeza, L., & Ouyang, H. (2011). A railway track dynamics model based on modal substructuring and a cyclic boundary condition. Journal of Sound and Vibration, 330(1), 75-86. doi:10.1016/j.jsv.2010.07.023Kalker, J. J. (1990). Three-Dimensional Elastic Bodies in Rolling Contact. Solid Mechanics and Its Applications. doi:10.1007/978-94-015-7889-9Xie, G., & Iwnicki, S. D. (2008). Simulation of wear on a rough rail using a time-domain wheel–track interaction model. Wear, 265(11-12), 1572-1583. doi:10.1016/j.wear.2008.03.016Igeland, A., & Ilias, H. (1997). Rail head corrugation growth predictions based on non-linear high frequency vehicle/track interaction. Wear, 213(1-2), 90-97. doi:10.1016/s0043-1648(97)00172-5Vila, P., Fayos, J., & Baeza, L. (2011). Simulation of the evolution of rail corrugation using a rotating flexible wheelset model. Vehicle System Dynamics, 49(11), 1749-1769. doi:10.1080/00423114.2011.552619Popp, K., Kruse, H., & Kaiser, I. (1999). Vehicle-Track Dynamics in the Mid-Frequency Range. Vehicle System Dynamics, 31(5-6), 423-464. doi:10.1076/vesd.31.5.423.8363Johnson, K. L. (1985). Contact Mechanics. doi:10.1017/cbo9781139171731Hiensch, M., Nielsen, J. C. O., & Verheijen, E. (2002). Rail corrugation in The Netherlands—measurements and simulations. Wear, 253(1-2), 140-149. doi:10.1016/s0043-1648(02)00093-5Jin, X., Xiao, X., Wen, Z., Guo, J., & Zhu, M. (2009). An investigation into the effect of train curving on wear and contact stresses of wheel and rail. Tribology International, 42(3), 475-490. doi:10.1016/j.triboint.2008.08.004Ilias, H., & Müller, S. (1994). A discrete-continuous track-model for wheelsets rolling over short wavelength sinusoidal rail irregularities. Vehicle System Dynamics, 23(sup1), 221-233. doi:10.1080/0042311930896951

Numerical mode matching for sound propagation in silencers with granular material

[EN] This work presents an efficient numerical approach based on the combination of the mode matching technique and the finite element method (FEM) to model the sound propagation in silencers containing granular material and to evaluate their acoustic performance through the computation of transmission loss (TL). The methodology takes into account the presence of three-dimensional (3D) waves and the corresponding higher order modes, while reducing the computational expenditure of a full 3D FEM calculation. First, the wavenumbers and transversal pressure modes associated with the silencer cross section are obtained by means of a two-dimensional FEM eigenvalue problem, which allows the consideration of arbitrary transversal geometries and material heterogeneities. The numerical approach considers the possibility of using different filling levels of granular material, giving rise to cross sections with abrupt changes of properties located not only in the usual central perforated passage, but also in the transition between air and material, that involves a significant change in porosity. After solving the eigenvalue problem, the acoustic fields (acoustic pressure and axial velocity) are coupled at geometric discontinuities between ducts through the compatibility conditions to obtain the complete solution of the wave equation and the acoustic performance (TL). The granular material is analysed as a potential alternative to the traditional dissipative silencers incorporating fibrous absorbent materials. Sound propagation in granular materials can be modelled through acoustic equivalent properties, such as complex and frequency dependent density and speed of sound. TL results computed by means of the numerical approach proposed here show good agreement with full 3D FEM calculations and experimental measurements. As expected, the numerical mode matching outperforms the computational expenditure of the full 3D FEM approach. Different configurations have been studied to determine the influence on the TL of several parameters such as the size of the material grains, the filling level of the chamber, the granular material porosity and the geometry of the silencer cross section.Project supported by a 2016 BBVA Foundation, Spain Grant for Researchers and Cultural Creators. The BBVA Foundation takes no responsibility for the opinions, remarks or content included in the project and/or the results thereof, which are the sole responsibility of the authors. Support of Generalitat Valenciana (Conselleria d'Educacio, Investigacid, Cultura i Esport), Spain through project Prometeo/2016/007 is also acknowledged.Sánchez Orgaz, EM.; Denia Guzmán, FD.; Baeza González, LM.; Kirby, R. (2019). Numerical mode matching for sound propagation in silencers with granular material. Journal of Computational and Applied Mathematics. 350:233-246. https://doi.org/10.1016/j.cam.2018.10.030S233246350Denia, F. D., Sánchez-Orgaz, E. M., Martínez-Casas, J., & Kirby, R. (2015). Finite element based acoustic analysis of dissipative silencers with high temperature and thermal-induced heterogeneity. Finite Elements in Analysis and Design, 101, 46-57. doi:10.1016/j.finel.2015.04.004Astley, R. J. (1996). FE mode-matching schemes for the exterior Helmholtz problem and their relationship to the FE-DtN approach. Communications in Numerical Methods in Engineering, 12(4), 257-267. doi:10.1002/(sici)1099-0887(199604)12:43.0.co;2-8Glav, R. (1996). THE POINT-MATCHING METHOD ON DISSIPATIVE SILENCERS OF ARBITRARY CROSS-SECTION. Journal of Sound and Vibration, 189(1), 123-135. doi:10.1006/jsvi.1996.0009GLAV, R. (2000). THE TRANSFER MATRIX FOR A DISSIPATIVE SILENCER OF ARBITRARY CROSS-SECTION. Journal of Sound and Vibration, 236(4), 575-594. doi:10.1006/jsvi.2000.2994Kirby, R. (2003). Transmission loss predictions for dissipative silencers of arbitrary cross section in the presence of mean flow. The Journal of the Acoustical Society of America, 114(1), 200-209. doi:10.1121/1.1582448Kirby, R. (2009). A comparison between analytic and numerical methods for modelling automotive dissipative silencers with mean flow. Journal of Sound and Vibration, 325(3), 565-582. doi:10.1016/j.jsv.2009.03.032Fang, Z., & Ji, Z. L. (2014). Numerical Mode Matching Approach for Acoustic Attenuation Predictions of Double-Chamber Perforated Tube Dissipative Silencers with Mean Flow. Journal of Computational Acoustics, 22(02), 1450004. doi:10.1142/s0218396x14500040Yang, L., Ji, Z. L., & Wu, T. W. (2015). Transmission loss prediction of silencers by using combined boundary element method and point collocation approach. Engineering Analysis with Boundary Elements, 61, 265-273. doi:10.1016/j.enganabound.2015.08.004Denia, F. D., Sánchez-Orgaz, E. M., Baeza, L., & Kirby, R. (2016). Point collocation scheme in silencers with temperature gradient and mean flow. Journal of Computational and Applied Mathematics, 291, 127-141. doi:10.1016/j.cam.2015.02.007Kirby, R. (2008). Modeling sound propagation in acoustic waveguides using a hybrid numerical method. The Journal of the Acoustical Society of America, 124(4), 1930-1940. doi:10.1121/1.2967837Denia, F. D., Martínez-Casas, J., Carballeira, J., Nadal, E., & Fuenmayor, F. J. (2018). Computational performance of analytical methods for the acoustic modelling of automotive exhaust devices incorporating monoliths. Journal of Computational and Applied Mathematics, 330, 995-1006. doi:10.1016/j.cam.2017.03.010Allard, J. F., & Atalla, N. (2009). Propagation of Sound in Porous Media. doi:10.1002/9780470747339Li, J., Zhao, S., & Ishihara, K. (2013). Study on acoustical properties of sintered bronze porous material for transient exhaust noise of pneumatic system. Journal of Sound and Vibration, 332(11), 2721-2734. doi:10.1016/j.jsv.2012.12.031Cobo, P., & Simón, F. (2016). A comparison of impedance models for the inverse estimation of the non-acoustical parameters of granular absorbers. Applied Acoustics, 104, 119-126. doi:10.1016/j.apacoust.2015.11.006Kirby, R., & Lawrie, J. B. (2005). A point collocation approach to modelling large dissipative silencers. Journal of Sound and Vibration, 286(1-2), 313-339. doi:10.1016/j.jsv.2004.10.016Murphy, J. E., & Chin‐Bing, S. A. (1989). A finite‐element model for ocean acoustic propagation and scattering. The Journal of the Acoustical Society of America, 86(4), 1478-1483. doi:10.1121/1.398708Pierce, A. D. (1990). Wave equation for sound in fluids with unsteady inhomogeneous flow. The Journal of the Acoustical Society of America, 87(6), 2292-2299. doi:10.1121/1.399073Selamet, A., & Ji, Z. L. (1998). ACOUSTIC ATTENUATION PERFORMANCE OF CIRCULAR EXPANSION CHAMBERS WITH OFFSET INLET/OUTLET: I. ANALYTICAL APPROACH. Journal of Sound and Vibration, 213(4), 601-617. doi:10.1006/jsvi.1998.1514Selamet, A., Xu, M. B., Lee, I.-J., & Huff, N. T. (2005). Analytical approach for sound attenuation in perforated dissipative silencers with inlet/outlet extensions. The Journal of the Acoustical Society of America, 117(4), 2078-2089. doi:10.1121/1.1867884Denia, F. D., Selamet, A., Fuenmayor, F. J., & Kirby, R. (2007). Acoustic attenuation performance of perforated dissipative mufflers with empty inlet/outlet extensions. Journal of Sound and Vibration, 302(4-5), 1000-1017. doi:10.1016/j.jsv.2007.01.005Payri, F., Broatch, A., Salavert, J. M., & Moreno, D. (2010). Acoustic response of fibrous absorbent materials to impulsive transient excitations. Journal of Sound and Vibration, 329(7), 880-892. doi:10.1016/j.jsv.2009.10.015P. Glover, Petrophysics MSc Course Notes, MSc Lecture Notes, University of Leeds

Dynamics of damped rotating solids of revolution through an Eulerian modal approach

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.The authors gratefully acknowledge the support for this work provided by the Project TRA2010-15669 (Ministerio de Ciencia e Innovacion).Martínez Casas, J.; Fayos Sancho, J.; Denia Guzmán, FD.; Baeza González, LM. (2012). Dynamics of damped rotating solids of revolution through an Eulerian modal approach. Journal of Sound and Vibration. 331(4):868-882. https://doi.org/10.1016/j.jsv.2011.10.003S868882331

Acoustic modelling of large aftertreatment devices with multimodal incident sound fields

[EN] The influence of multimodal incident sound fields on the acoustic behaviour of large aftertreatment devices (ATD) is analysed in detail. The mode matching method is applied to the compatibility conditions of the three-dimensional (3D) acoustic fields at the device geometric discontinuities, leading to the computation of the complex wave amplitudes in all the subdomains involved and the corresponding transmission loss (TL). To have a realistic model, 3D propagation must be considered in the inlet/outlet ducts and chambers, while 1D wave propagation has to be assumed along the small capillaries of the catalytic converter/particulate filter monoliths of the ATD; therefore, these monoliths can be replaced by plane wave four pole transfer matrices from an acoustical point of view [1]. On the other hand, for large ATD inlet ducts such as those found in heavy-duty and off-road engines, the usual models with plane incident wave excitation are not accurate since the onset of higher order incident modes in the inlet duct is expected for the frequency range of interest. Therefore, a TL variation is likely to occur depending on these modes, similar to the results found in large dissipative silencers [2]. Results are presented for three different multimodal incident sound field hypotheses [3]: equal modal amplitude (EMA), equal modal power (EMP) and equal modal energy density (EMED). A relevant influence on the sound attenuation is found for the test problems considered in the current investigation. References [1] Denia, F. D., Martínez-Casas, J., Carballeira, J., Nadal, E., Fuenmayor, F. J., Computational performance of analytical methods for the acoustic modelling of automotive exhaust devices incorporating monoliths. Journal of Computational and Applied Mathematics, 330: 995--1006, 2018. [2] Kirby, R., Lawrie, J. B., A point collocation approach to modelling large dissipative silencers. Journal of Sound and Vibration, 286: 313--339, 2005. [3] Mechel, F. P., Formulas of Acoustics. Berlin, Springer, 2008.The authors gratefully acknowledge Grants PID2020-112886RA-I00 and PID2020-118013RB-C21 funded by MCIN/AEI/10.13039/501100011033 and Project PROMETEO/2021/046 from Generalitat Valenciana.Denia, FD.; Sánchez-Orgaz, EM.; Martínez Casas, J.; Carballeira, J.; Baeza González, LM. (2021). Acoustic modelling of large aftertreatment devices with multimodal incident sound fields. Universitat Politècnica de València. 208-215. http://hdl.handle.net/10251/19055620821