A new structure study: Vibrational analyses of FGM convex-concave shells subjected to electro-thermal-mechanical loads surrounded by Pasternak foundation

A new structure that has just been found in this present, named to the convex-concave shell. Based on the change of radius according to the sine or cosine function, a type of rotating circular shell made of functionally graded materials (FGM) has appeared and been investigated in the paper. Characteristics of dynamics of the FGM convex-concave shell in thermal environment and surrounded by the elastic medium are analyzed by an analytical approach. The piezoelectric layers are bonded in the internal and external surfaces of the shells. By using the classical thin shell theory, Von Karman-Donnell geometrical nonlinearity assumption, the governing equations are established and the Galerkin's method is applied to investigate the nonlinear dynamical behaviors of the shells. The numerical results are calculated and validated to the previous literatures of the cylindrical shells-a special case of this structure. In addition, Finite Element Analysis (FEA) is also used to compare with these of the convex-concave shells in two types I and II. The effects of the electro-thermal environment, geometrical parameters and the elastic foundation are scrutinized by the numerical and 2D and 3D graphical results. The achieved results of the structure promise to contribute greatly to significant applications of aerospace, civil and mechanical engineering.