Analysis of Free Vibrations of Functionally Graded Porous Beams on Elastic Foundation in Thermal Environment Using Differential Quadrature Method

In this paper, the free vibrations of functionally graded porous beams with simple boundary conditions on an elastic foundation in a thermal environment were studied using the theory of third-order shear deformation. The properties of the material are temperature dependent and continuously change in the direction of the thickness of the beam and according to the power law distribution of the volume fraction of the material constituents. The uniform porosity distribution at the cross section is examined. Hamilton's principle was used to obtain the governing equations of motion. In order to discretize these equations, the generalized differential quadrature method has been used. Here, the effect of various parameters such as heat field type, temperature difference, power law index, porosity volume fraction, slenderness ratio and elastic foundation parameters on the natural frequencies of a functionally graded porous beam was studied for simple boundary conditions. The results, in addition to showing these effects on the thermomechanical behavior of the beam, also confirm the accuracy of the numerical method used.