In this paper, we obtain the black hole solution for the Ayón-Beato–García (ABG)-type black hole surrounded by a cloud of strings in Rastall gravity and calculate the scalar quasinormal modes of it for a massless scalar field. To have a better visualization of the results, we also introduce a new nonlinear electrodynamic source and obtain a black hole solution surrounded by a cloud of strings in the Rastall gravity. We see that the quasinormal modes are affected by the type of nonlinear electrodynamic sources in case of higher magnitudes of charge $q$. With increase in the magnitude of charge $q$, gravitational waves decay rapidly for the new black hole solution, while for the ABG black hole, the decay rate increases initially and finally starts to decrease near to $q=1$. We also study the impact of the cloud of strings and other model parameters, including the Rastall parameter on the quasinormal modes for both of the black holes. The gravitational waves decay slowly with increase in the cloud of strings parameter for both of the black holes. Dependency of quasinormal modes on the Rastall parameter is different from a surrounding dark energy field and the decay of gravitational waves may be slow or rapid depending on the value of this parameter.

在本文中，我们获得了拉斯特引力中被弦云包围的 Ayón-Beato–García (ABG) 型黑洞的黑洞解，并计算了它在无质量标量场中的标量准正态模态。为了更好地可视化结果，我们还引入了一个新的非线性电动力源，并获得了拉斯特引力中被弦云包围的黑洞解。我们看到，在较高电荷量的情况下，准正态模式受非线性电动力源类型的影响$q$. 随着电荷量的增加$q$，引力波对于新的黑洞解快速衰减，而对于 ABG 黑洞，衰减率开始增加，最后在接近$q=\mathrm{1个}$. 我们还研究了弦云和其他模型参数的影响，包括 Rastall 参数对两个黑洞的准正态模式。随着两个黑洞的弦云参数的增加，引力波缓慢衰减。准正态模式对 Rastall 参数的依赖性不同于周围的暗能量场，引力波的衰减可能是缓慢的或快速的，具体取决于该参数的值。