Fractional‐Order Control Equation Formulation and Performance Analysis of Viscoelastic Plates Based on Constitutive Model

Viscoelastic structures exhibit pronounced time memory effects and spatial nonlocal coupling under complex dynamic environments, which makes it difficult for traditional integer‐order models to achieve both accurate representation and numerical stability. To address this issue, a high‐precision dynamic analysis method for viscoelastic plates based on fractional‐order constitutive theory is proposed. By integrating the generalized fractional‐order Maxwell model with nonlocal elasticity theory, dynamic governing equations incorporating time fractional derivatives and spatial nonlocal operators are established, enabling a unified description of long‐term memory behavior and scale effects. A hybrid multialgorithm optimization framework is developed for global parameter identification, and a shifted Bernstein polynomial method is employed for efficient spatiotemporal discretization. Numerical results indicate that the proposed approach can stably capture the dynamic responses of viscoelastic plates across different material properties and structural scales, demonstrating good accuracy and numerical stability. This study provides an effective numerical approach and theoretical basis for the dynamic performance analysis of complex viscoelastic structures.