A hierarchical formulation is presented for the large displacement modal and transient analysis of rotating plates having different thicknesses, sizes, and settings angle with respect to the spinning axis. After derivation of the governing equations of motion by the Principle of Virtual Displacements, the finite element discretization yields a set of nonlinear ordinary-differential equations for the generalized coordinates including gyroscopic terms, centrifugal/Euler accelerations and spin-softening effects. A Total Lagrangian approach is adopted. The modal analysis is performed by a two-step procedure. The static shape of the structure deformed by the centrifugal force is first defined. Subsequently, eigenfrequencies and mode shapes are computed by a classical eigenvalue problem past the static configuration previously computed. The transient analysis of the plates subject to a varying angular velocity is tackled by solving the nonlinear equations of motion by the Generalized-\(\alpha \) method coupled to the Newmark’s approximation for the velocity and acceleration fields. It has been numerically proven that accurate results can be obtained by the use of Murakami’s Zig-Zag Function which a-priori enforces the interlaminar discontinuity of the displacements’slopes in the Equivalent Single Layer axiomatic model, thus avoiding higher-order polynomial representations for the displacement fields, or the use of Layer-Wise theories.

针对具有不同厚度、尺寸和相对于旋转轴的设置角度的旋转板的大位移模态和瞬态分析，提出了一种分层公式。通过虚拟位移原理推导运动控制方程后，有限元离散化为广义坐标生成一组非线性常微分方程，包括陀螺项、离心/欧拉加速度和自旋软化效应。采用全拉格朗日方法。模态分析分两步进行。首先定义由离心力变形的结构的静态形状。随后，通过先前计算的静态配置的经典特征值问题计算特征频率和模式形状。\(\alpha \)方法耦合到速度和加速度场的纽马克近似。数值证明，通过使用 Murakami 的 Zig-Zag 函数可以获得准确的结果，该函数先验地强制等效单层公理模型中位移斜率的层间不连续性，从而避免了高阶多项式表示位移场，或使用分层理论。