Investigation of the Effects of Dimensional Inaccuracies on the First Natural Frequency of Cellular Lattice Structures

ADMT Journal

دوره 15، شماره 3، آذر 2022، صفحه 109-117   

نوع مقاله: Original Article

شناسه دیجیتال (DOI): 10.30486/admt.2022.1946219.1324

نویسندگان

Amir Hosein Samimi؛ Mohammad Reza Karamooz-Ravari^* ؛ Reza Dehghani

Faculty of Mechanical and Materials Engineering Kerman Graduate University of Advanced Technology, Iran

چکیده

Lattice structures have attracted a great deal of attention for being used in different industries due to unique properties such as high strength-to-weight ratio and high damping coefficient. These metamaterials might suffer from dimensional inaccuracies, i.e., variable strut’s diameter, wavy struts, micropores, and deviation from the designed cross-sectional area, which arise from the fabrication process. These inaccuracies can drastically affect their mechanical response. In this paper, the effects of different dimensional inaccuracies, including variable struts’ diameter, wavy struts, and material concentration at nodes, on the frequency response of different cellular lattice structures are studied. To do so, a finite element model is constructed using Timoshenko beam elements, and the natural frequencies are obtained for four different lattices. The obtained results show that, by increasing the average diameter, the natural frequency increases drastically, whereas by increasing the amount of variation in the struts’ diameter and waviness the natural frequency decreases by a small amount. It is also observed that the lattice structures whose main deformation mechanism is axial loading are more sensitive to the change of average struts’ diameter. In addition, the natural frequency increases as the concentration of material in the vicinity of the nodes increases. The effect of material concentration inaccuracy is more pronounced for the first lattice for which the number of struts meeting at one node is the smallest.

کلیدواژه‌ها

Beam؛ Lattice Structures؛ Natural Frequency؛ Vibration

مراجع

• Ashby, M. F., Evans, T., Fleck, N. A., Hutchinson, J. W., Wadley, H. N. G., and Gibson, L. J., Metal Foams: A Design Guide, Butterworth-Heinemann, Oxford, UK, Chaps. 4, 5, 2000.
• Banhart, J., Manufacturing Routes for Metallic Foams, Jom, Vol. 52, No. 12, 2000, pp. 22-27, DOI:10.1007/s11837-000-0062-8.
• Meisel, N. A., Williams, C. B., and Druschitz, A., Lightweight Metal Cellular Structures Via Indirect 3D Printing and Casting, Proceedings of The International Solid Freeform Fabrication Symposium, Austin, United States, 2012, pp. 162-176.
• Di Taranto, R. A., Theory of Vibratory Bending for Elastic and Viscoelastic Layered Finite-Length Beams, Appl. Mech, Vol. 32, No. 4, 1965, pp. 881-886, DOI:1115/1.3627330.
• Kim, H. Y., Hwang, W., Effect of Debonding on Natural Frequencies and Frequency Response Functions of Honeycomb Sandwich Beams, Composite Structures, Vol. 55, No. 1, 2002, pp. 51-62, DOI:1016/S0263-8223(01)00136-2.
• Lou, J., Ma, L., and Wu, L. Z., Free Vibration Analysis of Simply Supported Sandwich Beams With Lattice Truss Core, Materials Science and Engineering: B, Vol. 177, No. 19, 2012, pp. 1712-1716, DOI:1016/j.mseb.2012.02.003.
• Xu, M., Qiu, Z., Free Vibration Analysis and Optimization of Composite Lattice Truss Core Sandwich Beams with Interval Parameters, Composite Structures, Vol. 106, 2013, pp. 85-95, DOI:1016/j.compstruct.2013.05.048.
• Niu, B., Yan, J., and Cheng, G., Optimum Structure with Homogeneous Optimum Cellular Material for Maximum Fundamental Frequency, Structural and Multidisciplinary Optimization, Vol. 39, No. 2, 2009, pp. 115-132.
• Azmi, M. S., Ismail, R., Hasan, R., Alkahari, M. R., and Tokoroyama, T., Vibration Analysis of FDM Printed Lattice Structure Bar, Proceedings of SAKURA Symposium on Mechanical Science and Engineering, Nagoya, Japan, September, 2017, pp. 33-35.
• Andresen, S., Bäger, A., and Hamm, C., Eigenfrequency Maximisation by Using Irregular Lattice Structures, Journal of Sound and Vibration, Vol. 465, 2020, 115027.
• Braun, M., Ivanez, I., and Aranda-Ruiz, J., Numerical Analysis of The Dynamic Frequency Responses of Damaged Micro-Lattice Core Sandwich Plates, The Journal of Strain Analysis for Engineering Design, Vol. 55, No. 1-2, 2020, pp. 31-41, DOI: 1177/0309324719890958.
• Monkova, K., Vasina, M., Zaludek, M., Monka, P. P., and Tkac, J., Mechanical Vibration Damping and Compression Properties of a Lattice Structure, Materials, Vol. 14, No. 6, 2021, 1502, DOI: 3390/ma14061502.
• Wang, X., Zhang, P., Ludwick, S., Belski, E., and To, A. C., Natural Frequency Optimization of 3D Printed Variable-Density Honeycomb Structure Via a Homogenization-Based Approach, Additive Manufacturing, Vol. 20, 2018, pp. 189-198, DOI: 1016/j.addma.2017.10.001.
• Ravari, M. K., Kadkhodaei, M., Badrossamay, M., and Rezaei, R., Numerical Investigation on Mechanical Properties of Cellular Lattice Structures Fabricated by Fused Deposition Modeling, International Journal of Mechanical Sciences, Vol. 88, 2014, pp. 154-161, DOI:1016/j.ijmecsci.2014.08.009.
• Ravari, M. K., Kadkhodaei, M., A Computationally Efficient Modeling Approach for Predicting Mechanical Behavior of Cellular Lattice Structures, Journal of Materials Engineering and Performance, Vol. 24, No. 1, 2015, pp. 245-252, DOI:1007/s11665-014-1281-4.
• Zhou, J., Shrotriya, P., and Soboyejo, W. O., On the Deformation of Aluminum Lattice Block Structures: From Struts to Structures, Mechanics of Materials, Vol. 36, No. 8, 2004, pp. 723-737, DOI:1016/j.mechmat.2003.08.007.
• Galarreta, S. R., Jeffers, J. R., and Ghouse, S., A Validated Finite Element Analysis Procedure for Porous Structures, Materials & Design, Vol. 189, 2020, 108546, DOI:1016/j.matdes.2020.108546.
• Syam, W. P., Jianwei, W., Zhao, B., Maskery, I., Elmadih, W., and Leach, R., Design and Analysis of Strut-Based Lattice Structures for Vibration Isolation, Precision Engineering, Vol. 52, 2018, pp. 494-506, DOI:10.1016/j.precisioneng.2017.09.010.
• Echeta, I., Feng, X., Dutton, B., Leach, R., and Piano, S., Review of Defects in Lattice Structures Manufactured by Powder Bed Fusion, The International Journal of Advanced Manufacturing Technology, Vol. 106, No. 5, 2020, pp. 2649-2668, DOI:10.1007/s00170-019-04753-4.
• Arabnejad, S., Johnston, R. B., Pura, J. A., Singh, B., Tanzer, M., and Pasini, D., High-Strength Porous Biomaterials for Bone Replacement: A Strategy to Assess the Interplay Between Cell Morphology, Mechanical Properties, Bone Ingrowth and Manufacturing Constraints, Acta biomaterialia, Vol. 30, 2016, pp. 345-356.
• Cuadrado, A., Yánez, A., Martel, O., Deviaene, S., and Monopoli, D., Influence of Load Orientation and of Types of Loads on The Mechanical Properties of Porous Ti6Al4V Biomaterials, Materials & Design, Vol. 135, 2017, pp. 309-318, DOI:10.1016/j.matdes.2017.09.045.