Multiscale thermoelastic vibration analysis of functionally graded nanobeams using nonlocal and memory-dependent effects

This study examines the vibration analysis of a functionally graded (FG) nanobeam with exponential material variation (metal to ceramic). It integrates Eringen’s nonlocal theory to account for size effects and the Moore-Gibson-Thompson theory of generalized thermoelasticity, including memory dependence. The simply supported beam, exposed to sinusoidal pulse heating, is investigated using the Laplace transform and Zakian method. Results demonstrate the influence of the nonlocal parameter, FGM grading, pulse width, kernel functions, and delay time on the nanobeam’s lateral vibration, temperature, and displacement, offering insights for microstructure design and optimization.

本研究针对材料呈指数分布（金属向陶瓷过渡）的功能梯度（functionally graded, FG）纳米梁开展振动分析。研究整合艾林根非局部理论以考量尺寸效应，并采用摩尔-吉布森-汤普森广义热弹性理论，纳入记忆依赖性因素。针对受正弦脉冲加热作用的简支梁，采用拉普拉斯变换与扎基安法进行研究。结果表明，非局部参数、功能梯度材料梯度特性、脉冲宽度、核函数及延迟时间对纳米梁的横向振动、温度场与位移场均存在影响，可为微结构设计与优化提供理论参考。