Abstract

The interest of the present paper is the analysis of free vibration of imperfect functionally graded (FG) beams resting on foundations (with two elastic parameters). The FG beam is made of temperature-dependent metal (Al)/ceramic (Al₂O₃) material, which is graded in the thickness direction and subjected to various thermal loads (uniform and nonuniform). The appearance of microvoids is considered as porosity in the body structure. Two models of the symmetric porosity distribution are examined. The studied one-dimensional (1D) structure is modeled by employing simple three-variable higher-order integral formulations. Zero traction on the free surface of the 1D structure is gained by using the sinusoidal warping function in the current model, which avoids correction factors. Analytical modeling of structures is carried out using the Hamilton principle and Navier approach to derive the equations of motion and the analytical solution of the current model. Several examples of the free vibration analysis are presented in graphical and tabular forms. A detailed parametric analysis is performed to illustrate the impact of several beam parameters, such as dimensions, inhomogeneity and porosity indices, as well as of the foundation reaction on the fundamental frequency of imperfect FG beams.

中文翻译：

---

温克勒-帕斯捷尔纳克基础上热载荷下不完美 FG 梁的动力特性研究

摘要

本文的兴趣是分析基于基础（具有两个弹性参数）的不完美功能梯度（FG）梁的自由振动。_{FG梁由与温度相关的金属（Al）/陶瓷（Al 2} O ₃ ）材料制成，该材料在厚度方向上分级并承受各种热载荷（均匀和非均匀）。微孔的出现被认为是主体结构中的孔隙率。研究了对称孔隙率分布的两个模型。通过采用简单的三变量高阶积分公式对所研究的一维 (1D) 结构进行建模。通过使用当前模型中的正弦扭曲函数，可以在一维结构的自由表面上获得零牵引力，从而避免了校正因子。使用汉密尔顿原理和纳维方法进行结构分析建模，导出运动方程和当前模型的解析解。自由振动分析的几个例子以图形和表格的形式给出。进行了详细的参数分析，以说明几个梁参数的影响，例如尺寸、不均匀性和孔隙率指数，以及地基反应对不完美 FG 梁基频的影响。