The vibration of the cylindrically curved sandwich plate with rheological core and nanocomposite face sheets rested on the Winkler–Pasternak foundation

In this research, the vibration analysis of a cylindrically curved sandwich plate rested on Winkler–Pasternak foundation is investigated. The curved sandwich plate consists of a rheological core and nanocomposite top and bottom layers which are included in polyvinylidene fluoride matrix and carbon nanotubes fiber. The core has electric properties, and it is affected by applying electric fields. At first, the governing relations for different layers are written, separately, in order to determine the constitutive equations of the cylindrically curved sandwich plate. Then, differential motion equations are derived by applying the energy method and Hamilton’s principle. With regard to achieving the set of coupled equations, an appropriate analytical approach is proposed to solve them which can be considered as SSCC and SSSS boundary conditions. Also, it is observed that increasing the volume fraction of carbon nanotubes in face sheets leads to increase in the stability of the electro-rheological sandwich plate. This finding can be employed to design building smart structures, military, aviation, marine and automotive.