Application of the modified Fourier series method and the genetic algorithm for calibration of small‐scale parameters in the nonlocal strain gradient nanobeams

Abstract

In recent years, nonlocal strain gradient theory (NSGT) has been widely applied by researchers for the analysis of nanostructures. In this theory, the appropriate selection of small‐scale parameters and the type of high‐order boundary conditions is of great importance. In the current paper, free vibrations of carbon nanotubes are studied using a nonlocal strain gradient Timoshenko beam model, and the small‐scale parameters are calibrated based on the molecular dynamics (MD) results. The calibration process is conducted by defining an optimization problem, and the genetic algorithm is applied for obtaining the best values of the small‐scale parameters. The governing equations are derived based on Hamilton's principle and solved analytically using the modified Fourier series method. The variational consistent high‐order boundary conditions are obtained applying the weighted residual approach. The small‐scale parameters are calibrated for the first three natural frequencies considering two different boundary conditions. Moreover, the type of high‐order boundary conditions that is more consistent with the MD results is determined. The outcomes of this paper provide an appropriate reference for researchers who are using the NSGT for the analysis of micro/nanobeams.

Application of black box genetic algorithm in network security vulnerability mining

“…By analyzing Figure 2, it can be seen that Method 1 has a minimum false detection rate of 6.3% for five network vulnerabilities, namely file download vulnerabilities, and a maximum false detection rate of 8.3%, namely HTTP Header injection vulnerabilities. The false detection rate of methods is between 7.4% and 8.3% [2][3], with a relatively high false detection rate. The lowest false detection rate of the method proposed in this paper is 0.3%, which is a literature download vulnerability.…”

“…To better realize the system network security vulnerability mining, it is necessary to comprehensively perceive the system network situation and then improve the overall performance of security vulnerability mining. The network environment is composed of attack hosts, client hosts, servers, switches, routers, and hubs [2][3]. In this paper, the network system and the set attack process in the network situation awareness model are used to carry out security situation awareness, and the intrusion detection system, firewall, and security log information data of each host are obtained.…”

“…The optimized system network security vulnerability mining work program is shown in Figure 1. In the operation of the black-box genetic algorithm with result feedback, a new genetic algorithm is constructed according to the final execution result of the ioctl function, and the genetic variation mechanism of this new genetic algorithm can be expressed as Formula (2).…”

Improved Particle Swarm Optimization Algorithm in Site Selection and Capacity of Distributed Power Supply

“…Particle swarm optimization generally chooses the maximum number of iterations or meets a predefined minimum classification condition. The specific algorithm flow is as follows [11][12] (1) Begin. Input the initial data of the distribution network, obtain the information of each node and branch, and determine the upper and lower limits of the voltage of each node.…”

Integral nonlocal stress gradient elasticity of functionally graded porous Timoshenko nanobeam with symmetrical or anti‐symmetrical condition

“…Arda and Aydogdu [21] studied the influence of longitudinal magnetic field on the flexural vibration problem of nonlocal strain gradient Euler‐Bernoulli nanobeams. Mohammadian [22] studied the appropriate selection of small‐scale parameters and the type of high‐order boundary conditions through free vibrations of carbon nanotubes.…”