Abstract Nonlinear vibration of nanobeams embedded in the linear and nonlinear elastic materials under magnetic and temperature effects is investigated in this study. Von Karman’s strain–displacement relation is applied to a nonlocal Euler–Bernoulli beam model. Equation of motion is derived using Hamilton’s principle. Galerkin’s method is applied to decompose the nonlinear partial differential equation into a nonlinear ordinary differential equation (NODE). The NODE is solved using He’s method. The nanobeams are embedded in the Winkler, Pasternak, and nonlinear elastic media. The effects of low and high temperatures, nonlocal parameter, magnetic force, amplitude, and linear and nonlinear elastic materials are examined.

中文翻译：

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非线性弹性介质中纳米梁非线性振动的热应力和磁效应

摘要 本研究研究了嵌入在线性和非线性弹性材料中的纳米梁在磁和温度效应下的非线性振动。Von Karman 的应变-位移关系应用于非局部 Euler-Bernoulli 梁模型。运动方程是使用汉密尔顿原理推导出来的。应用伽辽金法将非线性偏微分方程分解为非线性常微分方程(NODE)。NODE 使用 He 方法求解。纳米梁嵌入在 Winkler、Pasternak 和非线性弹性介质中。研究了低温和高温、非局部参数、磁力、振幅以及线性和非线性弹性材料的影响。