Abstract

This paper deals with dynamic analysis of functionally graded beams on elastic foundation considering damping effect. It is assumed that the mechanical properties of the material vary along the beam thickness. The fourth-order differential equation is analytically solved by means Green's function method, and exact answer is achieved. Damping effect, which is an intrinsic property of structures with great influence on the forced vibration of mechanical systems is included in the analysis. However, due to difficulty involved, it is usually neglected in the analysis of structures. Furthermore, the effect of rotary inertia is considered in the problem formulations. Green’s function method is a straightforward way to model physical problems subjected to arbitrary loads and affected by various parameters, such as, elastic foundation, damping, geometry and mechanical properties. It could be a unique solution to gain the exact answers via the superposition manner. To demonstrate the accuracy and efficiency of the presented solution, dynamic response of the beam under different harmonic loads is obtained and compared to available results in some cases.

摘要

本文研究了考虑阻尼效应的弹性地基上功能梯度梁的动力分析。假设材料的机械特性随梁的厚度而变化。利用格林函数法对四阶微分方程进行了解析求解，得到了精确解。分析中包括阻尼效应，它是结构的固有特性，对机械系统的受迫振动影响很大。但由于难度较大，在结构分析中通常被忽略。此外，在问题公式中考虑了旋转惯性的影响。格林函数法是对承受任意载荷并受各种参数影响的物理问题进行建模的直接方法，例如弹性基础、阻尼、几何和机械性能。通过叠加的方式得到准确的答案可能是一个独特的解决方案。为了证明所提出解决方案的准确性和效率，获得了梁在不同谐波载荷下的动态响应，并与某些情况下的可用结果进行了比较。