Dynamics Sensitivity Analyses of Functionally Graded Porous (FGP) Curved Beams with Variable Curvatures and General Boundary Conditions

Abstract

A method is proposed to obtain the exact solution for the dynamic analysis of functionally graded porous (FGP) curved beams with general boundary conditions and variable curvatures. First, the model of a curved beam of variable curvature is constructed, and then the beam is divided into a number of free beam segments via a multi-segment segmentation (MSS) strategy. Second, the first-order shear deformation theory (FSDT) is adopted to obtain the displacement fields of each segment, and then the kinetic energy and potential energy of the structure are expressed by the displacement field. Finally, the exact solution is obtained by the Hamilton principle. Using the springs to simulate various boundary conditions, the frequency parameters, modal shapes and forced vibration responses of the structure with elastic boundary conditions are calculated, with the convergence and correctness verified. Finally, effects of the FGP curved beams, such as porosity distribution types, porosity ratios, boundary condition types, geometry parameters and load types, are investigated in detail.