Free Vibration Characteristics Analysis of Damping Sandwich Rotational Plate Structures

A unified modeling framework is presented in this work to predict the free vibration and loss factor characteristics of damping sandwich rotational plates. The formulation starts from the first-order shear deformation theory, where the zigzag hypothesis and interlayer displacement continuity are combined to couple the displacement fields of the individual plies. An artificial spring scheme is adopted to enforce the layer–layer compatibility and the external boundary restraints, which leads to a Lagrangian functional composed of the kinetic energy, the strain energy, and the potential energies contributed by the boundary and coupling springs. The displacement unknowns are discretized with Chebyshev polynomials of the first kind, and the natural frequencies and damping loss factors are extracted by solving the resulting eigenvalue problem with the Rayleigh–Ritz method. Convergence tests are conducted, and the reliability of the model is validated against finite element results. Finally, a series of numerical examples is presented to systematically investigate the effects of key model parameters on the vibration characteristics of the structure. The results indicate that increasing the thicknesses of the inner and outer layers of the damping sandwich rotational plate structure can significantly raise the natural frequencies. Increasing the inner diameter helps to reduce the area of the low-frequency region, where the difference between the two sides exceeds 40 Hz, caused by the close thicknesses of the inner and outer layers. When only the outer boundary is clamped, the natural frequencies of the annular plate are more than twice those of the solid rotational plate, although the solid rotational plate yields a larger loss factor. When only the outer circular edge is fixed, increasing the total thickness of the structure can effectively raise the natural frequencies, with a maximum increase exceeding 110 Hz, while the loss factor decreases significantly.