Active control of wave propagation in nonlinear planar networks using piezoelectric actuation

Due to the fascinating effects of nonlinearity on the wave propagation and dynamic properties of periodic structures, nonlinear phononic crystals have been an important research topic in recent years. However, while a lot of efforts were devoted to the wave propagation analysis of nonlinear chains, 2D planar lattices with weak nonlinearities have been left relatively unexplored. Hence, this work presents an active control technique of wave propagation in nonlinear planar lattices using piezoelectric actuation. To formulate the problem, the governing equations are derived for the transverse motion of weakly nonlinear lattices with square topology considering the effects of auxiliary piezoelectric springs. The Lindstedt-Poincare perturbation method is applied to obtain semi-analytical solutions of the governing equations. Furthermore, the analytical nonlinear dispersion relations are derived for the discrete nonlinear phononic lattices with triangular topology, for the first time. The results reveal that in addition to the effect of piezoelectric springs with both positive and negative gains on the dispersion curves, the wave directionality of nonlinear planar lattices is also affected by such modifications. Hence, a tuning approach is proposed to control the directionality and isotropy of wave propagation in nonlinear planar lattices, as well as their wave attenuation performance. According to the results, piezoelectric springs with negative control gain can open new tunable ultra-low frequency stop-bands in the dispersion curves of planar nonlinear lattices.(c) 2023 Elsevier B.V. All rights reserved.

Automated summary

Due to the intriguing effects of nonlinearity on wave propagation and dynamic properties, nonlinear phononic crystals have become a prominent research topic. However, there has been relatively little exploration of 2D planar lattices with weak nonlinearities. This study presents an active control technique using piezoelectric actuation to manipulate wave propagation in nonlinear planar lattices. By deriving governing equations and applying the Lindstedt-Poincare method, this study provides semi-analytical solutions and derives analytical nonlinear dispersion relations for these lattices for the first time. The results demonstrate the influence of piezoelectric springs on dispersion curves and wave directionality, proposing a tuning approach for controlling wave propagation characteristics and attenuation performance in nonlinear planar lattices.