Xuanang Liu

Xuanang Liu was awarded his MEng degree in Mechanical Engineering from Central South University (China) in 2012 and received his MSc degree in Advanced Mechanical Engineering from University of Bristol in 2013. From 2013, he is doing the PhD in nonlinear dynamics in University of Sheffield.

Research interests

  • Nonlinear dynamics
  • Nonlinear modal interaction
  • Nonlinear normal mode(NNM)
  • Backbone curves
  • Nonlinear reduced-order model (NROM)

Current research

My research focuses on two main aspects: nonlinear dynamic behaviour and nonlinear system identification. The study of nonlinear dynamic behaviour has focused on methods for finding backbone curves (or nonlinear normal modes (NNM)) of nonlinear multi-degree-of-freedom systems and continuous systems such as beams and plates. Using the normal form and numerical continuation techniques, I have investigated the amplitude-frequency response of forced-damped MDOF nonlinear systems, under both sine wave and random excitation. Novel features include N-1 and N modal interactions and natural frequency shifting due to membrane stresses in axially loaded structures. In addition, I have investigated the system identification of MDOF nonlinear systems based on reduced-order backbone curve models for practical nonlinear structures such as thin plates with random excitation, where nonlinear reduced order model and system identification techniques are verified using finite element model simulations. 

Forced response of a 3-DoF nonlinear system with multi-mode interaction superposition with backbone curves.

Estimated, analytical and measured backbone curves of a nonlinear rectangular plate.



  • Liu, X., Cammarano, A., Wagg, D.J., Neild, S.A. and Barthorpe, R.J., 2016. N-1 modal interactions of a three-degree-of-freedom system with cubic elastic nonlinearities. Nonlinear Dynamics, 83(1-2), pp.497-511.
  • Liu, X., Cammarano, A., Wagg, D.J., Neild, S.A. and Barthorpe, R.J., 2016. Nonlinear modal interaction analysis for a three degree-of-freedom system with cubic nonlinearities. In Nonlinear Dynamics, Volume 1 (pp. 123-131). Springer International Publishing.
  • Liu, X., Cammarano, A., Wagg, D.J. and Neild, S.A., 2016. A Study of the Modal Interaction Amongst Three Nonlinear Normal Modes Using a Backbone Curve Approach. In Nonlinear Dynamics, Volume 1 (pp. 131-139). Springer International Publishing.