Nonlinear Dynamics

, Volume 94, Issue 4, pp 2575–2612 | Cite as

Nonlinear dynamics of a viscoelastic sandwich beam with parametric excitations and internal resonance

  • Bo Zhu
  • Youheng Dong
  • Yinghui Li
Original Paper


Nonlinear dynamical behaviors of an axially accelerating viscoelastic sandwich beam subjected to three-to-one internal resonance and parametric excitations resulting from simultaneous velocity and tension fluctuations are investigated. The direct method of multiple scales is adopted to obtain a set of first-order ordinary differential equations and associated boundary conditions. The frequency and amplitude response curves along with their stability and bifurcation are numerically studied. A great number of dynamic behaviors are presented in the form of phase portraits, time traces, Poincaré sections, and FFT power spectra. Due to modal interaction, various periodic, quasiperiodic, and chaotic behaviors are displayed, depending on the initial conditions. The largest Lyapunov exponent is carried out to determine the midly chaotic response by the convergent form of exponents. Numerical results show various oscillatory behaviors indicating the influence of internal resonance and coupled effects of fluctuating axial velocity and tension.


Axially accelerating viscoelastic sandwich beam Internal resonance Parametric resonance Method of multiple scales Bifurcation Stability 



The authors are grateful for the support of the National Natural Science Foundation of China (Nos. 11372257, 11472064, 11602208, and 51674216) and the project of Chongqing University of Science and Technology (No. Shljzyh2017-007).


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.School of Mechanics and EngineeringSouthwest Jiaotong UniversityChengduChina

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