Moving load excited dynamics of multi-layered imperfect microplates based on various micromechanical models. (English) Zbl 07816990
Summary: This paper presents an investigation into the importance of micromechanical models in the analysis of forced vibrations of multi-layered microplates under a moving load. The microplate has a core fabricated from functionally graded materials and face sheets consisting of metal foam. The problem is modelled via a quasi-3D shear deformable method and the modified couple stress theory. This study assumes that the core material follows a power gradation pattern. Various micromechanical models, i.e., the Hashin-Shtrikman bounds, Voigt-Reuss-Hill, Voigt, Reuss, and Tamura, are applied to estimate the material characteristics of the core. The face sheets, composed of metal foams, possess closed- and open-cell solid porosities. System’s response of time history type is determined by numerically solving the coupled motion equations obtained using a force-moment balance method. A finite element analysis is conducted for a simplified macroplate system, and the agreement between the numerical results, via the proposed theoretical approach and the theory developed in this paper, is found to be very good. The results show that the micromechanical models influence the modelled mechanical properties of the core layer, consequently impacting the numerical results for the moving-load excited response of the multi-layered microsystem.
Keywords:
moving load; multi-layered microplate; micromechanical models; functionally graded materials; metal foamReferences:
| [1] | Abaqus/standard user\'s manual and Abaqus CAE manual. Version 6, 14, (2014), Dassault Systemes Simulia Corp: Dassault Systemes Simulia Corp Providence, RI, USA |
| [2] | Ahmadi, M.; Nikkhoo, A., Utilization of characteristic polynomials in vibration analysis of non-uniform beams under a moving mass excitation, Applied Mathematical Modelling, 38, 2130-2140, (2014) · Zbl 1427.74080 |
| [3] | Akavci, S.; Tanrikulu, A., Static and free vibration analysis of functionally graded plates based on a new quasi-3D and 2D shear deformation theories, Composites Part B: Engineering, 83, 203-215, (2015) |
| [4] | Akbarzadeh, A.; Abedini, A.; Chen, Z., Effect of micromechanical models on structural responses of functionally graded plates, Composite Structures, 119, 598-609, (2015) |
| [5] | Bakhshi Khaniki, H.; Hosseini-Hashemi, S., The size-dependent analysis of multilayered microbridge systems under a moving load/mass based on the modified couple stress theory, The European Physical Journal Plus, 132, 1-18, (2017) |
| [6] | Bogunia, L.; Buchen, S.; Weinberg, K., Microstructure characterization and stochastic modeling of open-cell foam based on μCT-image analysis, GAMM-Mitteilungen, 45, Article e202200018 pp., (2022) · Zbl 1539.74091 |
| [7] | Caporale, A.; Darban, H.; Luciano, R., Nonlocal strain and stress gradient elasticity of Timoshenko nano-beams with loading discontinuities, International Journal of Engineering Science, 173, Article 103620 pp., (2022) · Zbl 07498573 |
| [8] | Chi, S.-H.; Chung, Y.-L., Mechanical behavior of functionally graded material plates under transverse load—Part I: Analysis, International Journal of Solids and Structures, 43, 3657-3674, (2006) · Zbl 1121.74396 |
| [9] | Civalek, Ö.; Uzun, B.; Yaylı, M.Ö., On nonlinear stability analysis of saturated embedded porous nanobeams, International Journal of Engineering Science, 190, Article 103898 pp., (2023) · Zbl 07700730 |
| [10] | De Buhan, P.; Bleyer, J.; Hassen, G., Elastic, plastic and yield design of reinforced structures, (2017), Elsevier |
| [11] | Dimitrovová, Z., Complete semi-analytical solution for a uniformly moving mass on a beam on a two-parameter visco-elastic foundation with non-homogeneous initial conditions, International Journal of Mechanical Sciences, 144, 283-311, (2018) |
| [12] | Dong, L.; Liu, H.; Riffat, S., Development of small-scale and micro-scale biomass-fuelled CHP systems-A literature review, Applied Thermal Engineering, 29, 2119-2126, (2009) |
| [13] | Eringen, A. C.; Edelen, D., On nonlocal elasticity, International Journal of Engineering Science, 10, 233-248, (1972) · Zbl 0247.73005 |
| [14] | Esen, I.; Abdelrahman, A. A.; Eltaher, M. A., Dynamics analysis of timoshenko perforated microbeams under moving loads, Engineering with Computers, 1-17, (2020) |
| [15] | Feizi, S.; Javadiyan, S.; Cooksley, C. M.; Shaghayegh, G.; Psaltis, A. J.; Wormald, P.-J.; Vreugde, S., Green synthesized colloidal silver is devoid of toxic effects on primary human nasal epithelial cells in vitro, Food and Chemical Toxicology, 157, Article 112606 pp., (2021) |
| [16] | Feizi, S.; Cooksley, C. M.; Nepal, R.; Psaltis, A. J.; Wormald, P.-J.; Vreugde, S., Silver nanoparticles as a bioadjuvant of antibiotics against biofilm-mediated infections with methicillin-resistant Staphylococcus aureus and Pseudomonas aeruginosa in chronic rhinosinusitis patients, Pathology, 54, 453-459, (2022) |
| [17] | Frýba, L., Vibration of solids and structures under moving loads, (1999), Thomas: Thomas Telford |
| [18] | Ghayesh, M. H.; Farokhi, H.; Amabili, M., Nonlinear behaviour of electrically actuated MEMS resonators, International Journal of Engineering Science, 71, 137-155, (2013) |
| [19] | Ghayesh, M. H.; Farokhi, H.; Zhang, Y.; Gholipour, A., Nonlinear coupled moving-load excited dynamics of beam-mass structures, Archives of Civil and Mechanical Engineering, 20, 1-11, (2020) |
| [20] | Gibson, I.; Ashby, M. F., The mechanics of three-dimensional cellular materials, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 382, 43-59, (1982) |
| [21] | Guo, L.; Xin, X.; Shahsavari, D.; Karami, B., Dynamic response of porous E-FGM thick microplate resting on elastic foundation subjected to moving load with acceleration, Thin-Walled Structures, 173, Article 108981 pp., (2022) |
| [22] | Hashin, Z.; Shtrikman, S., A variational approach to the theory of the elastic behaviour of multiphase materials, Journal of the Mechanics and Physics of Solids, 11, 127-140, (1963) · Zbl 0108.36902 |
| [23] | Hill, R., The elastic behaviour of a crystalline aggregate, Proceedings of the Physical Society. Section A, 65, 349, (1952) |
| [24] | Hong, H.; Ni, L.; Sun, H., Application and prospect of MEMS technology to geophysics, (2021 IEEE 16th International Conference on Nano/Micro Engineered and Molecular Systems (NEMS), (2021), IEEE), 1863-1866 |
| [25] | Hosseini, S. M., Shock-induced nonlocal coupled thermoelasticity analysis (with energy dissipation) in a MEMS/NEMS beam resonator based on Green-Naghdi theory: A meshless implementation considering small-scale effects, Journal of Thermal Stresses, 40, 1134-1151, (2017) |
| [26] | Jalaei, M.; Thai, H.; Civalek, Ӧ., On viscoelastic transient response of magnetically imperfect functionally graded nanobeams, International Journal of Engineering Science, 172, Article 103629 pp., (2022) · Zbl 07498571 |
| [27] | Jiang, Y.; Li, L.; Hu, Y., A nonlocal surface theory for surface-bulk interactions and its application to mechanics of nanobeams, International Journal of Engineering Science, 172, Article 103624 pp., (2022) · Zbl 07498569 |
| [28] | Karamanli, A., Transient vibration analysis of strain gradient multi-directional functionally graded microplates under a moving concentrated load, Composite Structures, 308, Article 116678 pp., (2023) |
| [29] | Karami, B.; Ghayesh, M. H., Vibration characteristics of sandwich microshells with porous functionally graded face sheets, International Journal of Engineering Science, 189, Article 103884 pp., (2023) · Zbl 07700721 |
| [30] | Karami, B.; Shahsavari, D.; Janghorban, M.; Li, L., Influence of homogenization schemes on vibration of functionally graded curved microbeams, Composite Structures, 216, 67-79, (2019) |
| [31] | Khorgade, M. P.; Gaidhane, A., (2011 UkSim 13th International Conference on Computer Modelling and Simulation, (2011), IEEE), 522-527, Applications of MEMS in Robotics and BioMEMS |
| [32] | Kim, D.; Lee, J.; Nomura, T.; Dede, E. M.; Yoo, J.; Min, S., Topology optimization of functionally graded anisotropic composite structures using homogenization design method, Computer Methods in Applied Mechanics and Engineering, 369, Article 113220 pp., (2020) · Zbl 1506.74282 |
| [33] | Koizumi, M., FGM activities in Japan, Composites Part B: Engineering, 28, 1-4, (1997) |
| [34] | Kong, S., A review on the size-dependent models of micro-beam and micro-plate based on the modified couple stress theory, Archives of Computational Methods in Engineering, 29, 1-31, (2022) |
| [35] | Kulshreshtha, A.; Dhakad, S., Preparation of metal foam by different methods: A review, Materials Today: Proceedings, 26, 1784-1790, (2020) |
| [36] | Lavan, D. A.; McGuire, T.; Langer, R., Small-scale systems for in vivo drug delivery, Nature Biotechnology, 21, 1184-1191, (2003) |
| [37] | Le, C. I.; Nguyen, D. K., Nonlinear vibration of three-phase bidirectional functionally graded sandwich beams with influence of homogenization scheme and partial foundation support, Composite Structures, 307, Article 116649 pp., (2023) |
| [38] | Li, Z.; He, Y.; Lei, J.; Guo, S.; Liu, D.; Wang, L., A standard experimental method for determining the material length scale based on modified couple stress theory, International Journal of Mechanical Sciences, 141, 198-205, (2018) |
| [39] | Liu, P.; Chen, G.-F., Porous materials: processing and applications, (2014), Elsevier |
| [40] | Liu, H.-F.; Luo, Z.-C.; Hu, Z.-K.; Yang, S.-Q.; Tu, L.-C.; Zhou, Z.-B.; Kraft, M., A review of high-performance MEMS sensors for resource exploration and geophysical applications, Petroleum Science, 19, 2631-2648, (2022) |
| [41] | Malekzadeh, P.; Fiouz, A.; Razi, H., Three-dimensional dynamic analysis of laminated composite plates subjected to moving load, Composite Structures, 90, 105-114, (2009) |
| [42] | Malikan, M.; Eremeyev, V. A., On time-dependent nonlinear dynamic response of micro-elastic solids, International Journal of Engineering Science, 182, Article 103793 pp., (2023) · Zbl 07646847 |
| [43] | Mindlin, R. D.; Eshel, N., On first strain-gradient theories in linear elasticity, International Journal of Solids and Structures, 4, 109-124, (1968) · Zbl 0166.20601 |
| [44] | Mindlin, R.; Tiersten, H., Effects of couple-stresses in linear elasticity, Archive for Rational Mechanics and Analysis, 11, 415-448, (1962) · Zbl 0112.38906 |
| [45] | Mori, T.; Tanaka, K., Average stress in matrix and average elastic energy of materials with misfitting inclusions, Acta metallurgica, 21, 571-574, (1973) |
| [46] | Mota, A. F.; Loja, M. A.R.; Barbosa, J. I.; Rodrigues, J. A., Porous functionally graded plates: An assessment of the influence of shear correction factor on static behavior, Mathematical and Computational Applications, 25, 25, (2020) |
| [47] | Nazzaro, F.; Fratianni, F.; Coppola, R., Microtechnology and nanotechnology in food science, Green Technologies in Food Production and Processing, 471-494, (2012) |
| [48] | Obregón, R.; Ramón-Azcón, J.; Ahadian, S.; Shiku, H.; Bae, H.; Ramalingam, M.; Matsue, T., The use of microtechnology and nanotechnology in fabricating vascularized tissues, Journal of Nanoscience and Nanotechnology, 14, 487-500, (2014) |
| [49] | Ouyang, H., Moving-load dynamic problems: A tutorial (with a brief overview), Mechanical Systems and Signal Processing, 25, 2039-2060, (2011) |
| [50] | Reddy, J.; Chin, C., Thermomechanical analysis of functionally graded cylinders and plates, Journal of Thermal Stresses, 21, 593-626, (1998) |
| [51] | Reuss, A., Berechnung der fließgrenze von mischkristallen auf grund der plastizitätsbedingung für einkristalle, ZAMM-Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, 9, 49-58, (1929) · JFM 55.1110.02 |
| [52] | Roberts, A. P.; Garboczi, E. J., Elastic moduli of model random three-dimensional closed-cell cellular solids, Acta Materialia, 49, 189-197, (2001) |
| [53] | Roberts, A. P.; Garboczi, E. J., Computation of the linear elastic properties of random porous materials with a wide variety of microstructure, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 458, 1033-1054, (2002) · Zbl 1059.74005 |
| [54] | Roohi, A. H.; Naeini, H. M.; Gollo, M. H.; Soltanpour, M.; Abbaszadeh, M., On the random-based closed-cell metal foam modeling and its behavior in laser forming process, Optics & Laser Technology, 72, 53-64, (2015) |
| [55] | Roy, S.; Chakraborty, G.; DasGupta, A., On the wave propagation in a beam-string model subjected to a moving harmonic excitation, International Journal of Solids and Structures, 162, 259-270, (2019) |
| [56] | Sarparast, H.; Ebrahimi-Mamaghani, A., Vibrations of laminated deep curved beams under moving loads, Composite Structures, 226, Article 111262 pp., (2019) |
| [57] | Sarparast, H.; Alibeigloo, A.; Borjalilou, V.; Koochakianfard, O., Forced and free vibrational analysis of viscoelastic nanotubes conveying fluid subjected to moving load in hygro-thermo-magnetic environments with surface effects, Archives of Civil and Mechanical Engineering, 22, 172, (2022) |
| [58] | Shahmohammadi, M. A.; Mirfatah, S. M.; Salehipour, H.; Civalek, Ö., On nonlinear forced vibration of micro scaled panels, International Journal of Engineering Science, 182, Article 103774 pp., (2023) · Zbl 07646840 |
| [59] | Shen, H.-S.; Wang, Z.-X., Assessment of Voigt and Mori-Tanaka models for vibration analysis of functionally graded plates, Composite Structures, 94, 2197-2208, (2012) |
| [60] | Şimşek, M.; Aydın, M., Size-dependent forced vibration of an imperfect functionally graded (FG) microplate with porosities subjected to a moving load using the modified couple stress theory, Composite Structures, 160, 408-421, (2017) |
| [61] | Şimşek, M.; Aydın, M.; Yurtcu, H.; Reddy, J., Size-dependent vibration of a microplate under the action of a moving load based on the modified couple stress theory, Acta Mechanica, 226, 3807-3822, (2015) · Zbl 1323.74060 |
| [62] | Şimşek, M., Dynamic analysis of an embedded microbeam carrying a moving microparticle based on the modified couple stress theory, International Journal of Engineering Science, 48, 1721-1732, (2010) · Zbl 1231.74275 |
| [63] | Şimşek, M., Vibration analysis of a functionally graded beam under a moving mass by using different beam theories, Composite Structures, 92, 904-917, (2010) |
| [64] | Şimşek, M., Bi-directional functionally graded materials (BDFGMs) for free and forced vibration of Timoshenko beams with various boundary conditions, Composite Structures, 133, 968-978, (2015) |
| [65] | Song, Q.; Shi, J.; Liu, Z.; Wan, Y., Dynamic analysis of rectangular thin plates of arbitrary boundary conditions under moving loads, International Journal of Mechanical Sciences, 117, 16-29, (2016) |
| [66] | Tamura, I., Strength and ductility of Fe-Ni-C alloys composed of austenite and martensite with various strength, (Proceedings of the third international conference on strength of metals and alloys. Proceedings of the third international conference on strength of metals and alloys, Cambridge, Institute of Metals, (1973)), 611-615, 1973 |
| [67] | Thomas, S.; Mishra, R. K.; Asiri, A. M., Sustainable polymer composites and nanocomposites, (2019), Springer |
| [68] | Toupin, R., Elastic materials with couple-stresses, Archive fo Rational Mechanics and Analysis, 11, 385-414, (1962) · Zbl 0112.16805 |
| [69] | Tran, T. T.; Pham, Q.-H.; Nguyen-Thoi, T., Dynamic analysis of functionally graded porous plates resting on elastic foundation taking into mass subjected to moving loads using an edge-based smoothed finite element method, Shock and Vibration, 2020, (2020) |
| [70] | Tran, H.-Q.; Vu, V.-T.; Tran, M.-T., Free vibration analysis of piezoelectric functionally graded porous plates with graphene platelets reinforcement by pb-2 Ritz method, Composite Structures, 305, Article 116535 pp., (2023) |
| [71] | Uzun, B.; Kafkas, U.; Deliktaş, B.; Yaylı, M.Ö., Size-dependent vibration of porous bishop nanorod with arbitrary boundary conditions and nonlocal elasticity effects, Journal of Vibration Engineering & Technologies, 11, 809-826, (2023) |
| [72] | Vo, D.; Zhou, K.; Rungamornrat, J.; Bui, T. Q., Spatial arbitrarily curved microbeams with the modified couple stress theory: Formulation of equations of motion, European Journal of Mechanics-A/Solids, 92, Article 104475 pp., (2022) · Zbl 1507.74201 |
| [73] | Voigt, W., Ueber die Beziehung zwischen den beiden Elasticitätsconstanten isotroper Körper, Annalen der physik, 274, 573-587, (1889) · JFM 21.1039.01 |
| [74] | Wang, Z.; Gao, J.; Chang, K.; Meng, L.; Zhang, N.; Guo, Z., Manufacturing of open-cell aluminum foams via infiltration casting in super-gravity fields and mechanical properties, RSC Advances, 8, 15933-15939, (2018) |
| [75] | Wang, S.; Ding, W.; Li, Z.; Xu, B.; Zhai, C.; Kang, W.; Yang, W.; Li, Y., A size-dependent quasi-3D model for bending and buckling of porous functionally graded curved nanobeam, International Journal of Engineering Science, 193, Article 103962 pp., (2023) · Zbl 07776198 |
| [76] | Wiśniewska, A.; Egner, H., Optimization of functionally graded structural members by means of new effective properties estimation method, Materials, 12, 3139, (2019) |
| [77] | Xue, Y.; Jin, G.; Ma, X.; Chen, H.; Ye, T.; Chen, M.; Zhang, Y., Free vibration analysis of porous plates with porosity distributions in the thickness and in-plane directions using isogeometric approach, International Journal of Mechanical Sciences, 152, 346-362, (2019) |
| [78] | Yang, F.; Chong, A.; Lam, D. C.C.; Tong, P., Couple stress based strain gradient theory for elasticity, International Journal of Solids and Structures, 39, 2731-2743, (2002) · Zbl 1037.74006 |
| [79] | Yang, J.; Chen, Y.; Xiang, Y.; Jia, X., Free and forced vibration of cracked inhomogeneous beams under an axial force and a moving load, Journal of Sound and Vibration, 312, 166-181, (2008) |
| [80] | Yang, Y.; Kunpang, K.; Lam, C.; Iu, V., Dynamic behaviors of tapered bi-directional functionally graded beams with various boundary conditions under action of a moving harmonic load, Engineering Analysis with Boundary Elements, 104, 225-239, (2019) · Zbl 1464.74344 |
| [81] | Yee, K.; Ong, O. Z.S.; Ghayesh, M. H.; Amabili, M., Various homogenisation schemes for vibration characteristics of axially FG core multilayered microbeams with metal foam face layers based on third order shear deformation theory, Applied Mathematical Modelling, 125, 189-217, (2024) |
| [82] | Young, D. J.; Zorman, C. A.; Mehregany, M., MEMS/NEMS devices and applications, 359-387, (2010), Springer Handbook of Nanotechnology |
| [83] | Zhang, Q.; Liu, H., On the dynamic response of porous functionally graded microbeam under moving load, International Journal of Engineering Science, 153, Article 103317 pp., (2020) · Zbl 07228653 |
| [84] | Zhao, C., Review on thermal transport in high porosity cellular metal foams with open cells, International Journal of Heat and Mass Transfer, 55, 3618-3632, (2012) |
| [85] | Zheng, Y.; Karami, B.; Shahsavari, D., On the vibration dynamics of heterogeneous panels under arbitrary boundary conditions, International Journal of Engineering Science, 178, Article 103727 pp., (2022) · Zbl 07575009 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
