Elastic SH Wave Propagation in Trigonometric Periodic Gradient Materials

Seismic waves threaten structural integrity, yet homogeneous materials lack capacity for targeted wave manipulation, and existing inverse design approaches for functionally graded materials (FGMs) lack explicit physical interpretability. Here, this research propose bidirectional 2D‐FGMs with a trigonometric periodic model governed by dual non‐uniform parameters (, ) and analytically solves the variable‐coefficient wave equation via the complex variable method. The results show that the width‐direction parameter controls peak oscillation and trough sharpening, while the thickness‐direction parameter modulates waveform shape—revealing distinct physical roles. Dual‐parameter synergy achieves 61% higher attenuation efficiency than single‐parameter optimization. The optimal configuration satisfies and , which reduces the maximum displacement amplitude to 56.5% of the homogeneous case. These findings provide a physically interpretable framework and quantitative design guidelines for inverse‐engineering seismic‐resistant FGMs.