Exact solutions for free vibration analysis of train body by Carrera unified formulation (CUF) and dynamic stiffness method (DSM)

Exact solutions for free vibration analysis of train body by Carrera unified formulation (CUF) and dynamic stiffness method (DSM)

Xiao Liu, Alfonso Pagani, Dalun Tang, Xiang Liu

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Abstract. A novel approach for free vibration analysis of train body structures is introduced by using the Carrera Unified Formulation (CUF) and Dynamic Stiffness Method (DSM). Higher-order kinematic fields are developed using the Carrera Unified Formulation, which allows for straightforward implementation of any-order theory without the need for ad hoc formulations, in the case of beam theories. In particular, the parallel axis theorem is introduced on the basis of the Taylor expansion cross-sectional displacement variables, which unifies the different shape subsections of the train into the same coordinate system. The Principle of Virtual Displacements is used to derive the governing differential equations and the associated natural boundary conditions. An exact dynamic stiffness matrix is then developed by relating the amplitudes of harmonically varying loads to those of the responses. Finally, the Wittrick–Williams (WW) algorithm was used to carry out the free vibration analysis of the train body and the natural frequencies and corresponding modal shapes are presented.

Vibration Analysis, Train Body, Parallel Axis Theorem, Carrera Unified Formulation, Dynamic Stiffness Method

Published online 9/1/2023, 8 pages
Copyright © 2023 by the author(s)
Published under license by Materials Research Forum LLC., Millersville PA, USA

Citation: Xiao Liu, Alfonso Pagani, Dalun Tang, Xiang Liu, Exact solutions for free vibration analysis of train body by Carrera unified formulation (CUF) and dynamic stiffness method (DSM), Materials Research Proceedings, Vol. 33, pp 49-56, 2023

DOI: https://doi.org/10.21741/9781644902677-8

The article was published as article 8 of the book Aerospace Science and Engineering

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

[1] Ribeiro D, Calçada R, Delgado R, Zabel MB, V. Finite-element model calibration of a railway
vehicle based on experimental modal parameters, Vehicle System Dynamics. 51 (2013) 821-856. https://doi.org/10.1080/00423114.2013.778416
[2] Zaouk AK, Marzougui D, Bedewi NE. Development of a Detailed Vehicle Finite Element Model Part I: Methodology, International Journal of Crashworthiness. 5 (2000) 25-36.
[3] Yoon SC, Kim YS, Kim JG, Park SH, Lee HU. A Study on the Structural Fracture of Body
Structure in Railroad Car, Key Engineering Materials. 577 (2013) 301-304. https://doi.org/10.4028/www.scientific.net/KEM.577-578.301
[4] Kurtaran H, Buyuk M, Eskandarian A. Ballistic impact simulation of GT model vehicle door
using finite element method, Theoretical & Applied Fracture Mechanics. 40 (2003) 113-121. https://doi.org/10.1016/S0167-8442(03)00039-9
[5] Wang Wei, Xin Yong. Finite element modeling and modal analysis of vehicle frame, Mechanical Design and Manufacturing. 11 (2009) 53-54. https://doi.org/10.3969/j.issn.1001-3997.2009.11.024
[6] Shen Zhenhong, Zhao Honglun. Research on Finite Element Modeling Method of Rail Vehicle Sandwich Plate Structure, Electric Locomotive and Urban Rail Vehicle. 30 (2007) 42-45. https://doi.org/10.3969/j.issn.1672-1187.2007.01.013
[7] E. Carrera, A. Pagani, J.R. Banerjee. Linearized buckling analysis of isotropic and composite beam-columns by Carrera Unified Formulation and Dynamic Stiffness Method, Mechanics of Advanced Material and Structures. 9 (2016) 1092–1103. https://doi.org/10.1080/15376494.2015.1121524
[8] M. Dan, A. Pagani, E. Carrera. Free vibration analysis of simply supported beams with solid and thin-walled cross-sections using higher-order theories based on displacement variables, Thin-Walled Structures. 98 (2016) 478-495. https://doi.org/10.1016/j.tws.2015.10.012
[9] A. Pagani, E. Carrera, J.R. Banerjee, P.H. Cabral, G. Caprio, A. Prado. Free vibration analysis of composite plates by higher-order 1D dynamic stiffness elements and experiments, Composite Structures. 118.5 (2014) 654-663. https://doi.org/10.1016/j.compstruct.2014.08.020