- Crespo da Silva, and Glynn, C. “Nonlinear flexural-flexural-torsional dynamics of inextensional beams. I. Equations of motion,” Journal of Structural Mechanics, Vol. 6, No. 4, pp. 437-448, 1978.##
- Crespo da Silva, M. and Glynn, C. “Nonlinear flexural-flexural-torsional dynamics of inextensional beams. II. Forced motions,” Journal of Structural Mechanics, Vol. 6, No. 4, pp. 449-461, 1978.##
- Zavodney, D. and Nayfeh, A. “The non-linear response of a slender beam carrying a lumped mass to a principal parametric excitation: theory and experiment,” International Journal of Non-Linear Mechanics, Vol. 24, No. 2, pp. 105-125, 1989.##
- Nayfeh, A. H. and Pai, P. F. “Non-linear non-planar parametric responses of an inextensional beam,” International Journal of Non-Linear Mechanics, Vol. 24, No. 2, pp. 139-158, 1989.##
- Al-Qaisia, A., Hamdan, M. and Al-Bedoor, B. “On the steady state response of a cantilever beam partially immersed in a fluid and carrying an intermediate mass,” Shock and Vibration, Vol. 7, No. 4, pp. 179-194, 2000.##
- Al-Qaisia, A. and Hamdan, M. “Bifurcations and chaos of an immersed cantilever beam in a fluid and carrying an intermediate mass,” Journal of Sound and Vibration, Vol. 253, No. 4, pp. 859-888, 2002.##
- Delgado-Velázquez, I. “Nonlinear vibration of a cantilever beam,” 2007.##
- Motallebi, A., Irani, S. and Sazesh, S. “Analysis on jump and bifurcation phenomena in the forced vibration of nonlinear cantilever beam using HBM,” Journal of the Brazilian Society of Mechanical Sciences and Engineering, Vol. 38, No. 2, pp. 515-524, 2016.##
- Nayfeh, A. and Serhan, S. “Response statistics of non-linear systems to combined deterministic and random excitations,” International Journal of Non-Linear Mechanics, Vol. 25, No. 5, pp. 493-509, 1990.##
- Rong, H.-w., Xu, W. and Fang, T. “Principal response of Duffing oscillator to combined deterministic and narrow-band random parametric excitation,” Journal of Sound and Vibration, Vol. 210, No. 4, pp. 483-515, 1998.##
- Hai-wu, R., Wei, X., Xiang-dong, W., Guang, M. and Tong, F. “Principal response of van der pol-duffing oscillator under combined deterministic and random parametric excitation,” Applied Mathematics and Mechanics, Vol. 23, No. 3, pp. 299-310, 2002.##
- Zhu, W. and Wu, Y. “First-passage time of Duffing oscillator under combined harmonic and white-noise excitations,” Nonlinear Dynamics, Vol. 32, No. 3, pp. 291-305, 2003.##
- Chen, L. and Zhu, W. “Stochastic jump and bifurcation of Duffing oscillator with fractional derivative damping under combined harmonic and white noise excitations,” International Journal of Non-Linear Mechanics, Vol. 46, No. 10, pp. 1324-1329, 2011.##
- Anh, N. and Hieu, N. “The Duffing oscillator under combined periodic and random excitations,” Probabilistic Engineering Mechanics, Vol. 30, pp. 27-36, 2012.##
- Haiwu, R., Wei, X., Guang, M. and Tong, F. “Response of a Duffing oscillator to combined deterministic harmonic and random excitation,” Journal of sound and vibration, Vol. 242, No. 2, pp. 362-368, 2001.##
- Zhu, H.-T. and Guo, S.-S. “Periodic Response of a Duffing Oscillator Under Combined Harmonic and Random Excitations,” Journal of Vibration and Acoustics, Vol. 137, No. 4, pp. 041015, 2015.##
- Feng, Z., Lan, X. and Zhu, X. “Principal parametric resonances of a slender cantilever beam subject to axial narrow-band random excitation of its base,” International Journal of Non-Linear Mechanics, Vol. 42, No. 10, pp. 1170-1185, 2007.##
- Feng, Z., Lan, X. and Zhu, X. “Explanation on the importance of narrow-band random excitation characters in the response of a cantilever beam,” Journal of Sound and Vibration, Vol. 325, No. 4, pp. 923-937, 2009.##
- Feng, Z., Zhu, X. and Lan, X. “Stochastic jump and bifurcation of a slender cantilever beam carrying a lumped mass under narrow-band principal parametric excitation,” International Journal of Non-Linear Mechanics, Vol. 46, No. 10, pp. 1330-1340, 2011.##
- Ge, G., Solitons, Z. J. C. Li, and Fractals, “A modified stochastic averaging method on single-degree-of-freedom strongly nonlinear stochastic vibrations,” Vol. 91, pp. 469-477, 2016.##
- Ge, G. and Yan, W. J. J. o. V. “Cantilever model with curvature nonlinearity and longitudinal inertia excited by lateral basal moments being Gaussian white noise,” Vol. 20, No. 1, pp. 677-690, 2018.##
- Ge, G., Bo, Z. J. C. and Applications, M. w. “Response of a cantilever model with a surface crack under basal white noise excitation,” Vol. 76, No. 11-12, pp. 2728-2743, 2018.##
- Ge, G., Liu, J. J. C. Solitons, and Fractals, “Stochastic averaging on a nonlinear oscillator with coordinate-dependent mass excited by Gaussian white noises,” Vol. 143, pp. 110609, 2021.##
- Rao, S. S. "Mechanical vibrations "Pearson Prentice Hall, Inc. NJ, 2004.##
- To, C. W. "Nonlinear random vibration: Analytical techniques and applications," CRC Press, 2011.##
- Roberts, J. and Spanos, P. “Stochastic averaging: an approximate method of solving random vibration problems,” International Journal of Non-Linear Mechanics, Vol. 21, No. 2, pp. 111-134, 1986.##
- Newland, D. E. "An introduction to random vibrations, spectral & wavelet analysis," Courier Corporation, 2012.##
- Lan, X., Feng, Z. and Lv, F. “Stochastic Principal Parametric Resonances of Composite Laminated Beams,” Shock and Vibration, Vol. 2014, 2014.##
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