The topic presented in this research is the calibration of small-scale parameters of non-classical continuum theories such as nonlocal strain gradient theory, strain gradient theory, stress-driven nonlocal elasticity, and strain-driven nonlocal elasticity. Governing equations of vibrational behavior of circular nanoplate and associated boundary conditions for each method derived using Hamilton's principle. Obtained governing differential equations from non-classical methods were solved using the general differential quadrature rule (GDQR). Then, the first natural frequencies for different radiuses and different size parameters were obtained. On the other hand, the first natural frequencies of circular nanoplates are calculated using molecular dynamics simulation based on AIREBO and Tersoff potentials for different radiuses. Fast Fourier transform (FFT) was utilized to calculate natural frequencies based on the molecular dynamics simulation. Using the accurate size parameter is an important point in the application of non-classical continuum theories. To obtain the size parameters related to different non-classical methods, the results of molecular dynamics compared to those of nan-classical methods and simulated annealing (SA) algorithm optimization technique was utilized. Results show that stress-driven nonlocal, strain-driven nonlocal, and strain gradient methods cannot predict the behavior predicted by molecular dynamics for all ranges of radius. In other words, the responses of these three methods for any value of the size parameters (in some interval radius) and results of the molecular dynamics method are not equal for a few numbers of studied radii. In contrast to these three methods, the nonlocal strain gradient method predicts the results obtained by molecular dynamics well for all radii. The results of this paper are very useful for researchers in the field of non-classical continuum mechanics.

本研究的主题是校准非经典连续介质理论的小尺度参数，例如非局部应变梯度理论、应变梯度理论、应力驱动的非局部弹性和应变驱动的非局部弹性。圆形纳米板振动行为的控制方程和使用汉密尔顿原理推导出的每种方法的相关边界条件。从非经典方法获得的控制微分方程使用一般微分求积规则（GDQR）求解。然后，获得不同半径和不同尺寸参数的第一固有频率。另一方面，使用基于AIREBO和Tersoff 的分子动力学模拟计算圆形纳米片的第一自然频率不同半径的电位。基于分子动力学模拟，利用快速傅里叶变换 (FFT) 计算固有频率。使用准确的尺寸参数是非经典连续统理论应用中的一个重点。为了获得与不同非经典方法相关的尺寸参数，利用分子动力学结果与纳米经典方法和模拟退火（SA）算法优化技术的结果进行比较。结果表明，应力驱动的非局部、应变驱动的非局部和应变梯度方法无法预测分子动力学对所有半径范围预测的行为。换句话说，这三种方法对任何尺寸参数值（在某个区间半径内）的响应和分子动力学方法的结果对于少数研究半径是不相等的。与这三种方法相比，非局部应变梯度方法可以很好地预测所有半径的分子动力学结果。本文的结果对非经典连续介质力学领域的研究人员非常有用。