Abstract

As the main contribution, a nonlocal strain gradient theory (NSGT) is developed in conjugation with the generalized differential quadrature method (GDQM) to analyze the free vibration of a transversely graded nanoshell subjected to magnetic and thermal loads derived by using the first-order shear deformation theory (FSDT) and Hamilton’s principle. Comparisons with other common methods have shown the validity of the presented NSGT-GDQM hybrid approach. The effects of power-law exponent, nonlocal parameter, strain gradient parameter, magnetic potential, angular velocity, and temperature for both simply supported and clamped boundary conditions of a nanoshell composed of BaTiO₃ and CoFe₂O₄ materials were investigated. Sensitivity analysis illustrates that more resolution will be available with clamped boundaries. With increasing the temperature gradient, the absolute value of the sensitivity increases and the maximum sensitivity value occurs always on the critical buckling point. Finally, comparing two studied boundary conditions revealed that if there is any temperature rise limit, the clamped boundary condition is suggested because of more sensitivity. Though the temperature gradient could be more than 400 K in the case of simply supported edges, the maximum absolute sensitivity could be obtained is about 0.12 wherein the case of clamped boundary condition it was about 0.17.

摘要

作为主要贡献，非局部应变梯度理论（NSGT）与广义微分求积法（GDQM）相结合，用于分析横向梯度纳米壳在磁载荷和热载荷下的自由振动变形理论（FSDT）和汉密尔顿原理。与其他常用方法的比较表明了所提出的 NSGT-GDQM 混合方法的有效性。幂律指数、非局部参数、应变梯度参数、磁势、角速度和温度对由 BaTiO ₃和 CoFe ₂ O _{4组成的纳米壳的简支和钳位边界条件的影响}材料进行了调查。敏感性分析表明，使用钳位边界可以获得更高的分辨率。随着温度梯度的增加，灵敏度的绝对值增加，并且最大灵敏度值总是出现在临界屈曲点上。最后，比较两个研究的边界条件表明，如果有任何温升限制，则建议使用钳位边界条件，因为它更敏感。尽管在简单支撑边缘的情况下温度梯度可能超过 400 K，但可以获得的最大绝对灵敏度约为 0.12，其中在钳位边界条件的情况下约为 0.17。