Dynamics of a non-uniform Euler-Bernoulli beam: sensitivity study in the parameter space
DOI:
https://doi.org/10.5890/JAND.2018.06.009Abstract
The dynamics and spectrum of vibrations of non-uniform Euler-Bernoulli beam were investigated. The beam cross section varies linearly in direction of its length. Spacial and temporal solutions were investigated, spacial by Differential transform Method and temporal by four order Runge Kutta. A comparison between temporal numerical solutions and generalized Landau analytical approximations was conducted. There is a significant region, in parameter spaces, that the generalized Landau solution works well, and that there is a region, in parameter space, where the system behaves as it was periodic for practical reasons, thus we name it as almost stable attractor. It was shown that the solutions are strongly sensible to parameters that are related to geometrical and physical proprieties of the beam, it means that a small deviation on parameters can change the dynamics from convergent to divergent, and between those regimes, there is a region on parameter space that the model imitates a periodic system.References
[1] Marion, J.B. and Thornton, S.T. (1995), Classical Dynamics of Particles and Systems (Fort Worth: Saunders College Pub.).
[2] de Magalhaes, A.B. and Oliveira, A.C. (2016), Physics Letters A, 380(4), 554,
[3] Oyarzabal, R., Jr., J.S., Batista, A.,de Souza, S.,Caldas, I.,Viana, R., and Sanjuan, M. (2016), Physics Letters A, 380(18-19), 1621,
[4] Bonetti, R.C., de Souza, S.L.T., Batista, A.M., Jr, J.D.S., Caldas, I.L., Viana, R.L., Lopes, S.R., and Baptista, M.S. (2014), Journal of Physics A: Mathematical and Theoretical, 47(40), 405101.
[5] Seoane, Aguirre, J.M., Sanjuan, J., M.A., and Lai, Y.C. (2006), Chaos, 16(2), 023101,
[6] Barrio, R., Blesa, F., Sanjuán, M.A.F., and Seoane, J.M. (2012), International Journal of Bifurcation and Chaos, 22(6), 1230010.
[7] Landau, L. and Lifshits, E. Mechanics (Pergamon, 1976)
[8] de Barros, V.P. (2007), Revista Brasileira de Ensino de Física, 29(4), 549.
[9] Dias, C. and Alves, M. (2013), Journal of Sound and Vibration, 332(5), 1372,
[10] Hou, C. and Lu, Y. (2016), Journal of Sound and Vibration, 385, 104.
[11] Shali, S., Nagaraja, S.R., and Jafarali, P. (2016), IOP Conference Series: Materials Science and Engineering, 149(1), 012158.
[12] Abdelghany, S., Ewis, K., Mahmoud, A., and Nassar, M.M. (2015), Beni-Suef University Journal of Basic and Applied Sciences, 4(3), 185.
[13] Mao, X.Y.,Ding, H.,Lim, C., and Chen, L.Q. (2016), Journal of Sound and Vibration, 385, 267.
[14] Mignolet, M.P.,Przekop, A., Rizzi, S.A., and Spottswood, S.M. (2013), Journal of Sound and Vibration, 332(10), 2437.
[15] Abrate, S. (1995), Journal of Sound and Vibration, 185(4), 703.
[16] Balachandran, B. and Magrab, E.B. (2004), Vibrations (Cengage Learning).
[17] Brito, R.Y., Fabrino, D.L., and Oliveira, A. (2016), in Proceeding Series of the Brazilian Society of Compu- tational and Applied Mathematics, 10020.
[18] Jiang, H. and Zhang, J. (2008), Journal of Applied Mechanics, Transactions ASME, 75(6), 610191.
[19] García, D.A., Sampaio, R., and Rosales, M.B. (2016), Journal of the Brazilian Society of Mechanical Sciences and Engineering, 38(8), 2661. URL http://dx.doi.org/10.1007/s40430-015-0418-1.
[20] Biazar, J. and Mohammadi, F. (2010), Appl. Appl. Math. 5(10), 1726.
[21] Ebrahimi, F. and Mokhtari, M. (2015), Journal of the Brazilian Society of Mechanical Sciences and Engi- neering, 37(4), 1435. URL http://dx.doi.org/10.1007/s40430-014-0255-7.
[22] Malik, M. and Dang, H.H. (1998), Applied Mathematics and Computation, 96(1), 17.
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