Vibration analysis of non-uniform tapered beams with nonlinear FGM properties

This paper presents the free vibration analysis of a non-uniform cone beam with nonlinearly varying axial functionally graded material (FGM) properties. Based on the Adomian decomposition method and a proposed modified mathematical procedure, the vibration mode shapes and natural frequencies of a nonlinearly tapered FGM beam are analytically derived. Several vibration analyses for uniform and non-uniform FGM structures are presented and the results are compared with the existing ones to prove the effectiveness and accuracy of the proposed methodology. Additionally, vibration analysis of exponentially and trigonometrically tapered beams with nonlinearly axial varying FGM properties considering different geometry and material taper ratios was studied and presented. Based on this analytical model, ideal structural design can be efficiently achieved for many engineering applications, such as stability enhancement and energy harvesting.