Publications

2025

• Nonlinear dynamical phenomena in musical acoustics
  
  • Thomas Olivier
  • Vergez Christophe
  • Touzé Cyril
  , 2025.
• Enhancing damping performance below the bandgap in metamaterial beams with geometric nonlinearity and bistable attachments via nonlinear energy transfer
  
  • Wang Tao
  • Touzé Cyril
  • Li Haiqin
  • Tang Ye
  • Ding Qian
  Mechanical Systems and Signal Processing, Elsevier, 2025, 240, pp.113362. Nonlinear metamaterials embedded with bistable resonators enable efficient energy exchange between acoustic and optical branches via 1 : <i>n</i> internal resonances. Recognising that the low-frequency acoustic branch is typically low-damping while the optical one near the bandgap exhibits higher losses, tuning their frequency relationship promotes nonlinear coupling, offering substantial and robust passive damping below the bandgap. To validate the feasibility of this pathway, a theoretical investigation is carried out on a clamped–clamped metamaterial beam with bistable attachment, which is realised by employing a dual pre-curved beam structure to design an easily achievable micro-bistable resonator, then periodically embedding it into the host beam. The geometric nonlinearity of the host structure, modelled using the von Kármán beam theory, is considered to capture the coupling effects accurately. The dynamics of the nonlinear beam are reduced using nonlinear normal modes, computed via the direct parametrisation method for invariant manifolds, which are then assembled with the dynamic equations governing the internal resonators. This strategy provides an accurate reduced-order model of the coupled system, achieving a significant speed-up in the computing time. The nonlinear vibrations of the coupled system are then analysed through linear dispersion spectrum and nonlinear frequency response curves, demonstrating significant damping improvements below the bandgap. Reductions of up to 30 dB and 10 dB are observed in the first and second resonant peaks, respectively, benefiting from the rich nonlinear energy transfer phenomena, enabled by the combination of geometric nonlinearity and the bistable characteristics of the resonators. The parameter analysis provides optimisation guidelines for the parameters related to the bistable configurations of the dual pre-curved beam, where the linear frequency of the bistable resonators, which governs the coupling between the low-damping and the high-damping modes, should remain between one and three times the frequency of the target mode to achieve effective damping enhancement. (10.1016/j.ymssp.2025.113362)
  DOI : 10.1016/j.ymssp.2025.113362
• Simulation-free Reduced-order Modeling using Invariant Manifolds
  
  • Touzé Cyril
  • Vizzaccaro Alessandra
  , 2025. This chapter introduces the concept of invariant manifold as a key tool for model order reduction of dynamical systems.
• Nonlinear dispersion relationships and dissipative properties of damped metamaterials embedding bistable attachments
  
  • Wang Tao
  • Touzé Cyril
  • Li Haiqin
  • Ding Qian
  Nonlinear Dynamics, Springer Verlag, 2025. Damped metamaterials embedded with numerous micro-bistable attachments hold great potential in wave manipulation and vibration reduction. However, most of the studies are generally devoted to conservative systems, while neglecting a detailed analysis of wave attenuation mechanisms together with complex nonlinear dynamical phenomena. To address these limitations, the nonlinear dispersion relationships of metamaterials composed of internal bistable attachments, are here analysed numerically by combining the harmonic balance method and the extended periodic motion concept. The numerical methods, coupled with an arc-length continuation method, can obtain the dispersion spectrum, internal resonant branches, waveform, and damping ratio under any wave amplitude. Suitable post-processing also allows predicting both the local stability and the wave attenuation properties. To verify the effectiveness and accuracy of this algorithm and provide a comparison for multi-stable metamaterial, a mono-stable metamaterial with cubic-nonlinear resonators is taken as the first example. Then, the undamped dispersion properties and underdamped wave attenuation mechanisms in a nonlinear metamaterial composed of lattices with internal micro-bistable oscillators, are fully addressed using the proposed technique. The results underline that the metamaterial with embedded bistable oscillators has symmetric and asymmetric dispersion branches related to stable and unstable equilibrium points. For small amplitudes, the dynamics is governed by stable asymmetric dispersion solutions and exhibit linear dispersion behaviour with locally resonant bandgap. For medium amplitudes, the bandgap disappears, but only unstable dispersion branches remain over a broader frequency range, which may excite chaotic inter-well motion or targeted energy transfer, enabling a rapid attenuation of wave energy. Two kinds of responses are associated with 1:2/3/4/5 internal resonances from acoustic branches and S-shaped regions in symmetric optic branches. For large amplitudes, waves decay according to symmetric acoustic branches. Notably, regardless of wave amplitude, low-frequency waves always propagate due to extremely lightly damped asymmetric acoustic branches. (10.1007/s11071-024-10462-9)
  DOI : 10.1007/s11071-024-10462-9
• Reduced-order modeling for nonlinear vibrations of structures
  
  • Pierre Christophe
  • Thomas Olivier
  • Touzé Cyril
  , 2025, volume 1. This chapter is devoted to the presentation of model-order reduction techniques that are used in the field of structural vibrations. A special emphasis is placed on substructuring methods for localized nonlinearities and on nonlinear normal modes defined via invariant manifolds for distributed smooth nonlinearities, as key tools to perform efficient yet accurate dimensional reductions. Other reduction techniques such as proper orthogonal decomposition, implicit condensation, and modal derivatives are also briefly covered at the end of the survey. The contents of this chapter were written for the Handbook of Nonlinear Dynamics during the Summer of 2024.