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基于弯曲模型,进行框架叠合梁的自由振动分析。提出具有层细化弯矩分布的3结点单元。采用余弦函数求解横向剪切应变,避免了使用剪切修正因子。考虑了层表面连续条件和梁顶底面的边界条件。采用拉格朗日与Hermite差值方法进行有限元分析。特别要注意的是,未知数的个数与梁层数无关。为确定新单元的性能以获得弹性或有限元的精确解,对叠合梁进行机械振动试验。探讨了收敛速度与精确度,在不同边界条件下,新的有限元方法耗时低却获得非常精确的结果。承受横向正应力的两种模型均能考虑厚度模式。
Free Vibration Analysis of Frame Composite Beams Based on Bending Model. A 3-node cell with layer-thinning moment distribution is proposed. Using the cosine function to solve transverse shear strain, avoiding the use of shear correction factors. The continuous surface conditions and the boundary conditions of the bottom of the beam are considered. Finite element analysis is done by Lagrange and Hermite difference methods. It is important to note that the number of unknowns is independent of the number of beam layers. To determine the performance of a new unit to obtain an exact solution of elasticity or finite element, a mechanical vibration test is performed on the composite beam. The convergence speed and accuracy are discussed. Under different boundary conditions, the new finite element method consumes less time but obtains very accurate results. Both models that take lateral normal stresses can consider the thickness mode.