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Section B

Approximate solutions for nonlinear transverse vibrations of elastically restrained tapered beams

, &
Pages 901-915 | Received 04 Mar 2011, Accepted 31 Jan 2012, Published online: 19 Mar 2012

References

  • Abdel-Jaber , M. S. , Al-Qaisia , A. A. , Abdel-Jaber , M. and Beale , R. G. 2008 . Nonlinear natural frequencies of an elastically restrained tapered beam . J. Sound Vib , 313 : 772 – 783 .
  • Antman , S. 1995 . Nonlinear Problems of Elasticity , Berlin : Springer .
  • Cveticanin , L. 2005 . The homotopy-perturbation method for solving complex-valued differential equations with strong cubic nonlinearity . J. Sound Vib , 285 : 1171 – 1179 .
  • Durmaz , S. , Demirbað , S. Altay and Kaya , M. O. 2011 . Approximate solutions for nonlinear oscillation of a mass attached to a stretched elastic wire . Comput. Math. Appl , 61 : 578 – 585 .
  • Ganji , D. D. , Esmaeilpour , M. and Soleimani , S. 2010 . Approximate solutions to Van der Pol damped nonlinear oscillators by means of He's energy balance method result . Int. J. Comput. Math , 87 : 2014 – 2023 .
  • He , J. H. 2001 . Bookkeeping parameter in perturbation methods . Int. J. Nonlinear Sci. Num , 2 : 257 – 264 .
  • He , J. H. 2004 . The homotopy perturbation method for nonlinear oscillators with discontinuities . Appl. Math. Comput , 151 : 287 – 292 .
  • He , J. H. 2004 . He Chengtian's inequality and its applications . Appl. Math. Comput , 151 : 887 – 891 .
  • He , J. H. 2006 . Some asymptotic methods for strongly nonlinear equations . Int. J. Mod. Phys. B , 20 : 1141 – 1199 .
  • He , J. H. 2007 . Variational iteration method – some recent results and new interpretations . J. Comput. Appl. Math , 207 : 3 – 17 .
  • He , J. H. 2008 . An improved amplitude–frequency formulation for nonlinear oscillators . Int. J. Nonlinear Sci. Num , 9 : 211 – 213 .
  • He , J. H. 2008 . Max–min approach to nonlinear oscillators . Int. J. Nonlinear Sci. Num , 9 : 207 – 210 .
  • Hoseini , S. H. , Pirbodaghi , T. , Ahmadian , M. T. and Farrahi , G. H. 2009 . On the large amplitude free vibrations of tapered beams: an analytical approach . Mech. Res. Commun , 29 : 892 – 897 .
  • Mabie , H. H. and Rogers , C. B. 1964 . Transverse vibrations of tapered cantilever beams with end loads . J. Acoust. Soc. Am , 36 : 463 – 469 .
  • Nageswara Rao , B. and Venkateswara Rao , G. 1988 . Large amplitude vibrations of a tapered cantilever beam . J. Sound Vib , 127 : 173 – 178 .
  • Nayfeh , A. H. and Pai , P. F. 2004 . Linear and Nonlinear Structural Mechanics , Weinheim , , Germany : Wiley .
  • Rafei , M. , Ganji , D. D. , Daniali , H. and Pashaei , H. 2007 . The variational iteration method for nonlinear oscillators with discontinuities . J. Sound Vib , 305 : 614 – 620 .
  • Timoshenko , S. P. and Goodier , J. N. 1983 . Theory of Elasticity , 3 , Tokyo : McGraw-Hill .
  • Wang , S. Q. and He , J. H. 2008 . Nonlinear oscillator with discontinuity by parameter-expansion method . Chaos, Solitons and Fractals , 35 : 688 – 691 .

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