摘要
基于绝对节点坐标(absolute nodal coordinate formulation,ANCF)法研究了功能梯度薄椭圆柱壳的自由振动特性。采用三阶Bézier曲线拟合技术,对ANCF矩形壳单元初始周向切矢量和周向弧长进行了计算,从而避免了椭圆积分计算,增加了拟合精度。从动能表达式和格林应变张量与绝对位移的函数关系出发,推导了功能梯度薄椭圆柱壳单元的广义质量矩阵、广义弹性力列阵和广义刚度矩阵。利用达朗贝尔原理,建立了其非线性动力学微分方程组。在系统的平衡位置处,通过引入广义坐标的微小变化量,建立了功能梯度薄椭圆柱壳的线性运动微分方程方程组。通过数值计算,分析了梯度指标、椭圆截面偏心率及长径比对两端简支功能梯度薄椭圆柱壳固有频率的影响。结果表明,材料的弹性模量比、密度比和梯度指标对固有频率有着明显的影响;不锈钢-氧化铝壳的各阶固有频率(周向波数为1~3)随长径比的增大而减小;周向波数为1对应的固有频率随偏心率的增大而增大,且长径比是影响固有频率变化的主要因素。
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.
作者
范博
王忠民
侯思谦
FAN Bo;WANG Zhongmin;HOU Siqian(School of Mechanical and Precision Instrument Engineering,Xi'an University of Technology,710048 Xi'an,China;School of Civil Engineering and Architecture,Xi'an University of Technology,710048 Xi'an,China;Huanghe University of Science and Technology,450063 Zhengzhou,China)
出处
《应用力学学报》
北大核心
2025年第3期629-638,共10页
Chinese Journal of Applied Mechanics
基金
国家自然科学基金资助项目(No.11972286)
西安理工大学博士创新基金资助项目(No.30019902)。
关键词
绝对节点坐标法
功能梯度材料
薄椭圆柱壳
振动特性
absolute nodal coordinate formulation
functionally graded material
thin elliptic cylindrical shell
vibration characteristic
