<p>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 (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\Delta T_{cr}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Δ</mi> <msub> <mi>T</mi> <mrow> <mi mathvariant="italic">cr</mi> </mrow> </msub> </mrow> </math></EquationSource> </InlineEquation>) and the induced axial membrane force (<i>N</i>). 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 (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">$W_z$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>W</mi> <mi>z</mi> </msub> </math></EquationSource> </InlineEquation>) produces noticeable changes in <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\Delta T_{cr}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Δ</mi> <msub> <mi>T</mi> <mrow> <mi mathvariant="italic">cr</mi> </mrow> </msub> </mrow> </math></EquationSource> </InlineEquation> and the fundamental frequency (<InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\omega _{1}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>ω</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>), 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.</p>

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

期刊论文
发表日期：

2025年12月4日

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Huchhanagouda H. Patil,
Jeyaraj Pitchaimani

摘要

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 ( $\Delta T_{cr}$ $Δ T_{cr}$ ) 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 ( $W_z$ $W_{z}$ ) produces noticeable changes in $\Delta T_{cr}$ $Δ T_{cr}$ and the fundamental frequency ( $\omega _{1}$ $ω_{1}$ ), 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.