PSI - Issue 37

Rogério Lopes et al. / Procedia Structural Integrity 37 (2022) 73–80 R. F. Lopes et al./ Structural Integrity Procedia 00 (2019) 000 – 000

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3. Conclusions In this work, a simplified model of a passenger bus was implemented and studied to obtain the natural modes of vibration. An analytical model was deployed, in which the vehicle body was practically assumed rigid and only the suspension system contributed for the dynamic behavior of the whole structure. An equivalent model to characterize suspension system was taken into account where the equivalent stiffness tire elastic properties were used. The main relevant natural frequencies were obtained via a set of developed mathematical equations presented in a simplified format. The suspension behavior was included in order to assess a couple of motions provided by suspension flexibility. The analytical procedure allowed the determination of singular movements (when there was no combined movements) and tire deformation and radial loads were also included. Numerically, the model was solved using Finite Element Method (FEM) formulations considering passengers´ mass and the wind pressure as exterior loads. The FEM models were solved for different FE meshes. As a results, the mass increase induced the frequencies decreasing tendency. The opposite behavior took place when unexpected wind impacted the bus laterally that coinciding with other frequencies could induce the movement amplification. Regarding the comparison between numerical and analytical solutions, an acceptable agreement was verified between the analytical and numerical results, namely in the cas es of uniform lateral rotation “roll” or, “yaw” vertical axis rotation mode. In the case of translation modes, as purely vertical oscillation mode, a reasonable verification was thereby obtained. In all cases, the effect of damping on natural frequencies was neglected. This is a realistic option for sake of conservative solutions for suspension systems. At higher frequencies, the FEM model is more realistic since there are combined modes. The analytical method sounds to be efficient when lower frequencies is being studied. The results of the present study can be applicable in the modal analysis in transportation sectors. Acknowledgements Authors gratefully acknowledge the funding of Project POCI-01-0247-FEDER-039711- CRASH – Novas soluções tecnológicas de segurança passiva para autocarros, cofinanced by União Europeia, through Fundo Europeu de Desenvolvimento Regional (FEDER). Behzad V. Farahani sincerely acknowledges the funding received from Ministério da Educação e Ciência, Fundação para a Ciência e a Tecnologia (Portugal), under grant PTDC/EME EME/29339/2017. References Fu, Zhi-Fang, and Jimin He. 2001. Modal analysis : Elsevier. Georgiou, G., A. Badarlis, and S. Natsiavas. 2008. "Modelling and ride dynamics of a flexible multi-body model of an urban bus." Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 222 (2):143-154. doi: 10.1243/14644193JMBD130. Göhlich, Dietmar, Tu-Anh Fay, Dominic Jefferies, Enrico Lauth, Alexander Kunith, and Xudong Zhang. 2018. "Design of urban electric bus systems." Design Science 4:e15. doi: 10.1017/dsj.2018.10. Gombor, Balázs. 2005. "Dynamic analysis of a bus body frame: determination of the loads and stresses." Vehicle System Dynamics 43 (11):807 822. doi: 10.1080/00423110500273400. Lopes, Rogério, Behzad V. Farahani, Francisco Q. de Melo, Nuno V. Ramos, and Pedro M. G. P. Moreira. 2021. "Dynamic Modal Analysis of a Passenger Bus: Theoretical and Numerical Studies." Transportation Research Record :03611981211028863. doi: 10.1177/03611981211028863. Miller, Patrick, Alexandre G. de Barros, Lina Kattan, and S. C. Wirasinghe. 2016. "Public transportation and sustainability: A review." KSCE Journal of Civil Engineering 20 (3):1076-1083. doi: 10.1007/s12205-016-0705-0. Solaris, The CAF Group company. "ZERO EMISSIONS POWERTRAINS." Solaris Bus & Coach sp. z o.o., Product catalogue 2020/2021 .