Purpose

This study aims to develop the governing differential equation and to analyze the free vibration of a rotating non-uniform beam having a flexible root and setting angle for variations in operating conditions and structural design parameters.

Design/methodology/approach

Hamiltonian principle is used to derive the flapwise bending motion of the structure, and the governing differential equations are solved numerically by using differential quadrature with satisfactory accuracy and computation time.

Findings

The results obtained by using the differential quadrature method (DQM) are compared to results of previous studies in the open literature to show the power of the used method. Important results affecting the dynamics characteristics of a rotating beam are tabulated and illustrated in concerned figures to show the effect of investigated design parameters and operating conditions.

Originality/value

The principal novelty of this paper arises from the application of the DQM to a rotating non-uniform beam with flexible root and deriving new governing differential equation including various parameters such as rotary inertia, setting angle, taper ratios, root flexibility, hub radius and rotational speed. Also, the application of the used numerical method is expressed clearly step by step with the algorithm scheme.

中文翻译：

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基于微分正交法的柔性根部旋转双锥梁自由振动分析

目的

本研究旨在开发控制微分方程并分析具有柔性根部和设置角的旋转非均匀梁的自由振动，以适应操作条件和结构设计参数的变化。

设计/方法/方法

利用哈密顿原理推导出结构的襟翼弯曲运动，利用微分求积法对控制微分方程进行数值求解，精度和计算时间均令人满意。

发现

将使用微分正交法 (DQM) 获得的结果与公开文献中先前研究的结果进行比较，以显示所用方法的功效。影响旋转梁动力学特性的重要结果被列出并在相关图中说明，以显示研究的设计参数和操作条件的影响。

原创性/价值

本文的主要新颖之处在于将 DQM 应用于具有柔性根部的旋转非均匀梁，并推导出新的控制微分方程，包括各种参数，如旋转惯量、设置角、锥度比、根部柔度、轮毂半径和旋转速度。此外，所使用的数值方法的应用与算法方案分步清晰地表达出来。