In the present paper, nonlinear forced vibrations of an axial moving nanobeam which is vertically influenced by an external harmonic excitation and gravity is analyzed by considering the effects of linear damping. Considering certain assumptions, a nonlinear Euler-Bernoulli beam theory is developed. With the implementation of the nonlocal elasticity theory, the governing integro-partial-differential equation is obtained by using the Hamilton principle. The multiple scale method is employed to obtain a steady-state response for the size-dependent viscoelastic nanobeam with fixed-free boundary conditions. Subsequently, the trivial and non-trivial steady-state response and the bifurcation point types are examined. Finally, the effects of damping coefficient and nonlocal parameter on stability and bifurcation of trivial and non-trivial solutions are studied. It is found that the effect of nonlocal parameter on the steady-state response and the bifurcation point types is quite important.

在本文中，考虑了线性阻尼的影响，分析了轴向移动的纳米束的非线性强迫振动，该振动在垂直方向上受到外部谐波激励和重力的影响。考虑某些假设，建立了非线性欧拉-伯努利梁理论。随着非局部弹性理论的实施，利用汉密尔顿原理获得了控制积分偏微分方程。采用多尺度方法获得具有固定自由边界条件的尺寸依赖性粘弹性纳米束的稳态响应。随后，检查了平凡和非平凡的稳态响应以及分叉点类型。最后，研究了阻尼系数和非局部参数对平凡和非平凡解的稳定性和分支的影响。发现非局部参数对稳态响应和分叉点类型的影响非常重要。