An equivalent plate model for assessing the dynamic behavior of highly damped sandwich plates
Résumé
This article presents an equivalent plate modeling approach for assessing the dynamic behavior of highly damped multilayered plates, with a focus on adaptive structures with shape memory polymer core. The mechanical properties of these structures vary with frequency and temperature, and exceptional damping values are obtained near the glass transition temperature of the shape memory polymer. By modeling the system as an equivalent homogeneous and isotropic thin plate, the effective properties are analytically determined by retaining the real parts of the bending, shear (transverse) and extension (quasi-longitudinal) waves. Unlike other equivalent plate models, the damping loss factor is estimated using a power balance formulation accounting for the significance of multiple waves types, improving the description of the dissipation mechanism. The results show good agreement with the damping estimates obtained using the power input method and the full order finite element model of the sandwich plate. For a 4% damping value, the equivalent plate finite element model accurately predicts the vibroacoustic indicators of the adaptive sandwich plate, while significantly reducing the modeling complexity. Even at exceptionally high damping levels (55% and 77%), the equivalent plate model captures the overall dynamic behavior of the structure. This proposed equivalent model offers a practical method for evaluating the vibroacoustic performance of highly damped multilayered plates and can be used to explore various behaviors of adaptive sandwich plates. Its reduced computation time makes it especially suitable for optimization problems, such as determining optimal temperatures for damping and stiffness control.
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