This article explores the stochastic stability of a three nanobeam system connected by Kerr type elastic layer, subjected to the magnetic effects and compressive axial forces. While considering nano beams rotary inertia is taken into account and differential equations of nanobeams are given according to Eringen's nonlocal elasticity theory. The impact of a longitudinal magnetic field on the behavior of the nanobeam system is described using Lorentz magnetic forces. The objective of this research paper is to investigate the moment and almost sure stability of the system. It analyzes the system's stability under white noise excitation by employing the contact transformation method and perturbation approach. Notably, we consider the case where the system exhibits low damping. The study focuses on examining the system's dynamic behavior and stability characteristics under these conditions. The stochastic stability of this system is investigated through moment Lyapunov exponents and Lyapunov exponents for the first time and interesting conclusions regarding the stability region of this system were obtained by varying various system parameters. These conclusions are presented in a visual manner and discussed.

本文探讨了由克尔型弹性层连接的三纳米梁系统在磁效应和压缩轴向力作用下的随机稳定性。在考虑纳米梁的转动惯量时，根据Eringen非局部弹性理论给出了纳米梁的微分方程。使用洛伦兹磁力描述纵向磁场对纳米束系统行为的影响。本研究论文的目的是研究系统的矩和几乎确定的稳定性。采用接触变换法和摄动法分析了白噪声激励下系统的稳定性。值得注意的是，我们考虑系统表现出低阻尼的情况。该研究的重点是检查这些条件下系统的动态行为和稳定性特征。首次通过矩Lyapunov指数和Lyapunov指数研究了该系统的随机稳定性，并通过改变各种系统参数获得了关于该系统稳定区域的有趣结论。这些结论以可视化的方式呈现并进行讨论。