Abstract

This paper, for the first time, presents the thermal shock response of porous functionally graded (FG) sandwich curved beams subjected to thermal shocks. The authors have used a higher-order layerwise beam theory developed for the analysis. This new layerwise theory has a higher-order displacement field for the core and a linear displacement field for top and bottom facesheets maintaining the continuity of displacement at the layer interface. The top and bottom layers of the functionally graded sandwich curved beam are made of pure ceramic and pure metal constituent, respectively, and the core is considered to be made of functionally graded material (FGM) having porosity. The top surface of the beam is subjected to thermal shocks the bottom surface is kept at a reference temperature or is thermally insulated. The solution for the nonlinear temperature profile is obtained using the Crank-Nicolson method. An eight-noded isoparametric element having seven degrees of freedom per node is used to develop the finite element formulation. The governing differential equation is obtained using the Hamilton’s principle, and the resulting transient problem is solved using the Newmark constant acceleration integration method. The effects of curvature, thickness, core to facesheet thickness ratio, intensity of the thermal shock, porosity coefficient, and boundary conditions are investigated on thermally induced vibration response of porous FG sandwich curved beams. The analysis reveals that the proposed finite element formulation is straight forward, accurate, and widely applicable for the analysis of porous functionally graded sandwich curved beams.

摘要

本文首次介绍了受热冲击影响的多孔功能梯度 (FG) 夹层曲梁的热冲击响应。作者使用了为分析而开发的高阶分层梁理论。这种新的分层理论具有用于核心的高阶位移场和用于顶部和底部面板的线性位移场，以保持层界面处位移的连续性。功能梯度夹层曲梁的顶层和底层分别由纯陶瓷和纯金属组成，芯部被认为是由具有孔隙率的功能梯度材料（FGM）制成。梁的顶面受到热冲击，底面保持在参考温度或隔热。使用 Crank-Nicolson 方法获得非线性温度曲线的解。每个节点具有七个自由度的八节点等参元素用于开发有限元公式。使用哈密顿原理获得控制微分方程，并使用 Newmark 恒定加速度积分方法求解由此产生的瞬态问题。研究了曲率、厚度、芯与面板厚度比、热冲击强度、孔隙率系数和边界条件对多孔 FG 夹层曲梁的热致振动响应的影响。分析表明，所提出的有限元公式直接、准确，并且广泛适用于多孔功能梯度夹层曲梁的分析。