Base-excited random vibration of quasi-periodic controllable viscoelastic sandwich plates with distributed supporting masses

This article extends random-vibration analysis of controllable viscoelastic sandwich structures to quasi-periodic two-dimensional plates with distributed supporting masses under base excitation—a configuration still rarely treated in the literature. Quasi-periodicity represents manufacturing imperfections, material variability, and service-induced damage instead of an ideal repeating cell; these departures can shift dynamic response enough to matter for performance. A framework is developed for quasi-periodic face thickness, core modulus, and lumped masses in both in-plane directions, with explicit spatial perturbations and detuning. Coupled transverse–longitudinal partial differential equations for the parameter-varying sandwich plate are derived and reduced to ordinary differential equations through Galerkin projection. Within linear stochastic spectral theory, frequency-response relations and displacement power spectral densities are formulated for incremental detuning about a periodic reference. Numerical studies show that quasi-periodic core modulus and supporting-mass layouts strongly influence resonance and anti-resonance amplitudes, whereas face-thickness quasi-periodicity matters more away from the plate center. The results support vibration-control design for quasi-periodic magnetorheological (MR) sandwich plates and inform dynamic optimization of practical built-up structures.