Investigation of Dynamic Characteristics of Imperfect FG Beams on the Winkler–Pasternak Foundation under Thermal Loading

The interest of the present paper is the analysis of free vibration of imperfect functionally graded (FG) beams resting on foundations (with two elastic parameters). The FG beam is made of temperature-dependent metal (Al)/ceramic (Al₂O₃) material, which is graded in the thickness direction and subjected to various thermal loads (uniform and nonuniform). The appearance of microvoids is considered as porosity in the body structure. Two models of the symmetric porosity distribution are examined. The studied one-dimensional (1D) structure is modeled by employing simple three-variable higher-order integral formulations. Zero traction on the free surface of the 1D structure is gained by using the sinusoidal warping function in the current model, which avoids correction factors. Analytical modeling of structures is carried out using the Hamilton principle and Navier approach to derive the equations of motion and the analytical solution of the current model. Several examples of the free vibration analysis are presented in graphical and tabular forms. A detailed parametric analysis is performed to illustrate the impact of several beam parameters, such as dimensions, inhomogeneity and porosity indices, as well as of the foundation reaction on the fundamental frequency of imperfect FG beams.