Transient vibration responses of a porosity-dependent functionally graded nanobeam under different impulsive loadings have been investigated in the context of non-local strain gradient theory. Three impulse loads of rectangular-type, linear-type and sine-type have been applied to top surface of nanobeam. Two porosity distribution types known as even and uneven are discussed. Governing equations of the nanobeam are solved via inverse Laplace transform approach to express the dynamic deflections. One can see that the transient response of nano-size beams is influenced by the type and location of pulse load, porosities volume fractions, porosities distributions, non-local and strain gradient coefficients.

在非局部应变梯度理论的背景下，研究了在不同脉冲载荷下，孔隙度相关的功能梯度纳米束的瞬态振动响应。将矩形，线性和正弦波三种脉冲载荷施加到纳米束的顶表面。讨论了两种孔隙度分布类型，称为均匀分布和不均匀分布。通过逆拉普拉斯变换方法求解纳米束的控制方程，以表达动态挠度。可以看到，纳米束的瞬态响应受脉冲载荷的类型和位置，孔隙率体积分数，孔隙率分布，非局部和应变梯度系数的影响。