Vibrations Evaluation of Functionally Graded Porous Beams in Thermal Surroundings by Generalized Differential Quadrature Method

This study investigates how to obtain the natural frequency of functionally graded porous beams simply supported on an elastic substrate in thermal surroundings by the theory of third-order shear deformation. Temperature constantly changes in the beam thickness direction and step with the distribution of volume fraction power law of the ingredient has been affected on the material attributes. The distribution of uniform porosity at the pass phase is examined. To achieve the equations of governing, Hamilton's principle was carried out. To discretize these equations, the generalized differential quadrature method has been used. First, the approach's convergence is shown. Comparison with the results of other articles was performed for validation. Here, the impacts of numerous factors like index of power law, heat field type, temperature difference, slenderness ratio, and porosity coefficient and elastic substrate factors of a functionally graded porous beam on the natural frequencies were studied for simple boundary conditions. In addition to displaying these parameters’ impact on the beam’s thermomechanical evaluation, the conclusions also confirm the accuracy of the numerical technique used.