<p>Structural responses under multi-frequency excitations, such as earthquakes, often involve complex vibration modes due to the coupling of high- and low-frequency components. Conventional neural networks suffer from spectral bias, making it difficult to capture high-frequency features. In addition, noise and missing data in seismic records further degrade the reliability of traditional numerical schemes such as the Newmark method and Physics-Informed Neural Networks (PINNs). To address these challenges, this study proposes a Fourier-enhanced Physics-Informed Kolmogorov–Arnold Network (FPIKAN). The framework integrates the interpretability of the Kolmogorov–Arnold Network (KAN) with Fourier-based input encoding, and parameterizes activation functions via Fourier series to enhance spectral representation and parameter efficiency. A physics-constrained loss combining equation residuals and regularization ensures physical consistency. Numerical experiments demonstrate that FPIKAN achieves superior accuracy, stability, and robustness, effectively overcoming the limitations of PINNs in high-frequency learning, even under conditions with noisy or low-frequency sampled input data.</p>