基于复合单元模型的轴向功能梯度梁的振动分析

his paper presents a simple yet accurate approach to analyze the free and forced vibrations of axially functionally graded (AFG) beams. The governing equations of the beam is derived by Lagrange's equations and then discretized by the composite element method. Numerical simulations are presented to show the effects of Young's modulus variation, mass density variation, and slenderness ratios, on the dynamic characteristics of the AFG beams. The natural frequencies obtained from the proposed method are found to be in close agreement with those from finite element and other methods. The forced vibration responses of the AFG beam are also calculated from the proposed method and compared with those obtained from the finite element method (FEM). Time histories from both methods are found to match very well. This further indicates the correctness of the present method for forced vibration analysis of the AFG beam.