Propagation of fundamental and third harmonics along a nonlinear seismic metasurface

ABS T R A C T To protect civil structures from seismic damage, metasurfaces have been designed to control the propagation of Rayleigh wave along the free surface of an elastic half-space. The introduction of nonlinearity may uncover novel phenomena and provide new avenues in the design of seismic metasurfaces. In this work, the propagation of Rayleigh wave along a nonlinear metasurface consisting of an array of Duffing oscillators attached on the free surface of an elastic half-space, is investigated. In comparison with pervious works on seismic metasurfaces, the generation of third harmonic is taken into account and both the dispersions of fundamental and third harmonics propagating along the nonlinear seismic metasurface are derived via the harmonic balance approach. Then, numerical studies are conducted to reveal the effects of both the hardening and softening nonlinearities on the dispersion and third harmonic generation. Additionally, finite element simulations are carried out to validate our analytical solutions. Our results show that the dispersion of fundamental wave is sensitive to the system's nonlinearity. There exists a band gap for the corresponding linear metasurface induced by the resonance of attached oscillators. Introducing a hardening nonlinearity may close the linear band gap, and introducing a softening nonlinearity can help to obtain a low-frequency band gap. The present work is expected to broaden the design and application of seismic metasurfaces.