Vibration analysis of functionally graded porous piezoelectric deep curved beams resting on discrete elastic supports

Abstract This paper presents a modified variational method for the dynamic analysis of functionally graded piezoelectric (FGPM) deep curved beams with porosity (FGPP beam) resting on an arbitrary number of discrete elastic foundations (EFs). The material properties including the electrical and porous property are assumed to continuously vary in the thickness direction. A modified principle is developed to impose the continuity constrains on the internal and boundaries of the beam in both mechanical and electric field, which allows any linearly independent, complete basis functions to achieve satisfactory solutions. The shear, inertial and curvature effects of the moderately thick deep curved beams are also introduced in the energy functionals. The superior convergence, accuracy and efficiency of the proposed method are validated by comparing the proposed results with those available in literature. Series of numerical examples are presented for the free and transient vibration of the FGPP beams with different material properties. The influences of the power-law index, porosity, applied electric voltage and the EFs on the natural frequencies and transient dynamic responses of the FGPP beams are examined. Especially, the combined effects of porosity properties with other material properties on the dynamic characteristics of the FGPP beams are firstly presented, which are of significance for optimal design of corresponding smart structures.