Determination of eigen vibration modes for three-layer plates using the example of solar panels

Authors

  • Iaroslav Lavrenko Department of Dynamics and Strength of Machine and Strength of Materials, National Technical University of Ukraine «Igor Sikorsky Kyiv Polytechnic Institute», Kyiv, Ukraine https://orcid.org/0000-0002-4384-4866
  • Olena Chaikovska Department of Theory, Practice and Translation of German, National Technical University of Ukraine «Igor Sikorsky Kyiv Polytechnic Institute», Kyiv, Ukraine https://orcid.org/0000-0001-9945-4296
  • Sofiia Yakovlieva Structural engineer at FAM GmbH, Magdeburg, Germany

DOI:

https://doi.org/10.46299/j.isjea.20230202.10

Keywords:

solar panel, anti-sandwich, Kirchhoff theory, Reisner-Mindlin theory, eigen modes, finite element method, ABAQUS

Abstract

Solar panels are considered as three-layer plates with a thick hard outer layer and a thin soft inner layer. To describe the mechanical behavior of the plates on the example of a solar panel, a model for anti-sandwich plates was used. The literature review includes scientific articles describing models for analytical and numerical calculations of three-layer plates. During the scientific study of the mechanical behavior of the solar plate under the influence of external factors, the method of finite element analysis using the element of the spatial shell was used. This type of elements is used for theories of single and multilayer plates. Shell elements were used for calculations and modeling of the natural forms of vibrations of three-layer plates. The paper presents scientific studies under static loading under different exposure conditions, as well as an analysis of self-oscillations of a three-layer plate using the Kirchhoff and Mindlin theories as an example. As part of the scientific work, a study of the mechanical model of a thin solar panel was carried out using finite element analysis in the ABAQUS program, taking into account different temperature conditions. The article provides analytical calculations of the application of various theories to determine the natural forms of plate vibrations.

References

Lopez, A., Roberts, B., Heimiller, D., Blair, N., Porro, G. (2012). U.S. Renewable Energy Technical Potentials: A GIS-Based Analysis. National Renewable Energy Laboratory Document 7, 1-40, ISBN: NREL/TP-6A20-51946. DOI: NREL/TP-6A20-51946.

Naumenko, K. und Eremeyev, V. A. (2014). A layer-wise theory for laminated glass and photovoltaic panels. Composite Structures 112(1), 283–291. ISSN: 02638223. DOI: 10 .1016/j.compstruct.2014.02.009.

Schulze, S.-H., Pander, M., Naumenko, K. und Altenbach, H. (2012). Analysis of laminated glass beams for photovoltaic applications. International Journal of Solids and Structures 49(15-16), 2027–2036. ISSN: 0020-7683. DOI: 10.1016/j.ijsolstr.2012.03.028. URL: http://dx.doi.org/10.1016/j.ijsolstr.2012.03.028.

Abaqus User’s Manual. Version 6.14. (2014).Dassault Systèmes Simulia Corp. Providence, RI, USA. URL: http://www-archive.ccee.iastate.edu/abaqus/Documentation/docs/v6.14/.

Quora. What is shear locking in FEA. Available at: https://www.quora.com/What-is-shear-locking-in-FEA

Backwoodssolar. Solar panels. Available at: http://www.backwoodssolar.com/products/solar-panels.

Assmus, M., Naumenko, K. und Altenbach, H. (2016). A multiscale projection approach for the coupled global-local structural analysis of photovoltaic modules. Composite Structures 158, 340–358. ISSN: 02638223. DOI: 10.1016/j.compstruct.2016.09.036. URL: http://dx.doi.org/10.1016/j.compstruct.2016.09.036.

Eisenträger, J., Naumenko, K., Altenbach, H. und Köppe, H. (2015). Application of the first-order shear deformation theory to the analysis of laminated glasses and photovoltaic panels. International Journal of Mechanical Sciences 96-97, 163–171. ISSN: 00207403. DOI: 10.1016/j.ijmecsci.2015.03.012. URL: http://dx.doi.org/10.1016/j.ijmecsci.2015.03.012.

Eisenträger, J., Naumenko, K., Altenbach, H. und Meenen, J. (2015). A user-defined finite element for laminated glass panels and photovoltaic modules based on a layer-wise theory. Composite Structures 133(December), 265–277. ISSN: 02638223. DOI: 10.1016/j.compstruct.2015.07.049.

Naumenko, K. und Eremeyev, V. A. (2014). A layer-wise theory for laminated glass and photovoltaic panels. Composite Structures 112(1), 283–291. ISSN: 02638223. DOI: 10 .1016/j.compstruct.2014.02.009.

Weps, M., Naumenko, K., Altenbach, H. (2013). Unsymmetric three-layer laminate with soft core for photovoltaic modules. Composite Structures 105, 332-339. ISSN: 02638223. DOI: 10.1016/j.compstruct.2013.05.029.

Klinkel, S., Gruttmann, F., Wagner, W. (1999). A Continuum Based 3D – Shell Element for Laminated Structures. Continuum 71, 43-62. DOI: 10.1.1.727.6818.

Juhre D. (2015). Finite-Elemente-Methode. Available at: https://kipdf.com/finite-element-methode-jun-prof-dr-ing-daniel-juhre-institut-fr-mechanik-fakultt_5ab55e3a 1723dd389ca4c88b .html

Wierzbicki, T. (2013). MIT Course: Plates and Shells. Available at: https://ocw.mit.edu/courses/2-081j-plates-and-shells-spring-2007/

Altenbach, H., Altenbach, J und Naumenko, K. (2004). Ebene Flächentragwerke, 1–210. ISBN: 9783642058417. DOI: 10.1007/978-3-662-06431-3

Hosseini, S., Remmers, J., Verhoosel, C., de Borst, R. (2014). An isogeometric continuum shell element for non-linear analysis. Computer Methods in Applied Mechanics and Engineering 271, 1-22. ISSN: 00457825. ISBN: 978-1-4577-0079-8. DOI: 10.1016/j.cma.2013.11.023. URL: http://dx.doi.org/10.1016/j.cma.2013.11.023

Andelfinger, U., Ramm, E. (1993). EAS-elements for two-dimensional, three-dimensional, plate and shell structures and their equivalence to HR-elements. International Journal for Numerical Methods in Engineering 36 (8), 1311-1337. ISSN: 10970207. DOI: 10.1002/nme.1620360805.

Yamashita, H., Valkeapää, A., Jayakumar, P., Sugiyama, H. (2015). Continuum Mechanics Based Bilinear Shear Deformable Shell Element Using Absolute Nodal Coordinate Formulation. Journal of Computational and Nonlinear Dynamics 10 (5). ISSN: 1555-1415. DOI: 10.1115/1.4028657.

Flores, F., Nallim, L., Oller, S. (2017). Formulation of solid-shell finite elements with large displacements considering different transverse shear strains approximations. Finite Elements in Analysis and Design 130, 39-52. ISSN: 0168874X. DOI: 10.1016/j.finel.2017.03.001. URL: http://linkinghub.elsevier.com/retrieve/pii/S0168874X16304528

Naceur, H., Shiri, S., Coutellier, D., Batoz, J. L. (2013). On the modeling and design of composite multilayered structures using solid-shell finite element model. Finite Elements in Analysis and Design 70-71, 1-14. ISSN: 0168874X. DOI: 10.1016/j.finel.2013.02.004. URL: http://dx.doi.org/10.1016/j.finel.2013.02.004

Dvorkin, E., Bathe, K.-J. (1984). A continuum mechanics based four‐node shell element for general non‐linear analysis. Engineering Computations 1 (1), 77-88. ISSN: 0264-4401. ISBN: 02644401. DOI: 10.1108/eb023562. URL: http://www.emeraldinsight.com/doi/10.1108/eb023562

Bischoff, M., Ramm, E. (1997). Shear deformable shell elements for large strains and rotations. International Journal for Numerical Methods in Engineering 40 (23), 4427-4449. DOI: 10.1002/(SICI)1097-0207(19971215)40:23<4427::AID-NME268>3.0.CO;2-9. Available at: http://doi.wiley.com/10.1002/%28SICI%291097-0207%2819971215%2940%3A23%3C4427%3A%3AAID-NME268%3E3.0.CO%3B2-9

Tho, N. C., Thom, D. V., Cong, P. H., Zenkour, A. M., Doan, D. H., Minh, P. V. (2023). Finite element modeling of the bending and vibration behavior of three-layer composite plates with a crack in the core layer. Composite Structures, Volume 305. https://doi.org/10.1016/j.compstruct.2022.116529

Sarafraz, M., Seidi, H., Kakavand, F., Viliani, N.S. (2023). Free vibration and buckling analyses of a rectangular sandwich plate with an auxetic honeycomb core and laminated three-phase polymer/GNP/fiber face sheets. Thin-Walled Structures, Volume 183. https://doi.org/10.1016/j.tws.2022.110331

Eratbeni, M.G., Rostamiyan, Y. (2022). Vibration behavior of a carbon fiber-reinforced polymer composite sandwich panel: Rhombus core versus elliptical core. Polimer composites. https://doi.org/10.1002/pc.27201

Wang, J., Wang, C., Chen, R. et al. (2022). Residual Compressive Strength of Aluminum Honeycomb Sandwich Structures with CFRP Face Sheets after Low-velocity Impact. Appl Compos Mater. https://doi.org/10.1007/s10443-022-10092-7

Xiong, X.Z.C., Yin, J., Zhou, H., Zou, Y., Fan, Z., Deng, H. (2023). Experimental study and modeling analysis of planar compression of composite corrugated, lattice and honeycomb sandwich plates. Composite Structures, Volume 308. https://doi.org/10.1016/j.compstruct.2023.116690.

Downloads

Published

2023-04-01

How to Cite

Lavrenko, I., Chaikovska, O., & Yakovlieva, S. (2023). Determination of eigen vibration modes for three-layer plates using the example of solar panels. International Science Journal of Engineering & Agriculture, 2(2), 103–116. https://doi.org/10.46299/j.isjea.20230202.10