Rapid heating of FGM plates resting on elastic foundation

IF 2.2 3区 工程技术 Q2 MECHANICS Archive of Applied Mechanics Pub Date : 2024-11-04 DOI:10.1007/s00419-024-02688-1
A. Salmanizadeh, M. R. Eslami, Y. Kiani
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Abstract

In this research, the thermally induced vibration of the plates on the elastic foundation has been investigated. The plate is made of functionally graded materials (FGMs) that is graded along the thickness. All mechanical and thermal properties dependent on temperature are taken into account. To apply the temperature dependence of thermomechanical properties, the well-known Touloukian equation is used. The two-parameter elastic foundation, Winkler–Pasternak, is considered to be linear, isotropic, and homogeneous. The general formulation and equations governing the phenomenon of thermally induced vibration have been written under the assumptions of linear uncouple thermoelasticity. The one-dimensional transient heat conduction equation has been discretized with the help of the finite element method in the direction of thickness, and it has been solved over time by applying the Crank–Nicolson method. Also, the thermally induced force and moment resultants in each time step have been calculated based on the temperature profile. To obtain the equations of motion, Hamilton’s principle based on the first-order shear deformation theory has been used, and the obtained equations and boundary conditions have been discretized by applying the generalized differential quadrature (GDQ) method and solved by using Newmark time marching scheme.

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快速加热弹性地基上的 FGM 板
本研究对弹性地基上板材的热诱导振动进行了研究。板由沿厚度方向分级的功能分级材料(FGMs)制成。所有与温度相关的机械性能和热性能都被考虑在内。为了应用热机械特性的温度依赖性,使用了著名的 Touloukian 方程。双参数弹性地基 Winkler-Pasternak 被认为是线性、各向同性和均质的。热诱导振动现象的一般公式和方程是在线性非耦合热弹性假设下编写的。一维瞬态热传导方程借助有限元法在厚度方向上进行了离散化,并通过使用 Crank-Nicolson 方法进行了时间求解。此外,还根据温度曲线计算了每个时间步的热诱导力和力矩结果。为了获得运动方程,使用了基于一阶剪切变形理论的汉密尔顿原理,并通过应用广义微分正交(GDQ)方法对获得的方程和边界条件进行了离散化,并使用纽马克时间行进方案进行了求解。
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来源期刊
CiteScore
4.40
自引率
10.70%
发文量
234
审稿时长
4-8 weeks
期刊介绍: Archive of Applied Mechanics serves as a platform to communicate original research of scholarly value in all branches of theoretical and applied mechanics, i.e., in solid and fluid mechanics, dynamics and vibrations. It focuses on continuum mechanics in general, structural mechanics, biomechanics, micro- and nano-mechanics as well as hydrodynamics. In particular, the following topics are emphasised: thermodynamics of materials, material modeling, multi-physics, mechanical properties of materials, homogenisation, phase transitions, fracture and damage mechanics, vibration, wave propagation experimental mechanics as well as machine learning techniques in the context of applied mechanics.
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