Nano/micro-beam deflections: Investigation of subjected forces and applications

Micro- and Nano beam MEMS devices possess a broad range of applications owing to their capability to produce precise mechanical motion and sensing capabilities at a small scale. In the field of biomedicine, these devices have been employed in applications such as tissue engineering, lab-on-a-chip systems, and implantable devices. Medical devices, particularly those involved in drug delivery, are significantly impacted by the forces applied to them. Therefore, it is imperative to carefully evaluate the effects of axial force and optimize the device's design to ensure that it can endure the forces it will encounter during operation. Despite being relatively weak, the van der Waals force warrants careful consideration when working at the micro- and nanoscales. In this research, the nonlinear equation obtained by the Galerkin method for a doubly clamped nano/micro-beam under the effect of Van der Waals (vdW) force was solved. The Homotopy Perturbation Method (HPM) and the Akbari Ganji Method (AGM) are introduced to investigate the nonlinear problem in this paper analytically. To validate and investigate the accuracy of the AG and HP methods, the obtained results were compared to the Runge-Kutta approach. The obtained results for all data sets showed the high accuracy of the AG and HP methods. Also, this paper investigated the effect of axial force N on beam type N/MEMS deflection. The axial force N effect in both tensional (N > 0) and compressive (N < 0) modes has been investigated. Due to the obtained results, increasing the axial force compressively increases the deflection of the beam. However, this trend is reversed for the tensional axial force.