This paper aims to analyze dynamic response of axially functionally graded (FG) Timoshenko beams on Winkler–Pasternak elastic foundation. Spring constant and material inhomogeneity are used as research parameters in the dynamic analysis. In this study, ODEs in Laplace domain are calculated by using complementary functions method. The analysis is performed in the Laplace domain, and calculations are converted to the time domain by using Durbin’s algorithm. The effects of material gradient index, translational and rotational spring constants, slenderness ratio, different boundary conditions and impulsive loads on the dynamic response of FG Timoshenko beams are investigated.

中文翻译：

---

温克勒-帕斯捷尔纳克弹性地基上功能梯度铁木辛哥梁的振动分析

本文旨在分析 Winkler-Pasternak 弹性基础上轴向功能梯度 (FG) Timoshenko 梁的动力响应。弹簧常数和材料不均匀性被用作动态分析中的研究参数。本研究采用互补函数法计算拉普拉斯域中的常微分方程。分析是在拉普拉斯域中进行的，使用杜宾算法将计算转换到时域。研究了材料梯度指数、平移和旋转弹簧常数、长细比、不同边界条件和冲击载荷对 FG Timoshenko 梁动态响应的影响。