On the Free Vibration Behavior of Temperature-Dependent Bidirectional Functionally Graded Curved Porous Beams

Abstract

Based on a quasi-3D beam formulation, study on frequencies of bidirectional functionally graded (BDFG) curved porous beam in thermal environment is carried out. In severe thermal conditions, where BDFGs are considered to be highly efficient, temperature affects the properties of the BDFG beams. Consequently, this study focuses on the free vibration of porous BDFG curved beams by considering the effective temperature-dependent properties as a function of position across the thickness and thermal rise. The displacement field used contains indeterminate terms and involves a few variables to define. The mechanical characteristics of the curved beam are supposed to be temperature-dependent and graded in both axial and transverse direction depending on various porosity patterns. The governing equations of the simply supported curved porous beam are derived using the principal of virtual works and are then solved utilizing the Navier solution. The accuracy of the current formulation is tested by checking its results with other relevant publications found in the literature. Through a parametric study, we examine the impact of materials properties temperature-dependence, grading indexes, porosity distribution, radius of curvature and other parameters on the frequencies of curved bidirectional functionally graded porous beams. The results reveal that these parameters have a great influence on the free vibration response of porous BDFG curved beams. These results can serve as reference solutions for future investigations.