Harmonic Mastery in Time-Modulated Linear Elastic Unit Cells

In a recent scholarly inquiry led by Ghodake (2023), the primary focus was the exploration of nonlinear responses within time-modulated linear materials. This investigation was primarily motivated by the desire to gain a deeper comprehension of the intricate interactions involving power-amplified elastic waves, which hold significant utility in the context of nonlinear ultrasonic testing for applications related to structural health monitoring. This study centers on harnessing the harmonic manipulation capabilities of a novel unit cell, consisting of a time-independent linear material matched in impedance, sandwiched between two time-modulated linear materials. Through numerical experiments employing finite element methods, our investigation reveals the unit cells' versatile harmonic manipulation potential within phononic crystals. The numerical findings vividly depict how changes in time-modulation frequency impact the presence, absence, and distribution of harmonic energies. This intricate phenomenon arises from the interplay between linear and nonlinear elastic wave scattering due to time modulation, offering fresh insights into wave propagation dynamics complexities.