Session: VIB-08-02: Nonlinear Systems & Phenomena II

Paper Number: 97757

97757 - Dispersion Properties of Nonlinear Metamaterial Beams Hosting Nonlinear Resonators 

Wave propagation and stop band behavior of geometrically nonlinear metamaterial beams are investigated via the method of multiple scales. The frequency stop bands of the single nonlinear cell are found asymptotically. Subsequently, the frequency Metamaterials are the focus of fundamental research efforts targeted to unfold the extraordinary properties of cellular, architected and functionalized materials. Here a metamaterial beam with a periodic cellular structure is conceived to host arrays of nonlinear resonators. The system can be investigated the effects of the beam’s and resonators’ nonlinearities on the frequency stop bands.

Figure 1(a) shows the comparison of dispersion properties in terms of wave number β for a linear system and a nonlinear system with a hardening beam and softening resonators. On the other hand, Fig. 1(b) shows the variation of the stop band with respect to the amplitudes when the system exhibits different types of nonlinearity for the beam and the resonators.

The main conclusions can be summarized next. The nonlinearity has an influence on the size of stop band predicted by the linear problem. Notably, the stop band will be significantly enlarged with properly selected nonlinearity types of the beam and resonators. Moreover, the size of the stopband is always increased when the beam is hardening and the resonators are softening; conversely, a softening beam and hardening resonators lead to narrower stop bands.

Presenting Author: Yichang Shen SAPIENZA University of Rome

Presenting Author Biography: I am Yichang Shen, a young and enthusiastic researcher with more than five years of experience in vibrations analysis and control of thin structures like beams and shells. During my master’s research project, I investigated passive vibration suppression in thin structures. My Ph.D. project addressed the vibration analysis and reduced-order modeling of geometrically nonlinear structures. I am now a member of Professor Walter Lacarbonara’s group at SAPIENZA University of Rome as a postdoc since 03/2022.

Authors:

Yichang Shen SAPIENZA University of Rome
Walter Lacarbonara SAPIENZA University of Rome