Static Stability of Piezoelectric Bio-inspired Sandwich Plate
Main Article Content
Abstract
This paper focuses on the static stability analysis of a sandwich plate structure resting on an elastic foundation and subjected to the simultaneous action of axial compressive loading and a uniform temperature rise. The sandwich plate consists of three layers, with the core made of a bio-inspired material and the two face sheets composed of piezoelectric materials, in which seven different fiber distribution patterns of the core layer are considered. The equilibrium and strain-compatibility equations are formulated based on Reddy’s higher order shear deformation plate theory incorporating von Kármán geometric nonlinearity. These governing equations then are solved using the Bubnov–Galerkin method to derive the relationships between axial compressive load and deflection amplitude as well as the expressions for determining the critical axial compressive load. Subsequently, the effects of geometric parameters, elastic foundations coefficients, fiber distribution patterns and temperature increment on the static stability of the piezoelectric sandwich plate are investigated.
Keywords:
Static stability; sandwich plate; bio-inspired material; piezoelectric material; temperature increment.
References
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[2] A. Kalhori, M. J. Bayat, K. Asemi, Torsional and Axial Buckling Analysis of Bio-Inspired Helicoidal Laminated Composite Cylindrical Shells, Results in Engineering, Vol. 26, 2025, pp. 104808, https://doi.org/10.1016/j.rineng.2025.104808.
[3] M. Neubacher, F. Touni, K. Yamada, M. Nishikawa, B. Fiedler, Experimental and Numerical Investigation of Bio-inspired CFRP Structures with Layer Thickness Gradients, Composite Part B Engineering, Vol. 313, 2026, pp. 113409, https://doi.org/10.1016/j.compositesb.2026.113409.
[4] A. Karamanli, T. P. Vo, M. A. Eltaher, Comprehensive Analysis of Bio-Inspired Laminated Composites Plates Using a Quasi-3D Theory and Higher Order FE Models, Thin-walled Structures, Vol. 198, 2024, pp. 111735, https://doi.org/10.1016/j.tws.2024.111735.
[5] T. T. T. Thu, T. N. Anh, H. N. Thi, H. N. Thi, Transient Response of Doubly-curved Bio-Inspired Composite Shells Resting on Viscoelastic Foundation Subject to Blast Load Using Improved First-order Shear Theory and Isogeometric Approach, Defence Technology, Vol. 38, 2024, pp. 171-193, https://doi.org/10.1016/j.dt.2024.02.003.
[6] C. Wang, D. Su, Z. Xie, H. Wang, P. J. Hazell, Z. Zhang, M. Zhou, Dynamic Behaviour of Bio-inspired Heterocyclic Aramid Fibre-reinforced Laminates Subjected to Low-Velocity Drop-Weight Impact, Composite Part A: Applied Science and Manufacturing, Vol. 153, 2022, pp. 106733, https://doi.org/10.1016/j.compositesa.2021.106733.
[7] N. T. Do, Q. H. Pham, Dynamic Analysis of Bio-Inspired Helicoid Laminated Composite Plates Resting on Pasternak Foundation Excited By Explosive Loading, Defence Technology, Vol. 30, 2023, pp. 126-140, https://doi.org/10.1016/j.dt.2023.04.018.
[8] T. Lu, H. S. Shen, H. Wang, X. Chen, M. Feng, Optimization Design and Secondary Buckling of Bio-Inspired Helicoidal Laminated Plates under Thermomechanical Loads, Composite Structures, Vol. 321, 2023, pp. 117344, https://doi.org/10.1016/j.compstruct.2023.117344.
[9] S. A. Mohamed, N. Mohamed, M. A. Eltaher, Bending, Buckling and Linear Vibration of Bio-Inspired Composite Plates, Ocean Engineering, Vol. 259, 2022, pp. 111851, https://doi.org/10.1016/j.oceaneng.2022.111851.
[10] T. Q. Quan, N. V. Quyen, N. D. Duc, An Analytical Approach for Nonlinear Thermo-Electro-Elastic Forced Vibration of Piezoelectric Penta – Graphene Plates, European Journal of Mechanics A/Solids, Vol. 85, 2021,
pp. 104095, https://doi.org/10.1016/j.euromechsol.2020.104095.
[11] T. Liu, C. Li, C. Wang, W. Hu, T. Q. Bui, Geometrically Nonlinear Isogeometric Analysis of Smart Piezoelectric FG Plates Considering Thermal Effects of Piezoelectric Stress And Dielectric Constants, Composite Structures, Vol. 266, 2021, pp. 113795, https://doi.org/10.1016/j.compstruct.2021.113795.
[12] H. Tang, H. L. Dai, Dynamic Instability Zone Analysis of Laminated Piezoelectric Cylindrical Shell with Delamination under Hygrothermal Effects, Applied Mathematical Modelling, Vol. 99, 2021, pp. 27-40, https://doi.org/10.1016/j.apm.2021.04.014.
[13] S. Brischetto, D. Cesare, Three-dimensional Vibration Analysis of Multilayered Composite and Functionally Graded Piezoelectric Plates and Shells, Composite Structures, Vol. 346, 2024, pp. 118413, https://doi.org/10.1016/j.compstruct.2024.118413.
[14] M. Nasihatgozar, V. Daghigh, M. Eskandari, K. Nikbin, A. Simoneau, Buckling Analysis of Piezoelectric Cylindrical Composite Panels Reinforced with Carbon Nanotubes, International Journal of Mechanical Sciences, Vol. 107, 2016, pp. 69-79, https://doi.org/10.1016/j.ijmecsci.2016.01.010.
[15] A. Alibeigloo, Free Vibration Analysis of Functionally Graded Carbon Nanotube-Reinforced Composite Cylindrical Panel Embedded In Piezoelectric Layers by Using Theory of Elasticity, European Journal of Mechanics, A/Solids, Vol. 44, 2014, pp. 104-115, https://doi.org/10.1016/j.euromechsol.2013.10.002.
[16] X. G. Sun, W. C. Chi, J. Li, Y. Q. Wang, Three-dimensional Vibration Suppression of Flexible Beams under Multi-Directional Excitations Via Piezoelectric Actuators: Theoretical and Experimental Investigations, Alexandria Engineering Journal, Vol. 129, 2025, pp. 1039-1060, https://doi.org/10.1016/j.aej.2025.08.016.
[17] J. P. A. Nwatsock, J. F. R. A. Nonga, R. P. L. Sanga, C. A. Moubeke, C. Adoukatl, G. E. Ntamack, Active Vibration Control of an Elastic Piezoelectric Beam Subjected to Multi-Frequency Excitation, Results in Engineering, Vol. 27, 2025, pp. 106822, https://doi.org/10.1016/j.rineng.2025.106822.
[18] M. Sadeghi Gughari, A. R. Saidi, A. S. Rezaei, M. Askari, A. Naderi, Analytical Buckling Response of Sectorial Porous Plates Integrated with Piezoelectric Layers, Applied Mathematical Modelling, Vol. 101, 2022,
pp. 811-831, https://doi.org/10.1016/j.apm.2021.09.019.
[19] A. Shahdadi, H. Rahnama, Free Vibration of a Functionally Graded Annular Sector Plate Integrated with Piezoelectric Layers, Applied Mathematical Modelling, Vol. 79, 2020, pp. 341-361, https://doi.org/10.1016/j.apm.2019.10.039.
[20] K. Zheng, Active Vibration Control of Multiscale Porous Stepped Annular Plates with CNT/CF Reinforcement and Piezoelectric Layers: A 2D Axisymmetric FEM Approach, Results in Engineering, Vol. 27, 2025,
pp. 106564, https://doi.org/10.1016/j.rineng.2025.106564.
[21] N. T. Do, Q. H. Pham, Vibration and Dynamic Control of Piezoelectric Functionally Graded Porous Plates in the Thermal Environment Using FEM and Shi’s TSDT, Case Studies in Thermal Engineering, Vol. 47, 2023,
pp. 103105, https://doi.org/10.1016/j.csite.2023.103105.
[22] A. Aabid, M. Hrairi, M. A. Raheman, Y. E. Ibrahim, Enhancing Aircraft Crack Repair Efficiency Through Novel Optimization of Piezoelectric Actuator Parameters: a Design of Experiments and Adaptive Neuro-Fuzzy Inference System Approach, Heliyon, Vol. 10, 2024, pp. e32166, https://doi.org/10.1016/j.heliyon.2024.e32166.
[23] J. N. Reddy, N. D. Phan, Stability and Vibration of Isotropic, Orthotropic and Laminated Plates According to a Higher-Order Shear Deformation Theory, Journal of Sound and Vibration, Vol. 98, 1985, pp. 157-170, https://doi.org/10.1016/0022-460X(85)90383-9.