Isogeometric Analysis for Nonlocal Vibration Characteristics of BFGP Curved Nanobeams with Variable Nonlocal Parameters

Abstract

In this paper, for the first time, isogeometric analysis (IGA) and nonlocal theory are used to investigate the free vibration and transient response of bidirectional functionally graded porous (BFGP) curved nanobeams with elastic boundary conditions (BCs) and variable nonlocal parameters. Different from traditional boundary conditions, where a curved beam’s beginning and end positions are connected by an elastic system of straight and torsion springs, this allows for greater flexibility in controlling the stiffness of the springs to obtain arbitrary boundaries. One thing that sets this research apart from others is the hypothesis that the mechanical characteristics of the materials, including nonlocal parameters, are supposed to change according to Voigt schemes in the direction of thickness, length, and porosities of the beam. On the basis of higher-order shear curved beam theory, Hamilton’s principle is used to develop the curved nanobeam’s equations of motion. The accuracy of the proposed model is established by juxtaposing the current study’s findings with those of credible papers. A comprehensive examination has been conducted to analyze the impact of input parameters on the free vibration and transient response of BFGP curved nanobeams. Furthermore, the benchmark solutions elucidated in this work might serve as a valuable reference for analyzing the free vibration and transient response of BFGP curved nanobeams in other investigations.