Nonlinear dynamic analyses of a rotating ferromagnetic functionally graded cylindrical shell with initial geometric imperfections

IF 5.7 1区工程技术 Q1 ENGINEERING, CIVIL

Thin-Walled Structures Pub Date : 2025-04-11 DOI:10.1016/j.tws.2025.113264

Tao Yang , Yuda Hu

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Abstract

In this paper, the magneto-thermoelastic dynamic response of a rotating ferromagnetic functionally graded (FG) cylindrical shell with initial geometric imperfections is investigated. Considering the temperature dependence and spatial graded characteristics of physical properties, a combination of power-law distribution and temperature-dependent function is employed to formulate the equivalent physical parameters mathematically. Using the physical neutral surface as a reference and based on Donnell's nonlinear shell theory, constitutive equations are established for the FG cylindrical shell with initial geometric imperfections. Meanwhile, considering the effect of rotation, which induces both the centrifugal force and initial circumferential tension, expressions for kinetic energy and initial strain energy are presented. According to the electromagnetic elasticity theory, the Lorentz force generated by the eddy current effect and the nonlinear magnetization force due to spin magnetic moments are deduced. Subsequently, the nonlinear governing equations are established and discretized based on Hamilton's principle and Galerkin's method. Analytical solutions for the steady-state response are derived utilizing the multi-scale method, and stability conditions of the resonance response are determined by the Lyapunov theory. Afterward, numerical results are leveraged to perform detailed parametric studies on the vibration response of different resonance forms. Of particular interest in this process is the influence of initial geometric imperfections and external physical fields on the resonance behavior. This study offers a rigorous solution and deepens the understanding of the dynamic behavior of rotating imperfect cylindrical shells in multi-physical fields.

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具有初始几何缺陷的旋转铁磁功能梯度圆柱壳的非线性动力学分析

本文研究了具有初始几何缺陷的旋转铁磁功能梯度（FG）圆柱壳的磁热弹性动力学响应。考虑到物性的温度依赖性和空间梯度特征，采用幂律分布和温度依赖函数相结合的数学方法来表示等效物性参数。以物理中性面为参考，基于Donnell非线性壳理论，建立了具有初始几何缺陷的FG圆柱壳的本构方程。同时，考虑到旋转的影响，产生离心力和初始周向张力，给出了动能和初始应变能的表达式。根据电磁弹性理论，推导了涡流效应产生的洛伦兹力和自旋磁矩引起的非线性磁化力。然后，根据Hamilton原理和Galerkin方法建立非线性控制方程，并对其进行离散化。利用多尺度法推导了稳态响应的解析解，并利用李亚普诺夫理论确定了谐振响应的稳定条件。然后，利用数值结果对不同共振形式的振动响应进行了详细的参数化研究。在这一过程中特别令人感兴趣的是初始几何缺陷和外部物理场对共振行为的影响。该研究提供了一个严谨的解决方案，加深了对旋转非完美圆柱壳在多物理场中的动力学行为的理解。

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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.