考虑尺度效应的夹层楔形多孔梁动力学分析

基于修正偶应力理论, 研究了具有大范围旋转中心刚体-功能梯度夹层Euler-Bernoulli楔形多孔柔性微梁系统的动力学特性.楔形梁是中间层为不完全功能梯度层, 两表层为均质材料的功能梯度夹层结构, 它可以减小传统夹层结构由于层与层之间材料属性的不同导致脱粘类型损伤的影响.采用假设模态法描述变形, 考虑具有捕捉动力刚化效应的非线性耦合项, 计及von Kármán几何非线性应变, 运用第二类Lagrange方程, 导出了适用于较大变形的高次刚柔耦合动力学方程.对在平面内做大范围运动的中心刚体-功能梯度夹层Euler-Bernoulli楔形多孔微梁的动力学特性进行了详细研究.研究表明: 功能梯度夹层楔形梁表层结构高度、旋转角速度、功能梯度幂指数、尺度参数、孔隙度以及各层结构的体积分数对系统的动力学特性都有很大的影响; 功能梯度夹层楔形梁综合了功能梯度直梁和楔形梁的特性, 其相对于功能梯度直梁的固有频率增大, 同时使得孔隙度对结构固有频率变化趋势的影响不再与功能梯度直梁相同; 由于柔性梁变形能中具有横向与轴向的耦合势能, 系统在稳态下的平衡位置发生了迁移现象; 系统随着尺度参数的变化发生了频率转向与振型转换. 

DYNAMIC ANALYSIS OF SANDWICH TAPERED POROUS MICRO-BEAMS CONSIDERING SIZE EFFECT 1)

Based on the modified couple stress theory, a size-dependent dynamic model of large overall rotating hub-flexible sandwich tapered Euler-Bernoulli micro-beams made from functionally graded materials with porosities is developed to study their dynamic characteristics. The functionally graded sandwich tapered micro-beams are composed of a core with inperfect functionally graded materials sandwiched between two homogeneous face sheets, which can decline the influence of the traditional sandwich structure debonding damage caused by the mismatch of stiffness properties between their core and face sheets. The high-order rigid-flexible coupled dynamic equations of the system applied to large deformation are derived by considering the von Kármán geometric nonlinear strain and adopting Lagrange's equation of the second kind. The method of assumed modes is used to describe the chordwise and axial deformations of micro-beams. The dynamic stiffening effect is captured the nonlinear coupling term obtained by longitudinal shortening caused by the transverse bending deformation of the micro-beams. Then, under the effects of different parameters, such as the width of face sheets of the tapered micro-beams, rotating angular velocity, material gradient index, size-dependency, porosities and volume fractions of each layer structure, the dynamic characteristics of functionally graded sandwich micro-beams in the plane are investigated. The functionally graded sandwich tapered micro-beams combine the characteristics of the functionally graded rectangular micro-beams and the tapered micro-beams. Compared with the functionally graded rectangular micro-beams, these characteristics make the natural frequency of the functionally graded sandwich tapered micro-beams increase and lead to different influences of porosities on the natural frequencies of the structures. Moreover, since the coupling potential energy of the chordwise and axial motions is involved in the strain energy of the flexible micro-beams, the equilibrium position of the system migrates in the steady state. It is observed that interesting frequency veering and mode shift phenomena of the system are observed when the size-dependency changes.