Hashemian Mohammad, Jasim Dheyaa J, Sajadi S Mohammad, Khanahmadi Rahman, Pirmoradian Mostafa, Salahshour Soheil
Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Iran.
Department of Petroleum Engineering, Al-Amarah University College, Maysan, Iraq.
Heliyon. 2024 Apr 27;10(9):e30231. doi: 10.1016/j.heliyon.2024.e30231. eCollection 2024 May 15.
This research studied the dynamic stability of the Euler-Bernoulli nanobeam considering the nonlocal strain gradient theory (NSGT) and surface effects. The nanobeam rests on the Pasternak foundation and a sequence of inertial nanoparticles passes above the nanobeam continuously at a fixed velocity. Surface effects have been utilized using the Gurtin-Murdoch theory. Final governing equations have been gathered implementing the energy method and Hamilton's principle alongside NSGT. Dynamic instability regions (DIRs) are drawn in the plane of mass-velocity coordinates of nanoparticles based on the incremental harmonic balance method (IHBM). A parametric study shows the effects of NSGT parameters and Pasternak foundation constants on the nanobeam's DIRs. In addition, the results exhibit the importance of 2T-period DIRs in comparison to T-period ones. According to the results, the Winkler spring constant is more effective than the Pasternak shear constant on the DIR movement of nanobeam. So, a 4 times increase of Winkler and Pasternak constants results in 102 % and 10 % of DIR movement towards higher velocity regions, respectively. Furthermore, the effect of increasing nonlocal and material length scale parameters on the DIR movement are in the same order regarding the magnitude but opposite considering the motion direction. Unlike nonlocal parameter, an increase in material length scale parameter shifts the DIR to the more stable region.
本研究考虑非局部应变梯度理论（NSGT）和表面效应，研究了欧拉 - 伯努利纳米梁的动态稳定性。纳米梁置于帕斯塔纳克地基上，一系列惯性纳米颗粒以固定速度连续从纳米梁上方通过。采用古尔廷 - 默多克理论考虑表面效应。利用能量法和哈密顿原理以及NSGT推导出最终的控制方程。基于增量谐波平衡法（IHBM），在纳米颗粒的质量 - 速度坐标平面上绘制动态不稳定区域（DIRs）。参数研究表明了NSGT参数和帕斯塔纳克地基常数对纳米梁DIRs的影响。此外，结果表明与T周期的DIRs相比，2T周期的DIRs的重要性。根据结果，温克勒弹簧常数比帕斯塔纳克剪切常数对纳米梁的DIR运动影响更大。因此，温克勒常数和帕斯塔纳克常数分别增加4倍会导致DIR向更高速度区域移动102%和10%。此外，增加非局部和材料长度尺度参数对DIR运动的影响在量级上相同，但在运动方向上相反。与非局部参数不同，材料长度尺度参数的增加会使DIR向更稳定的区域移动。
