Nonlinear vibrational and rotational analysis of microbeams in nanobiomaterials using Galerkin decomposition and differential transform methods

Abstract

In this paper, a nonlinear vibrational and rotational analysis of microbeams in nanobiomaterials using Galerkin Decomposition (GDM) and Differential Transform Methods (DTM) is presented. The dependency of cell migration and growth on nanoscaffold porosity and pore size architecture in tissue regeneration is governed by a dynamic model for the nonlinear vibration and rotation of the microbeams of nanobiomaterials and represented by a set of nonlinear partial differential equations. The solutions of the governing model are obtained by applying GDM and DTM and good agreement is achieved with numerical Runge-Kutta method (RK4). From the results, it is observed that an increase in Duffing term resulted in the increase of the frequency of the micro-beam. An increase in the foundation term also resulted in a corresponding increase in the frequency of the system for both free and forced dynamic responses. This study will enhance the application of tissue engineering in the regeneration of damaged human body tissues.