This study examines the thermal buckling of a porous functionally graded (FG) piezoelectric sandwich beam with a porous core, supported on a Vlasov foundation, under various boundary conditions, including clamped and simply supported, prompted by industrial expansion and the application of piezoelectric sandwich materials. The face sheet layers of this structure, alongside the porous core, are examined for porosity. The equilibrium equations are formulated based on the Timoshenko beam theory and the principle of minimal potential energy. The influence of temperature on the sandwich beam has analyzed, and the characteristics of the face sheets and core layers have assessed in relation to the temperature effect, based on the heat transfer equation. The structural surfaces are represented as functionally graded materials (FGMs) with a modified power law distribution, consisting of BaTiO3 and PZT-5H, with a porous core fabricated from Ti–6Al–4V. The innovation of this study lies in the concurrent analysis of porous piezoelectric functionally graded material face sheets and a porous metallic core, supported by a Vlasov foundation, which facilitates a more accurate depiction of electro-thermo-mechanical coupling and substrate shear interaction than traditional sandwich beam models. The Vlasov foundation model is utilized to address the shear layer interaction of the substrate. In contrast, the porous piezoelectric functionally graded material layers offer a lightweight and multifunctional smart surface with active thermal and electrical responsiveness. Furthermore, several parameters are examined, including the density ratio of the face sheet FGM layers to the density of Vlasov’s foundation (ρFGM/ρFoundation), the aspect ratio, the core thickness-to-total thickness ratio, various types of porosity, the porosity coefficient, the porosity coefficient of the face sheet layer, and temperature variations. The findings indicate that augmenting the ratio of substrate thickness to structural thickness initially diminishes critical thermal buckling, subsequently leading to stabilization. This ratio (ρFGM/ρFoundation) is used to investigate the effect of the material properties of each layer on the thermal buckling behavior of the sandwich beam, showing how softening or stiffening Vlasov’s substrate relative to the FGM face sheet affects the thermal buckling. Augmenting the ratio of substrate density to FGM density enhances the critical buckling load. Increasing the ρFGM/ρFoundation from 5 to 10 results in a 6.4% reduction in the critical thermal buckling load. Moreover, as the temperature increases from 300 to 600 0 K, the critical thermal buckling load decreases by approximately 9.25%. Additionally, the buckling load of the second temperature function is 88.8% superior to that of the first temperature function. The critical thermal buckling load of the Type 2 core exceeds that of the Type 1 and Type 3 cores by approximately 8.42 and 10.99%, respectively. The second type of heat transfer pattern exerts the most substantial influence on the critical buckling load of the structure. This study offers novel insights into the coupled electro-thermo-mechanical stability of lightweight porous sandwich beams with active functionally graded material layers. This topic has not thoroughly explored in prior research. This work has applications in aerospace structures (including aircraft wings, helicopter anti-vibration plates, and satellites), intelligent lightweight robots (featuring sensor–actuator outer shells), active bioimplants (such as artificial bones with sensing or actuation functions), and smart coatings for electrical–mechanical thermal insulation.

Thermal buckling of a sandwich piezo-electric porous FG beam on Vlasov’s foundation with various boundary conditions

期刊论文
发表日期：

2026年2月15日

查看全文

Fatemeh Bargozini,
Mehdi Mohammadimehr,
Ali Ghorbanpour Arani

摘要

This study examines the thermal buckling of a porous functionally graded (FG) piezoelectric sandwich beam with a porous core, supported on a Vlasov foundation, under various boundary conditions, including clamped and simply supported, prompted by industrial expansion and the application of piezoelectric sandwich materials. The face sheet layers of this structure, alongside the porous core, are examined for porosity. The equilibrium equations are formulated based on the Timoshenko beam theory and the principle of minimal potential energy. The influence of temperature on the sandwich beam has analyzed, and the characteristics of the face sheets and core layers have assessed in relation to the temperature effect, based on the heat transfer equation. The structural surfaces are represented as functionally graded materials (FGMs) with a modified power law distribution, consisting of BaTiO₃ and PZT-5H, with a porous core fabricated from Ti–6Al–4V. The innovation of this study lies in the concurrent analysis of porous piezoelectric functionally graded material face sheets and a porous metallic core, supported by a Vlasov foundation, which facilitates a more accurate depiction of electro-thermo-mechanical coupling and substrate shear interaction than traditional sandwich beam models. The Vlasov foundation model is utilized to address the shear layer interaction of the substrate. In contrast, the porous piezoelectric functionally graded material layers offer a lightweight and multifunctional smart surface with active thermal and electrical responsiveness. Furthermore, several parameters are examined, including the density ratio of the face sheet FGM layers to the density of Vlasov’s foundation (ρ_FGM/ρ_Foundation), the aspect ratio, the core thickness-to-total thickness ratio, various types of porosity, the porosity coefficient, the porosity coefficient of the face sheet layer, and temperature variations. The findings indicate that augmenting the ratio of substrate thickness to structural thickness initially diminishes critical thermal buckling, subsequently leading to stabilization. This ratio (ρ_FGM/ρ_Foundation) is used to investigate the effect of the material properties of each layer on the thermal buckling behavior of the sandwich beam, showing how softening or stiffening Vlasov’s substrate relative to the FGM face sheet affects the thermal buckling. Augmenting the ratio of substrate density to FGM density enhances the critical buckling load. Increasing the ρ_FGM/ρ_Foundation from 5 to 10 results in a 6.4% reduction in the critical thermal buckling load. Moreover, as the temperature increases from 300 to 600 ⁰ K, the critical thermal buckling load decreases by approximately 9.25%. Additionally, the buckling load of the second temperature function is 88.8% superior to that of the first temperature function. The critical thermal buckling load of the Type 2 core exceeds that of the Type 1 and Type 3 cores by approximately 8.42 and 10.99%, respectively. The second type of heat transfer pattern exerts the most substantial influence on the critical buckling load of the structure. This study offers novel insights into the coupled electro-thermo-mechanical stability of lightweight porous sandwich beams with active functionally graded material layers. This topic has not thoroughly explored in prior research. This work has applications in aerospace structures (including aircraft wings, helicopter anti-vibration plates, and satellites), intelligent lightweight robots (featuring sensor–actuator outer shells), active bioimplants (such as artificial bones with sensing or actuation functions), and smart coatings for electrical–mechanical thermal insulation.