A unified physics-based framework for vibration prediction and design optimization of functionally graded trapezoidal thin plates

초록

Vibration analysis of functionally graded trapezoidal thin plates becomes computationally demanding when geometry and material parameters vary, because each new configuration typically requires a separate numerical simulation. This study presents a hybrid workflow for rapid vibration prediction and response reconstruction of such plates. First, a geometry-mapped reduced-order model (ROM) is developed to capture the free-vibration behavior without repeated full-order analyses. Second, an FFT-assisted harmonic physics-informed temporal network is used to extract dominant frequencies and reconstruct differentiable harmonic response components from sparse and noisy sensor signals. Third, a surrogate model is trained to predict modal frequencies and sensor-level harmonic coefficients directly from geometric and material inputs. The reduced-order model shows good agreement with analytical and finite-element benchmarks. The FFT-PINN achieved R2 values above 0.99 and normalized root mean square errors below 0.02 under high noise conditions (signal-to-noise ratio or SNR = 5) using a single sensor. The selected surrogate reproduced the ROM-generated frequency and harmonic-coefficient groups with test R2 values above 0.9995. A multi-objective design study is further used to illustrate the trade-off between the first natural frequency and plate area. The proposed workflow provides an efficient tool for vibration prediction, sparse-sensor reconstruction, and rapid design-space exploration of functionally graded trapezoidal thin plates.

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