Thermoelastic buckling and vibration analysis of shear and normal deformable three-phase bio-inspired composite beams under axially varying temperature fields

Abstract

The thermoelastic buckling and free vibration behaviors of a Three-Phase Composite (TPC) beam subjected to axially varying Non-Uniform Temperature (NUFT) fields is investigated by incorporating Temperature-Dependent (TD) elastic properties of both Carbon Nanotubes (CNTs) and the matrix. The Shear and Normal Deformable Beam Theory (SNDBT) is used to model the kinematics, and the governing equations are formulated through Hamilton’s principle and solved using the Ritz method. TD elastic properties of CNTs are accounted in terms of TD Hill’s constants. Dispersion issue of CNT is accounted in terms of partial and complete agglomeration effects for more realistic material modeling. The results indicate that the area beneath the NUFT distribution profiles serves as a meaningful parameter for interpreting both the critical buckling temperature (?Tcr) and the induced axial membrane force (N). NUFT-induced differential thermal expansion generates localized thermal strain variations, and the strain reverses its sign whenever the temperature at a point exceeds the spatially averaged temperature for the given NUFT. Consideration of thickness-stretching deformation (Wz) produces noticeable changes in ?Tcr and the fundamental frequency (?1), particularly for the beams with lower aspect-ratio, emphasizing its necessity in thick-beam modeling. The findings provide practical guidance for the design of lightweight, thermally stable composite structures deployed in aerospace and other thermal-environment-critical engineering systems. © The Author(s), under exclusive licence to Springer-Verlag GmbH Austria, part of Springer Nature 2025.