【摘要】 为实现多面片结构等几何振动力学问题高效高精求解，在多面片等几何分析过程中引入截断层次B样条技术实现等几何参数网格的局部细化，通过基于残差的误差指示器驱动多面片振动力学模型的局部细化；给出了振动结构动力学控制方程弱形式及自适应等几何模型一致质量矩阵计算方法，推导了无阻尼无外力条件下自适应多面片结构的等几何模态分析的广义特征值方程．数值算例表明；该方法相较于全局细分建模方式，线性振动力学问题求解效率提升94%以上，前三阶固有频率偏差小于0.3%，同时显著提升一阶固有频率收敛率，有效兼顾建模精度与求解效率，可为复杂结构的等几何振动分析奠定基础．更多还原

【Abstract】 To achieve efficient and high accurate solutions for isogeometric vibration mechanics of multi-patch structures,truncated hierarchical B-spline techniques was introduced into the isogeometric analysis of multi-patch structures to enable the local refinement of isogeometric parameter meshes. Local refinement of multi-patch vibration mechanics models was driven by a residual-based error indicator. The weak form of the dynamic control equations and the calculation approach for the consistent mass matrix of adaptive isogeometric models were presented for vibrating structures,and the associated computation strategy was put forward for the consistent mass matrix,as well as a generalized eigenvalue equation was derived for isogeometric modal analysis of adaptive multi-patch structures under undamped and force-free conditions.Numerical examples show that compared with global refinement modeling,the proposed method improves the solution efficiency for linear vibration mechanical problems by over 94%,with deviations in the first three natural frequencies of less than 0.3%,while significantly enhancing the convergence rate of the first natural frequency.It effectively balances modeling accuracy and solution efficiency,laying a foundation for isogeometric vibration analysis of complex structures.更多还原