自然弯扭梁的耦合振动特性分析

以自然弯扭梁理论为基础对具有一般横截面形状空间曲梁的耦合振动特性进行了研究。 在该梁的运动控制方程中，位移函数和广义翘曲坐标均被定义在形心轴上，且在分析中包括了转动惯量、横向剪切变形以及和扭转有关的翘曲对振动的影响。通过对数学计算软件MATHEMATICA的精确运用可以得到该梁振型的解析表达式，精确的固有频率则可用搜索的方法来确定。为了证明理论的有效性，对两端固支椭圆截面曲梁的固有频率和振型进行了求解，并把数值计算结果同使用PATRAN梁单元的有限元结果进行了比较。

Analysis of coupled vibrational behavior for naturally curved and twisted beams

Coupled vibrational behavior for spatial curved beams with general cross-sectional shapes, based on naturally curved and twisted beam theory, is theoretically investigated. In the governing equations of motion of the beams, all displacement functions and the generalized warping coordinate are defined at the centroid axis and also the effects of rotary inertia, transverse shear deformations and torsion-related warping are included in the present formulations. The explicit analytical expressions which give the vibrating mode shapes of the beams are derived by rigorous application of the computing package MATHEMATICA and a process of searching is used to determine the exact natural frequencies. In order to demonstrate the validity of the present theory, the natural frequencies and vibration modes of a curved beam of elliptic cross section with clamped-clamped boundary condition are evaluated and compared with the FE-results using PATRAN’s beam elements.