A unified variational method for vibration of functionally graded porous beams with variable curvature under arbitrary boundary condition

Abstract

Curved beams with variable curvature can be encountered in many engineering cases, but continuous and complex changes of the radius and center can lead to challenges for dynamic modeling of these structures. In this paper, a unified variational approach for vibration analysis of a beam with variable curvature is derived in global Cartesian coordinates. The material properties and porosity of the beam are continuously changed along the thickness direction. Continuity constraints are added to the adjacent sections of the beam using proposed variational principles to ensure that accurate solutions can be obtained with any basis functions and under arbitrary boundary conditions. Compared with the available results in the literatures or using FEM, the convergence and accuracy of this method are proved. Parabolic beams are developed as examples to demonstrate the robust performance of the proposed method for parameter study. The effects of power-law index, porosity and parabolic parameters on the natural frequencies of the beam with variable curvature are analyzed. Particularly, the influences of geometric shape on the natural frequencies of beam is presented under various boundary conditions, which has important guiding significance for the vibration research of irregularly curved beam structures.