考虑剪切效应的旋转FGM楔形梁刚柔耦合动力学建模与仿真

本文对一类中心刚体-柔性梁系统在大范围转动下的刚柔耦合动力学问题进行了研究. 柔性梁为功能梯度材料(functionally graded materials, FGM)楔形变截面梁,材料体积分数在梁轴向呈幂律分布变化. 以弧长坐标来描述柔性FGM梁的几何位移关系,分别使用倾角和拉伸应变变量描述柔性梁的横向弯曲和纵向拉伸变形,并计及剪切效应. 采用假设模态法离散变形场,运用第二类拉格朗日方程进行方程推导,得到系统考虑剪切效应的刚柔耦合动力学模型. 基于全新的刚柔耦合动力学建模理论,研究不同轴向材料梯度分布的FGM楔形梁,通过数值仿真计算,分析讨论不同的转速、梯度分布规律以及变截面参数对系统动力学特性的影响. 结果表明,剪切效应对大高跨比的FGM楔形梁的变形影响较为明显,不容忽略;材料梯度分布规律和截面参数的选取均会对旋转FGM楔形梁的动力学响应和频率产生较大影响. 本文提出的考虑剪切效应的倾角刚柔耦合动力学模型是对以往非剪切模型的进一步完善,可应用于工程中的 Timoshenko梁结构的动力学问题求解. 

DYNAMIC MODELING AND SIMULATION OF ROTATING FGM TAPERED BEAMS WITH SHEAR EFFECT

In this paper, the rigid-flexible coupling dynamics of the rigid-flexible beam system under large overall rotating motion is studied. The flexible beam is a functionally graded material (FGM) tapered beam, and its material properties are assumed to vary along the beam axis with a power law relation. The geometrical displacement relationship of the flexible FGM beam is described by the arc coordinate. The transverse bending and longitudinal stretching of the flexible beam are considered by the variables of the slope angle and the stretching strain, respectively, and the shear effect is taken into account. The assumed modes method is used to describe the deformation field, and Lagrange’s equations of the second kind are used to derive the equations to obtain the rigid-flexible coupling dynamic model considering the shear effect. Based on the new rigid-flexible coupling dynamics modeling theory, dynamics of the FGM tapered beams with different axial gradients are studied. The influences of different rotating speeds, gradient distributions and variable cross-section parameters on the dynamic characteristics of the system are analyzed by numerical simulations. The results show that the effect of shear on the deformation of FGM tapered beam with depth-span ratio is obvious. The distribution of the material gradient and the selection of the cross-section parameters will have a great influence on the dynamic responses and frequencies of the rotating FGM tapered beam. The rigid-flexible coupling dynamic model considering the shear effect is a further improvement of the previous non-shear model, which can be applied to solve the dynamic problems of the Timoshenko beam structures.