Dispersion analysis of magneto-elastic three-layered plates embedded in Winkler foundations with rotational and viscous damping effects

In this article, we mainly concern with the dispersion of three-layered sandwich plate focusing on long-wave low-frequency spectrum. In order to solve the problem of rupture or failure of three-layered sandwich structures in the engineering sectors, we intend to establish and enhance the dynamics of three-layered plate. We study three-layered plate, in which the layers are perfectly bonded and the outside sides of plate are supported by Winkler foundations. Furthermore, the effects of a magnetic field, rotation, and viscous damping are examined for elastic wave propagation in the long-wave low-frequency region. An anti-plane shear motion of a symmetric three-layered plate is investigated. For the sake of analysing the dispersion relations, the partial differential equations are reduced to equivalent ordinary differential equations using a harmonic solution assumption. For the symmetric structure, the dispersion relations relating to antisymmetric and symmetric modes are investigated and analysed under the impact of magnetic field force, viscous damping, and rotation. The resulting relationships for cut-off frequencies, stresses, and displacements associated with each layer of the plate are developed for both antisymmetric and symmetric modes. Finally, the effects of Winkler foundation stiffness, magnetic field intensity, viscous damping, and rotation on wave propagation in a three-layered plate for antisymmetric and symmetric modes are graphically depicted using some physical available data, and the effects of these excitations on wave dispersion within the long-wave low-frequency regime are fully evident. The research findings reveal that higher stiffness in the foundation and stronger magnetic fields ensure a long-wave low-frequency regime, while viscous damping and rotational effects also contribute to this assurance. Further research incorporating these physical effects and focusing on multi-layered and multi-material structures supported on Het’enyi and Pasternak foundations is encouraged to conduct a comprehensive dispersion analysis of complex structures. These insights have implications for practical applications in various industries and encourage further exploration in material science and structural design.