An accurate model for free vibration of porous magneto-electro-thermo-elastic functionally graded cylindrical shells subjected to multi-field coupled loadings

An accurate model for vibration of a porous magneto-electro-thermo-elastic functionally graded (METE-FG) cylindrical shell made of barium titanate (BaTiO₃) and cobalt diiron tetraoxide (CoFe₂O₄) with magneto-electro-thermal loadings is proposed within the framework of Hamiltonian system. Four types of porosity distribution profiles in the thickness direction are considered. By introducing a new total eigenvector, the higher-order governing differential equations are transformed into a set of lower-order equations. The exact solution for free vibration of METE-FG shells can be expanded in terms of specific symplectic eigenfunctions having seven possible explicit forms. Subsequently, analytical frequency equations and vibration mode shapes for METE-FG shells with various boundary conditions are derived simultaneously. A comparison study is presented to demonstrate the accuracy of the proposed model and very good agreement is observed. The effects of material properties and magneto-electro-thermal loadings on free vibration characteristics of METE-FG cylindrical shells are analyzed and discussed in detail.