Abstract.
The study of the vibration of large membranes is important due to its well-known applications. There exist various investigations for the above problem where the variables and parameters are given as crisp/exact. In practice, we may not have these parameters exactly but those may be known in some uncertain form. In the present paper, these uncertainties are taken as interval/fuzzy and the authors propose here a new method viz. that of the double parametric form of fuzzy numbers to handle the uncertain problem of large membranes. Finally, the problem has been solved using the Homotopy Perturbation Method (HPM). The present method performs very well in terms of computational efficiency. The reliability of the method is shown for obtaining an approximate numerical solution for different cases. Results are given in terms of plots and are also compared in special cases.
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References
Lord Rayleigh, The theory of sound (John William Strutt, Dover, 1945)
A. Yildirim, C. Ünlü, S.T. Mohyud-Din, Appl. Appl. Math. 1, 24 (2010)
S.T. Mohyud-Din, A. Yildirim, Comput. Math. Model 23, 228 (2012)
M.E. Sunny, R.K. Kapania, C. Sultan, AIAA J. 50, 1796 (2012)
S.L. Chang, L.A. Zadeh, IEEE Trans. Syst. Man. Cybernet 2, 30 (1972)
D. Dubois, H. Prade, Fuzzy Sets Syst. 8, 225 (1982)
O. Kaleva, Fuzzy Sets Syst. 24, 301 (1987)
O. Kaleva, Fuzzy Sets Syst. 35, 389 (1990)
S. Seikkala, Fuzzy Sets Syst. 24, 319 (1987)
S. Abbasbandy, T. Allahviranloo, Comput. Math. Appl. 2, 113 (2002)
J.J. Nieto, R. Rodríguez-López, D. Franco, Int. J. Unc. Fuzz. Knowl. Based Syst. 14, 687 (2006)
O. Akin, T. Khaniyev, O. Oruc, I.B. Turksen, Expert Syst. Appl. 40, 953 (2013)
T. Allahviranloo, E. Ahmady, N. Ahmady, Int. J. Comput. Math. 86, 730 (2009)
T. Allahvianloo, S. Abbasbandy, H. Rouhparvar, Appl. Soft Comput. 11, 2186 (2011)
Y. Chalco-Cano, H. Roman-Flores, Chaos Solitons Fractals 38, 112 (2008)
A. Khastan, J.J. Nieto, R. Rodriguez-Lopez, Fuzzy Sets Syst. 177, 20 (2011)
M. Ma, M. Friedman, A. Kandel, Fuzzy Sets Syst. 105, 133 (1999)
N. Mikaeilvand, S. Khakrangin, Neural Comput. Appl. 21, S307 (2012)
S. Palligkinis, G. Papageorgiou, I. Famelis, Appl. Math. Comput. 209, 97 (2009)
P. Prakash, V. Kalaiselvi, Int. J. Comput. Math. 86, 121 (2009)
S. Tapaswini, S. Chakraverty, Int. J. Fuzzy Inf. Eng. 4, 293 (2012)
S. Tapaswini, S. Chakraverty, Int. J. Artif. Intell. Soft Comput. 4, 58 (2014)
J.H. He, Comput. Methods Appl. Mech. Eng. 178, 257 (1999)
J.H. He, Int. J. Non-linear Mech. 35, 37 (2000)
O. Abdulaziz, I. Hashim, S. Momani, J. Comput. Appl. Math. 216, 574 (2008)
Z. Azimzadeh, A.R. Vahidi, E. Babolian, Indian J. Phys. 86, 721 (2012)
D. Behera, S. Chakraverty, Cent. Eur. J. Phys. 11, 792 (2013)
J. Biazar, H. Ghazvini, Phys. Lett. A 366, 79 (2007)
S. Chakraverty, D. Behera, Alexandria Eng. J. 52, 557 (2013)
F.G.M. Cui, J. Comput. Appl. Math. 235, 2405 (2011)
D.D. Ganji, Phys. Lett. A 335, 337 (2006)
T. Ozis, C. Akçi, Meccanica 46, 341 (2011)
C. Chun, Z. Naturforsch. A 65a, 59 (2010)
J.-H. Lu, C.L. Zheng, Z. Naturforsch. A 65a, 301 (2010)
M.M. Mousa, A. Kaltayev, Z. Naturforsch. A 65a, 511 (2010)
R. Sakthivel, C. Chun, J. Lee, Z. Naturforsch. A 65a, 633 (2010)
Y. Khan, Q. Wu, N. Faraz, A. Yildirim, S.T. Mohyud-Din, Z. Naturforsch. A 67a, 147 (2012)
M.A. Balci, A. Yildirim, Z. Naturforsch. A 66a, 87 (2011)
A. Kimiaeifar, Z. Naturforsch. A 66a, 461 (2011)
S. Abbasbandy, Appl. Math. Comput. 173, 493 (2006)
M.A. Noor, S.T. Mohyud-Din, Int. J. Nonlinear Sci. Numer. Simulat. 9, 395 (2008)
M. Jafari, M.M. Hosseini, S.T. Mohyud-Din, M. Ghovatmand, Int. J. Nonlinear Sci. Numer. Simulat. 11, 1047 (2010)
S.T. Mohyud-Din, M.A. Noor, K.I. Noor, Math. Prob. Eng. 2009, 1 (2009)
S.T. Mohyud-Din, A. Yildirim, S.A. Sezer, Z. Naturforsch. A 65a, 1033 (2010)
S.T. Mohyud-Din, M.A. Noor, K.I. Noor, Int. J. Nonlinear Sci. Numer. Simulat. 10, 581 (2009)
S.T. Mohyud-Din, M.A. Noor, K.I. Noor, Int. J. Nonlinear Sci. Numer. Simulat. 10, 223 (2009)
M.A. Noor, S.T. Mohyud-Din, Comput. Math. Appl. 58, 2182 (2009)
T. Allahviranloo, S. Hashemzehi, J. Appl. Math. Islam Azad Univ. Lahijan 5, 1 (2008)
E. Babolian, A.R. Vahidi, Z. Azimzadeh, Int. J. Ind. Math. 4, 353 (2012)
M. Ghanbari, Int. J. Ind. Math. 1, 19 (2009)
M. Matinfar, M. Saeidy, J. Math. Comput. Sci. 1, 377 (2010)
S. Tapaswini, S. Chakraverty, Int. J. Comput. Appl. 64, 5 (2013)
M. Hanss, Applied Fuzzy Arithmetic: An Introduction with engineering applications (Springer-Verlag, Berlin, 2005)
L. Jaulin, M. Kieffer, O.T. Didri, E. Walter, Applied interval analysis (Springer, 2001)
T.J. Ross, Fuzzy logic with engineering applications (Wiley Student Edition, 2007)
H.J. Zimmermann, Fuzzy set theory and its application (Kluwer Academic Publishers, Boston/Dordrecht/London, 2001)
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Tapaswini, S., Chakraverty, S. & Behera, D. Uncertain vibration equation of large membranes. Eur. Phys. J. Plus 129, 251 (2014). https://doi.org/10.1140/epjp/i2014-14251-7
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DOI: https://doi.org/10.1140/epjp/i2014-14251-7