基于ANCF的功能梯度薄椭圆柱壳的自由振动分析

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中图分类号：0326 文献标志码：A文章编号：1000-4939（2025）03-0629-10

Abstract ：Based on the absolute nodal coordinate formulation（ANCF），the free vibration characteristics of functionally graded thin eliptic cylindrical shells are investigated. Using the third-order Bézier curve fitting technique，the circumferential tangent vector and circumferential length of ANCF-rectangular-shell element are calculated，which avoids the elliptic integral calculation and increases the fiting accuracy.Based on the kinetic energy expression and the functional relationship between Green's strain tensor and absolute displacement，the generalized mass matrix，generalized elastic force column matrix and generalized stiffness matrixof functionally graded thin elliptic cylindrical shell are derived.The nonlinear dynamical diferential equations are established based on D'Alembert principle.At the equilibrium position of the system，the linear diferential equations of motion for the functionally graded thin eliptic cylindrical shell are established by introducing the small variation quantity of the generalized coordinates.Through numerical calculation， this paper analyzes the effects of different gradient indexes，eccentricity of eliptical section and length-radius ratio on the natural frequencies of functionally graded thin eliptic cylindrical shels with simply supported ends.The results show that the elastic modulus ratio，density ratio and gradient index of materials have obvious influences on the natural frequency；the natural frequencies of shell made of stainless steelalumina （circumferential wave number is 1～3 ） decrease with the increase of length-radius ratio； the natural frequency corresponding to the circumferential wave number of 1 increases with the increase of eccentricity ，and length-radius ratio is the main factor affecting the change of natural frequency.

KeyWords：absolute nodal coordinate formulation；functionally graded material；thin eliptic cylindrica shell；vibration characteristic

功能梯度材料的材料参数（如弹性模量、密度等）会因其材料的组成和结构等参数沿着某方向从一侧到另一侧的梯度分布变化，来适应不同条件下对材料力学性能的不同要求[1]。（剩余10697字）