Free vibration analysis of functionally graded thin elliptic cylindrical shell based on ANCF postprint

Abstract: Based on the absolute nodal coordinate formulation (ANCF), the free vibration characteristics of functionally graded thin elliptic 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 fitting 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 matrix of functionally graded thin elliptic cylindrical shell are derived. The nonlinear dynamical differential equations are established based on D'Alembert principle. At the equilibrium position of the system, the linear differential equations of motion for the functionally graded thin elliptic 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 elliptical section and length-radius ratio on the natural frequencies of functionally graded thin elliptic cylindrical shells 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 steel-alumina (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.