Exact solutions of free vibration of simply supported functionally graded piezoelectric sandwich cylinders using a modified Pagano method

The three-dimensional free vibration analysis of simply supported, functionally graded piezoelectric material sandwich circular hollow cylinders with different surface conditions is presented. The material properties of each functionally graded piezoelectric material layer are regarded as heterogeneous through the thickness coordinate, and obey an exponent-law dependent on this. Pagano's method is modified to be feasible for this study of functionally graded piezoelectric material sandwich cylinders, in which a displacement-based formulation is replaced by a mixed one; a set of the complex-valued solutions of the system equations is transferred to the corresponding set of real-valued solutions using Euler's formula; a successive approximation method is adopted to approximately transform each functionally graded piezoelectric material layer into homogeneous piezoelectric layers with an equal and small thickness for each layer in comparison with the mid-surface radius, and with the homogeneous material properties determined in an average thickness sense; and a transfer matrix method is developed so that the general solutions of system equations can be obtained layer-by-layer, which is significantly less time-consuming than usual. A parametric study of the influence of the mid-surface radius-to-thickness ratio, open- and closed-circuit surface conditions, the thickness ratio of each layer, and the material-property gradient index on the natural frequencies of functionally graded piezoelectric material sandwich cylinders is carried out.