基于一维高阶理论和模式识别算法,建立了考虑圆角截面特征的薄壁梁精细动力学模型,能够准确预测其三维动力学行为。首先,构建基于离散薄壁截面基函数的一维高阶初始模型,通过求解控制微分方程相关的广义特征值问题解耦各广义坐标的轴向变化模式。然后,构建广义特征矩阵并基于主成分分析算法获取基函数权值组合,用于重组具有明确物理意义的截面特征形变组合。为进一步降低模型自由度,根据精度需求按优先级顺序选取截面特征形变组合,构建改进的一维高阶模型用于工程计算。数值计算结果表明,与二维板壳模型相比,本文改进模型能够以前者1%的单元数准确预测圆角截面薄壁梁动力学特性及瞬态动力学行为,前15阶频率误差在1.4%以内,且能够广泛适用于长细比4以上的薄壁结构。
Abstract
Refined dynamic models of thin-walled beams with rounded corners are established based on one-dimensional higher order theory and pattern recognition algorithm, which is capable of accurately predicting their three-dimensional kinetic behaviors. First, an initial higher order model is formulated using the basis functions defined on the discrete cross-section, and axial vibration modes of generalized coordinates are decoupled by solving the generalized eigenvalue problem involved with the governing differential equations. Then the generalized eigen matrix is established to obtain the composition weight of each basis function with the application of principal component analysis, which is further used to “assemble” a set of deformation modes with clear structural interpretations. To further reduce the degrees of freedom of the new model, a reduced set of deformation modes are selected in the order of their priorities according to the accuracy requirements, and an improved one-dimensional higher order model is constructed for engineering calculations. Numerical results show that the presented model can accurately predict the dynamic characteristics and transient dynamic behaviors of thin-walled structures by employing 1% elements of compared two-dimensional plate/shell model, with frequency errors of the first 15order modes within 1.4%, and that it is applicable for thin-walled structures with slenderness ratios beyond 4.
关键词
薄壁结构 /
圆角截面 /
一维高阶理论 /
主成分分析 /
动力学建模 /
瞬态动力学行为
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Key words
thin-walled structure /
rounded corners /
one-dimensional higher order model /
principal components analysis /
dynamics modeling;transient dynamic behaviors
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