The influences of various auxetic cores on natural frequencies and forced vibration behavior of sandwich beam fabricated by 3D printer based on third -order shear deformation theory

Document Type : Research Paper


Faculty of Mechanical and Mechatronics Engineering, Imam Hossein University, Tehran, Iran


In this article, free and forced vibration analyses of 3D printed FG sandwich beam based on higher order beam theory is investigated. The core and face sheets of sandwich beam are integrally fabricated by 3D printer. Therefore, ignoring the delamination between face sheets and core is a correct assumption. Three different cells are considered for the core including Re- entrant auxetic cell, anti-tetrachiral auxetic cell and conventional honeycomb cell. These cells are arranged along the thickness of structure based on cell thickness in four various patterns. The effective mechanical properties of cells are estimated by analytical relations. Finite element methods and Lagrange equations are employed for obtaining the effective stiffness and mass matrices of the sandwich beam. Finally, the influences of various parameters including various types of cells, various patterns of cell along the thickness of structure, thickness coefficient, the geometry of cells such as the interior angle and dimensions of cells on natural frequencies and transient deflection of structure have been studied. The results denote that the arrangement of cells along the thickness plays an important role on the vibration response of structure. On the other hand, for uniform thickness distribution of cells, Re –entrant auxetic cell has higher natural frequencies than other cells while in FG arrangements of cells, anti-tetrachiral cell with pattern A has higher natural frequencies than Re-entrant auxetic cell.


Main Subjects

[1]          M. Gunasegeran, P. Edwin Sudhagar, Free and forced vibration analysis of 3D printed bioinspired sandwich beam using HSDT: Numerical and experimental study, Polymer Composites, Vol. 43, No. 6, pp. 3659-3677, 2022.
[2]          Z. Guo, G. Hu, J. Jiang, L. Yu, X. Li, J. Liang, Theoretical and experimental study of the vibration dynamics of a 3D-printed sandwich beam with an hourglass lattice truss core, Frontiers in Mechanical Engineering, Vol. 7, pp. 651998, 2021.
[3]          R. Rajpal, K. Lijesh, K. Gangadharan, Experimental investigation of 3D-printed polymer-based MR sandwich beam under discretized magnetic field, Journal of the Brazilian Society of Mechanical Sciences and Engineering, Vol. 40, pp. 1-11, 2018.
[4]          S. Ghannadpour, M. Mahmoudi, K. H. Nedjad, Structural behavior of 3D-printed sandwich beams with strut-based lattice core: Experimental and numerical study, Composite Structures, Vol. 281, pp. 115113, 2022.
[5]          S. Li, Z. Liu, V. Shim, Y. Guo, Z. Sun, X. Li, Z. Wang, In-plane compression of 3D-printed self-similar hierarchical honeycombs–static and dynamic analysis, Thin-Walled Structures, Vol. 157, pp. 106990, 2020.
[6]          Y. Solyaev, A. Babaytsev, A. Ustenko, A. Ripetskiy, A. Volkov, Static and dynamic response of sandwich beams with lattice and pantographic cores, Journal of Sandwich Structures & Materials, Vol. 24, No. 2, pp. 1076-1098, 2022.
[7]          K. Essassi, J.-L. Rebiere, A. E. Mahi, M. A. B. Souf, A. Bouguecha, M. Haddar, Experimental and numerical analysis of the dynamic behavior of a bio-based sandwich with an auxetic core, Journal of Sandwich Structures & Materials, Vol. 23, No. 3, pp. 1058-1077, 2021.
[8]          U. Sharif, B. Sun, I. Tariq, D. S. Ibrahim, O. O. Adewale, A. Zafar, Static and modal analysis of sandwich beam structure with magnetorheological honeycomb core, in Proceeding of, IEEE, pp. 19-23.
[9]          A. Ingrole, A. Hao, R. Liang, Design and modeling of auxetic and hybrid honeycomb structures for in-plane property enhancement, Materials & Design, Vol. 117, pp. 72-83, 2017.
[10]        M. Dryzek, W. Cecot, M. Tekieli, Experimental and multiscale computational static and dynamic study of 3D printed elements with mesostructure, Finite Elements in Analysis and Design, Vol. 215, pp. 103876, 2023.
[11]        Z. Wu, J. Wu, F. Lu, C. Zhang, Z. Liu, Y. Zhu, Free vibration analysis and multi-objective optimization of lattice sandwich beams, Mechanics of Advanced Materials and Structures, pp. 1-14, 2023.
[12]        U. Sharif, L. Chen, B. Sun, D. S. Ibrahim, O. O. Adewale, N. Tariq, An experimental study on dynamic behaviour of a sandwich beam with 3D printed hexagonal honeycomb core filled with magnetorheological elastomer (MRE), Smart Materials and Structures, Vol. 31, No. 5, pp. 055004, 2022.
[13]        M. Refat, E. Zappino, A. Racionero Sanchez-Majano, A. Pagani, Dynamic characterization of 3D printed lightweight structures, Advances in Aircraft and Spacecraft Science, Vol. 9, No. 4, pp. 301-318, 2022.
[14]        A. Hamrouni, J.-L. Rebiere, A. El Mahi, M. Beyaoui, M. Haddar, Experimental and finite element analyses of a 3D printed sandwich with an auxetic or non-auxetic core, Journal of Sandwich Structures & Materials, pp. 10996362231151454, 2023.
[15]        V. Kallannavar, S. Kattimani, Effect of temperature and porosity on free vibration characteristics of a doubly-curved skew laminated sandwich composite structures with 3D printed PLA core, Thin-Walled Structures, Vol. 182, pp. 110263, 2023.
[16]        M. Hedayatian, A. Daneshmehr, G. Liaghat, The efficiency of auxetic cores in sandwich beams subjected to low-velocity impact, International Journal of Applied Mechanics, Vol. 12, No. 06, pp. 2050061, 2020.
[17]        J. Gan, F. Li, K. Li, E. Li, B. Li, Dynamic failure of 3D printed negative-stiffness meta-sandwich structures under repeated impact loadings, Composites Science and Technology, pp. 109928, 2023.
[18]        A. Hamrouni, J.-L. Rebiere, A. El Mahi, M. Beyaoui, M. Haddar, Experimental and numerical investigation of the static behavior of a 3D printed bio-based anti-trichiral sandwich, Journal of Composite Materials, Vol. 57, No. 13, pp. 2161-2178, 2023.
[19]        M. Eryildiz, Experimental investigation and simulation of 3D printed sandwich structures with novel core topologies under bending loads, International Polymer Processing, No. 0, 2023.
[20]        X. Zhang, Y. Wang, M. Su, Experimental, numerical and analytical study to develop a design method for bending and shear resistances of 3D printed beetle elytron inspired sandwich plate (beetle elytron plate), Thin-Walled Structures, Vol. 183, pp. 110371, 2023.
[21]        Y. Jiang, Y. Li, 3D printed auxetic mechanical metamaterial with chiral cells and re-entrant cores, Scientific reports, Vol. 8, No. 1, pp. 1-11, 2018.
[22]        M. Najafi, H. Ahmadi, G. Liaghat, Investigation on the flexural properties of sandwich beams with auxetic core, Journal of the Brazilian Society of Mechanical Sciences and Engineering, Vol. 44, No. 2, pp. 61, 2022.
[23]        M. Najafi, H. Ahmadi, G. Liaghat, Evaluation of the mechanical properties of fully integrated 3D printed polymeric sandwich structures with auxetic cores: experimental and numerical assessment, The International Journal of Advanced Manufacturing Technology, Vol. 122, No. 9-10, pp. 4079-4098, 2022.
[24]        X. Zhang, H. Zhou, W. Shi, F. Zeng, H. Zeng, G. Chen, Vibration tests of 3D printed satellite structure made of lattice sandwich panels, AIAA Journal, Vol. 56, No. 10, pp. 4213-4217, 2018.
[25]        P. Boron, J. Chelmecki, J. M. Dulinska, N. Jurkowska, B. Ratajewicz, P. Stecz, T. Tatara, On the Possibility of Using 3D Printed Polymer Models for Modal Tests on Shaking Tables: Linking Material Properties Investigations, Field Experiments, Shaking Table Tests, and FEM Modeling, Materials, Vol. 16, No. 4, pp. 1471, 2023.
[26]        Y. Chai, S. Du, F. Li, C. Zhang, Vibration characteristics of simply supported pyramidal lattice sandwich plates on elastic foundation: Theory and experiments, Thin-Walled Structures, Vol. 166, pp. 108116, 2021.
[27]        C. Li, H.-S. Shen, H. Wang, Z. Yu, Large amplitude vibration of sandwich plates with functionally graded auxetic 3D lattice core, International Journal of Mechanical Sciences, Vol. 174, pp. 105472, 2020.
[28]        R. Wang, J. Shang, X. Li, Z. Luo, W. Wu, Vibration and damping characteristics of 3D printed Kagome lattice with viscoelastic material filling, Scientific reports, Vol. 8, No. 1, pp. 1-13, 2018.
[29]        M. H. Zamani, M. Heidari-Rarani, K. Torabi, A novel graded auxetic honeycomb core model for sandwich structures with increasing natural frequencies, Journal of Sandwich Structures & Materials, Vol. 24, No. 2, pp. 1313-1339, 2022.
[30]        L. Meng, X. Qiu, T. Gao, Z. Li, W. Zhang, An inverse approach to the accurate modelling of 3D-printed sandwich panels with lattice core using beams of variable cross-section, Composite Structures, Vol. 247, pp. 112363, 2020.
[31]        M. F. Ashby, L. J. Gibson, Cellular solids: structure and properties, Press Syndicate of the University of Cambridge, Cambridge, UK, pp. 175-231, 1997.
[32]        F. Kiarasi, M. Babaei, P. Sarvi, K. Asemi, M. Hosseini, M. Omidi Bidgoli, A review on functionally graded porous structures reinforced by graphene platelets, Journal of Computational Applied Mechanics, Vol. 52, No. 4, pp. 731-750, 2021.
[33]        M. Babaei, F. Kiarasi, K. Asemi, M. Hosseini, Functionally graded saturated porous structures: A review, Journal of Computational Applied Mechanics, Vol. 53, No. 2, pp. 297-308, 2022.
[34]        M. Khatoonabadi, M. Jafari, F. Kiarasi, M. Hosseini, M. Babaei, K. Asemi, Shear buckling response of FG porous annular sector plate reinforced by graphene platelet subjected to different shear loads, Journal of Computational Applied Mechanics, Vol. 54, No. 1, pp. 68-86, 2023.
[35]        F. Kiarasi, M. Babaei, S. Mollaei, M. Mohammadi, K. Asemi, Free vibration analysis of FG porous joined truncated conical-cylindrical shell reinforced by graphene platelets, Advances in nano research, Vol. 11, No. 4, pp. 361, 2021.
[36]        M. Babaei, K. Asemi, P. Safarpour, Buckling and static analyses of functionally graded saturated porous thick beam resting on elastic foundation based on higher order beam theory, Iranian Journal of Mechanical Engineering Transactions of the ISME, Vol. 20, No. 1, pp. 94-112, 2019.
[37]        S. Z. Gebrehiwot, L. Espinosa Leal, J. Eickhoff, L. Rechenberg, The influence of stiffener geometry on flexural properties of 3D printed polylactic acid (PLA) beams, Progress in additive manufacturing, Vol. 6, pp. 71-81, 2021.
[38]        S. Chahardoli, Flexural behavior of sandwich panels with 3D printed cellular cores and aluminum face sheets under quasi-static loading, Journal of Sandwich Structures & Materials, Vol. 25, No. 2, pp. 232-250, 2023.
Volume 54, Issue 2
June 2023
Pages 285-308
  • Receive Date: 10 May 2023
  • Revise Date: 18 May 2023
  • Accept Date: 19 May 2023