【摘要】 为分析具有复杂切口的功能梯度板自由振动响应，基于一种新的准三维高阶剪切变形理论（谱位移格式）的等几何分析方法被用来预测带切口板的动力特性。谱位移格式将未知位移场展开为厚度方向上特殊形式的切比雪夫级数，具有精度高，以及避免剪切闭锁问题的特性，对薄厚板的分析具有很好的通用性。利用达朗贝尔原理和虚功原理推导了功能梯度板自由振动的控制方程，并利用等几何方法对方程进行离散和求解。通过对数值算例的计算，以及与现有参考结果的比较，证明了提出的分析方法能够准确有效地分析具有复杂切口的功能梯度板自由振动问题。更多还原

【Abstract】 This paper aims to analyze the free vibration response of functionally graded plates with complex cutouts. An isogeometric analysis method based on a novel quasi-three-dimensional higher-order shear deformation theory called the spectral displacement formulation(SDF) is employed to predict the free vibration characteristics of the plates. The SDF can deal with the three-dimensional elasticity solution and naturally avoid the shear-locking problem, making it suitable for plates with varying thicknesses. The governing equations for free vibration of the plates are derived using the D’Alembert principle and the principle of virtual work, and the equations are discretized using isogeometric method. The results of several numerical examples are compared with existing reference solutions. It is concluded that the proposed analysis method can accurately and effectively analyze the free vibration of functionally graded plates with complex cutouts.更多还原