2D magneto-mechanical vibration analysis of a micro composite Timoshenko beam resting on orthotropic medium

IF 2.1 3区 工程技术 Q2 ENGINEERING, CIVIL Smart Structures and Systems Pub Date : 2021-01-01 DOI:10.12989/SSS.2021.27.1.001
M. Mehrabi, M. Mohammadimehr, F. Mousavinejad
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引用次数: 2

Abstract

In the present study, the free vibration analysis of a size-dependent micro composite Timoshenko beam model reinforced by various distributions of carbon nanotubes under temperature changes and two-dimensional magnetic field is investigated based on modified strain gradient theory. Also, the effects of environment are simulated by orthotropic elastic foundation and it is assumed that the material properties are temperature-dependent. Mathematical formulations are obtained using Hamilton's principle and the governing equations of motion are derived based on energy approach and variation method. These equations are solved using semi-analytical and numerical methods such as Navier's type solution, finite element method and generalized differential quadrature method for various boundary conditions. The obtained results of this study are compared with the other previous researches and there is a good agreement between them. The main purpose of this work is the comparison of various solution methods on the problem outputs. Thus, the results are compared together and the effects of solution approach on the dimensionless natural frequencies is developed. Moreover, the effects of length-to-thickness ratio, magnetic field, temperature changes, elastic foundation and carbon nanotubes volume fractions on the dimensionless natural frequencies are studied. The results of this article demonstrate that the micro composite Timoshenko beam reinforced by FG-O and FG-X CNTs have lowest and highest dimensionless natural frequency, respectively. It is investigated that the dimensionless natural frequency enhances by increasing the magnetic field in x and z-directions.
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正交各向异性介质上微复合Timoshenko梁的二维磁-机械振动分析
本文基于修正应变梯度理论,研究了温度变化和二维磁场作用下不同碳纳米管分布增强的尺寸相关微复合材料Timoshenko梁模型的自由振动分析。同时,采用正交各向异性弹性地基模拟了环境的影响,并假设材料的性能与温度有关。利用哈密顿原理推导了其数学表达式,并基于能量法和变分法推导了运动控制方程。在各种边界条件下,采用半解析和数值方法求解这些方程,如Navier型解、有限元法和广义微分正交法。本文的研究结果与前人的研究结果进行了比较,两者之间有很好的一致性。本工作的主要目的是对问题输出的各种求解方法进行比较。因此,对结果进行了比较,并讨论了求解方法对无量纲固有频率的影响。此外,还研究了长厚比、磁场、温度变化、弹性基础和碳纳米管体积分数对无量纲固有频率的影响。结果表明,FG-O和FG-X碳纳米管增强的微复合材料Timoshenko梁的无量纲固有频率最低,无量纲固有频率最高。研究了在x方向和z方向上增大磁场对无量纲固有频率的影响。
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来源期刊
Smart Structures and Systems
Smart Structures and Systems 工程技术-工程:机械
CiteScore
6.50
自引率
8.60%
发文量
0
审稿时长
9 months
期刊介绍: An International Journal of Mechatronics, Sensors, Monitoring, Control, Diagnosis, and Management airns at providing a major publication channel for researchers in the general area of smart structures and systems. Typical subjects considered by the journal include: Sensors/Actuators(Materials/devices/ informatics/networking) Structural Health Monitoring and Control Diagnosis/Prognosis Life Cycle Engineering(planning/design/ maintenance/renewal) and related areas.
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