Dynamic stability analysis of tapered rotating beams with 2D functionally graded materials: A comparative study of Floquet theory approaches

IF 5.7 1区工程技术 Q1 ENGINEERING, CIVIL

Thin-Walled Structures Pub Date : 2025-04-10 DOI:10.1016/j.tws.2025.113257

Moustafa S. Taima , Tamer A. El-Sayed , Michael I. Friswell

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Abstract

This study investigates the dynamic and stability characteristics of rotating beams made from two-dimensional functionally graded materials (2D FGMs) with tapered geometry. Dynamics refers to the beam’s inherent vibrational behavior determined by its natural frequencies and/or time responses, and stability examines whether the system’s response remains bounded (stable) or becomes unbounded (unstable) under periodic excitation. The material properties are defined using a power law distribution model. The stiffness and mass matrices are derived based on the principle of virtual energy and evaluated using Bernoulli–Euler beam theories. Unlike previous studies, which often focus on single approaches, this research employs Floquet theory with three distinct techniques to evaluate the state transition matrix (STM), offering a comprehensive comparative analysis. The techniques investigated are the first-order step approximation, the improved integration method, and the second-order step approximation. The comparison identifies the most efficient approach in terms of accuracy and computational time, addressing limitations of existing methods. The impact of mean rotating speed, hub radius, dynamic amplitude factor, functionally graded (FG) material indexes, and taper ratio on the stability characteristics of the rotating 2D FGMs tapered beam is thoroughly analyzed. The results provide valuable insights into the dynamic behavior and stability of such beams, guiding the design and optimization of advanced rotating beam structures. The results indicate that the second-order approximation for computing the transition matrix achieves higher accuracy in predicting the instability boundaries compared to the first-order approximation, while being less time consuming than the improved integration method.

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二维功能梯度材料锥形旋转梁的动力稳定性分析：Floquet理论方法的比较研究

本文研究了由具有锥形几何形状的二维功能梯度材料（2D fgm）制成的旋转梁的动态和稳定性特性。动力学是指由其固有频率和/或时间响应决定的梁的固有振动行为，稳定性检查系统的响应在周期性激励下是保持有界（稳定）还是变得无界（不稳定）。材料性质是用幂律分布模型定义的。根据虚能原理推导出了刚度矩阵和质量矩阵，并用伯努利-欧拉梁理论进行了计算。与以往的研究不同，本研究采用Floquet理论和三种不同的技术来评估状态转移矩阵（STM），提供了全面的比较分析。研究了一阶阶逼近法、改进积分法和二阶阶阶逼近法。比较确定了在精度和计算时间方面最有效的方法，解决了现有方法的局限性。深入分析了平均转速、轮毂半径、动幅系数、功能梯度材料指标和锥度比对旋转二维fgm锥形梁稳定特性的影响。研究结果为此类梁的动力性能和稳定性提供了有价值的见解，指导了先进旋转梁结构的设计和优化。结果表明，二阶近似法计算转移矩阵在预测不稳定边界方面比一阶近似法具有更高的精度，同时比改进的积分法耗时更短。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Thin-Walled Structures 工程技术-工程：土木

CiteScore

9.60

自引率

20.30%

发文量

801

审稿时长

66 days

期刊介绍： Thin-walled structures comprises an important and growing proportion of engineering construction with areas of application becoming increasingly diverse, ranging from aircraft, bridges, ships and oil rigs to storage vessels, industrial buildings and warehouses. Many factors, including cost and weight economy, new materials and processes and the growth of powerful methods of analysis have contributed to this growth, and led to the need for a journal which concentrates specifically on structures in which problems arise due to the thinness of the walls. This field includes cold– formed sections, plate and shell structures, reinforced plastics structures and aluminium structures, and is of importance in many branches of engineering. The primary criterion for consideration of papers in Thin–Walled Structures is that they must be concerned with thin–walled structures or the basic problems inherent in thin–walled structures. Provided this criterion is satisfied no restriction is placed on the type of construction, material or field of application. Papers on theory, experiment, design, etc., are published and it is expected that many papers will contain aspects of all three.