Free and forced vibrations of 2D-FGP curved nanobeams resting on elastic foundation in hygro-thermal environments with elastic boundary condition

Abstract

In this paper, isogeometric analysis (IGA) is used for the first time to explore the free and forced oscillation of two-directional functionally graded porous (2D-FGP) curved nanobeams with arbitrary boundary conditions. Materials used in the production of curved beams have mechanical qualities that change in both the longitudinal and thickness directions of the beam, as well as microscopic porosities that are distributed according to various regulations. The whole curving beam is reinforced by Pasternak’s foundation with two parameters in a hygro-thermal condition. Hamilton's essence is based on a quasi-3D beam model, and the nonlocal elasticity hypothesis is used to derive the governing equation of a 2D-FGP curved nanostructure. The validity of the suggested model is determined by comparing the results of the current study to those of reputable publications. By taking into consideration the free and forced oscillation responses of the curved nanobeam, the influences of parameters such as the power-law index, nonlocal parameter, porosity coefficient, temperature and moisture change, the opening angle of the beam, the stiffness of the elastic substrate, arbitrary boundary conditions, and the thickness-to-length ratio can be investigated. The benchmark solutions that have been detailed in this work may in the future be used as a reference for the free and forced behavior of 2D-FGP nanobeams that have a curved form, and this may be possible because of the findings of this study, especially for structural design engineers of this type.

Keywords

• Bidirectional functionally graded
• Porous material
• Arbitrary boundary condition
• IGA
• quasi-3D
• Curved nanobeam