Inverse design of non-periodic nonlinear metamaterials for nonlinear ultrasonics

Abstract

Previous work by the author gives an idea about the effective design of linear and phononic “periodic” metamaterial using shape optimization to suppress the system-generated 2nd harmonics of a longitudinal wave during nonlinear ultrasonic testing [Ghodake, J. Acoust. Soc. Am. 150, A149 (2021)]. That work considers only the geometric nonlinearity of the layered materials and sinusoidal waves as an input short pulse. The present work implements a shape optimization technique to obtain the optimal design parameters of the “non-periodic” metamaterial by considering both material and geometric nonlinearities of the layered materials present in the phononic crystal as this assumption is close to the real experimental situations. Gaussian short input pulses are considered in this study with two different objectives such as only reducing the amplitude of the 2nd harmonics and reducing the amplitude of 2nd harmonics, maximizing the amplitude of 1st harmonics as well as maintaining the Gaussian shape of the output pulse which makes this inverse problem challenging. This study demonstrates the applicability of the non-periodic metamaterial in practical situations and the importance of the proposed inverse design approach in linear and nonlinear elastic wave propagation applications such as ultrasonic waves and seismic waves.