Parametric Stability of Periodically Controllable Viscoelastic Sandwich Plates with Supported Masses Under Biaxial Longitudinal Excitation

Equipment platforms and large-span floors in buildings are often modeled as sandwich plates carrying discrete supported masses. If the in-plane support forces fluctuate periodically, bending stiffness is modulated in time and parametric instability can develop without direct transverse forcing, undermining vibration isolation. Prior work on viscoelastic sandwich plates has treated uniform layouts or isolated periodic design variables; how simultaneous spatial tailoring of face thickness, core moduli, and mass distribution interacts with biaxial longitudinal excitation is still open. Here we develop a coupled biaxial parametric stability formulation for periodically controllable viscoelastic sandwich plates with Kelvin–Voigt magnetorheological cores, extending the modeling framework in [1–3]. First-order shear deformation theory and Galerkin reduction yield a multi-degree-of-freedom system with periodic coefficients. Instability boundaries are obtained in one step through a direct eigenvalue procedure that couples Floquet theory, harmonic balance, and matrix eigenvalue analysis, avoiding branch-by-branch tracking. Finite element comparisons indicate that principal tongues appear near η ≈ 2ω_n, that matched periodicity in thickness and core modulus markedly increases stability margins, and that plate width, mass placement, and excitation waveform strongly reshape the safe operating region. The findings offer quantitative guidance for designing building-related sandwich foundations against parametric instability.