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http://dx.doi.org/10.12989/anr.2021.11.5.495

Physics-informed neural networks: A deep learning framework for solving the vibrational problems  

Wang, Xusheng (Xi'an University of Technology)
Zhang, Liang (School of Aerospace Engineering, Tsinghua University)
Publication Information
Advances in nano research / v.11, no.5, 2021 , pp. 495-519 More about this Journal
Abstract
The provided paper considers the vibrations of viscoelastic sandwich disk reinforced by graphene nano-platelets (GPLs) filled viscoelastic concrete (GPLRVC) honeycomb core and face sheets via deep learning. The optimum values of the parameters involved in the fully connected neural network are determined through the momentum-based optimizer. The strength of the method applied in this study comes from the high accuracy besides lower epochs needed to train the multi-layered network. The honeycomb core would be manufactured by aluminum according to its great stiffness and lightweight. The mixture rule and modified Halpin-Tsai model have been involved in creating an efficient concrete material constant. By applying energy methods, the system's governing equations have been extracted and solved through Generalize Differential Quadrature (GDQ) technique. In the given research, Kelvin-Voigt viscoelasticity has been applied to model viscoelastic properties. The time-dependent deflection would be solved applying the fourth-order Runge-Kutta computational approach. Then, a parametric study has been conducted to analyze the influences of the external and internal radius ratio, thickness to length ratio of the concrete, hexagonal core angle, the GPLs' weight fraction, and the honeycomb core's thickness to internal radius ratio on the vibrations of the viscoelastic sandwich disk considering face sheet of FG-GPLRVC and honeycomb core.
Keywords
deep learning; GDQ; honeycomb core; vibrations; viscoelastic sandwich disk;
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86 Safarpour, H., Hosseini, M. and Ghadiri, M. (2017a), "Influence of three-parameter viscoelastic medium on vibration behavior of a cylindrical nonhomogeneous microshell in thermal environment: An exact solution", J. Therm. Stress, 40(11), 1353-1367. https://doi.org/10.1080/01495739.2017.1350827.   DOI
87 Shariati, M., Mafipour, M.S., Ghahremani, B., Azarhomayun, F., Ahmadi, M., Trung, N.T. and Shariati, A. (2020g), "A novel hybrid extreme learning machine-grey wolf optimizer (ELMGWO) model to predict compressive strength of concrete with partial replacements for cement", Eng. Comput., 1-23. https://doi.org/10.1007/s00366-020-01081-0.   DOI
88 Han, J.B. and Liew, K. (1999), "Axisymmetric free vibration of thick annular plates", Int. J. Mech. Sci., 41(9), 1089-1109, https://doi.org/10.1016/S0020-7403(98)00057-5.   DOI
89 Al-Furjan, M., Habibi, M., Ghabussi, A., Safarpour, H., Safarpour, M. and Tounsi, A. (2020), "Non-polynomial framework for stress and strain response of the FG-GPLRC disk using three-dimensional refined higher-order theory", Eng. Struct., 228, 111496. https://doi.org/10.1016/j.engstruct.2020.111496.   DOI
90 Shokrgozar, A., Safarpour, H. and Habibi, M. (2020), "Influence of system parameters on buckling and frequency analysis of a spinning cantilever cylindrical 3D shell coupled with piezoelectric actuator", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 234(2), 512-529. https://doi.org/10.1177/0954406219883312.   DOI
91 Jiao, J., Ghoreishi, S.M., Moradi, Z. and Oslub, K. (2021), "Coupled particle swarm optimization method with genetic algorithm for the static-dynamic performance of the magneto-electro-elastic nanosystem", Eng. Comput., https://doi.org/10.1007/s00366-021-01391-x.   DOI
92 Shariati, A., Mohammad-Sedighi, H., Zur, K.K., Habibi, M. and Safa, M. (2020c), "On the vibrations and stability of moving viscoelastic axially functionally graded nanobeams", Materials, 13(7), 1707. https://doi.org/10.3390/ma13071707.   DOI
93 Wu, J. and Habibi, M. (2021), "Dynamic simulation of the ultra-fast-rotating sandwich cantilever disk via finite element and semi-numerical methods", Eng. Comput., 1-17. https://doi.org/10.1007/s00366-021-01396-6.   DOI
94 Ghabussi, A., Marnani, J.A. and Rohanimanesh, M.S. (2020b). "Improving seismic performance of portal frame structures with steel curved dampers", Structures, 24, pp. 27-40. https://doi.org/10.1016/j.istruc.2019.12.025.   DOI
95 Jiang, L., Zhang, B., Han, S., Chen, H. and Wei, Z. (2021), "Upscaling evapotranspiration from the instantaneous to the daily time scale: Assessing six methods including an optimized coefficient based on worldwide eddy covariance flux network", J. Hydrol., 596, 126135. https://doi.org/10.1016/j.jhydrol.2021.126135   DOI
96 Alimirzaei, S., Mohammadimehr, M. and Tounsi, A. (2019), "Nonlinear analysis of viscoelastic micro-composite beam with geometrical imperfection using FEM: MSGT electro-magneto-elastic bending, buckling and vibration solutions", Struct. Eng. Mech. 71(5), 485-502. https://doi.org/10.12989/sem.2019.71.5.485.   DOI
97 Gao, N., Luo, D., Cheng, B. and Hou, H. (2020b), "Teaching-learning-based optimization of a composite metastructure in the 0-10 kHz broadband sound absorption range", J. Acoust. Soc. Am., 148(2), EL125-129. https://doi.org/10.1121/10.0001678.   DOI
98 Gao, N., Tang, L., Deng, J., Lu, K., Hou, H. and Chen, K. (2021b), "Design, fabrication and sound absorption test of composite porous metamaterial with embedding I-plates into porous polyurethane sponge", Appl. Acoust., 175, 107845. https://doi.org/10.1016/j.apacoust.2020.107845.   DOI
99 Gao, N., Wang, B., Lu, K. and Hou, H. (2021c), "Complex band structure and evanescent Bloch wave propagation of periodic nested acoustic black hole phononic structure", Appl. Acoust., 177, 107906. https://doi.org/10.1016/j.apacoust.2020.107906.   DOI
100 Ghabussi, A., Habibi, M., NoormohammadiArani, O., Shavalipour, A., Moayedi, H. and Safarpour, H. (2020a), "Frequency characteristics of a viscoelastic graphene nanoplatelet-reinforced composite circular microplate", J. Vib. Control, 27(1-2), 101-118. https://doi.org/10.1177/1077546320923930.   DOI
101 Ghavanloo, E. and Fazelzadeh, S.A. (2011), "Flow-thermoelastic vibration and instability analysis of viscoelastic carbon nanotubes embedded in viscous fluid", Physica E, 44(1), 17-24. https://doi.org/10.1016/j.physe.2011.06.024.   DOI
102 Hashemi, H.R., Alizadeh, A.a., Oyarhossein, M.A., Shavalipour, A., Makkiabadi, M. and Habibi, M. (2019), "Influence of imperfection on amplitude and resonance frequency of a reinforcement compositionally graded nanostructure", Wave. Random Complex, 1-27, https://doi.org/10.1080/17455030.2019.1662968.   DOI
103 Jermsittiparsert, K., Ghabussi, A., Forooghi, A., Shavalipour, A., Habibi, M., won Jung, D. and Safa, M. (2020), "Critical voltage, thermal buckling and frequency characteristics of a thermally affected GPL reinforced composite microdisk covered with piezoelectric actuator", Mech. Based Des. Struct., 1-23, https://doi.org/10.1080/15397734.2020.1748052.   DOI
104 Wang, H., Zhang, H., Dousti, R. and Safarpour, H. (2021), "Dynamic simulation of moderately thick annular system coupled with shape memory alloy and multi-phase nanocomposite face sheets", Eng. Comput., 1-24. https://doi.org/10.1007/s00366-020-01246-x.   DOI
105 Xu, W., Pan, G., Moradi, Z. and Shafiei, N. (2021), "Nonlinear forced vibration analysis of functionally graded non-uniform cylindrical microbeams applying the semi-analytical solution", Compos. Struct., 114395. https://doi.org/10.1016/j.compstruct.2021.114395.   DOI
106 Zhang, X., Wang, Y., Wang, C., Su, C.Y., Li, Z. and Chen, X. (2018), "Adaptive estimated inverse output-feedback quantized control for piezoelectric positioning stage", IEEE T Cybernet., 49(6), 2106-2118. https://doi.org/10.1109/TCYB.2018.2826519.   DOI
107 Zhang, Y. and Li, Y. (2019), "Nonlinear dynamic analysis of a double curvature honeycomb sandwich shell with simply supported boundaries by the homotopy analysis method", Compos. Struct., 221, 110884. https://doi.org/10.1016/j.compstruct.2019.04.056.   DOI
108 He, X., Ding, J., Habibi, M., Safarpour, H. and Safarpour, M. (2021), "Non-polynomial framework for bending responses of the multi-scale hybrid laminated nanocomposite reinforced circular/annular plate", Thin Wall. Struct., 166 108019. https://doi.org/10.1016/j.tws.2021.108019.   DOI
109 Han, X., Chen, N., Yan, J., Liu, J., Liu, M. and Karellas, S. (2019), "Thermodynamic analysis and life cycle assessment of supercritical pulverized coal-fired power plant integrated with No. 0 feedwater pre-heater under partial loads", J. Clean. Prod., 233, 1106-1122. https://doi.org/10.1016/j.jclepro.2019.06.159   DOI
110 Weng, L., He, Y., Peng, J., Zheng, J. and Li, X. (2021), "Deep cascading network architecture for robust automatic modulation classification", Neurocomputing, 455, 308-324. https://doi.org/10.1016/j.neucom.2021.05.010   DOI
111 Wu, H., Zhu, J., Kitipornchai, S., Wang, Q., Ke, L.L. and Yang, J. (2020), "Large amplitude vibration of functionally graded graphene nanocomposite annular plates in thermal environments", Compos. Struct., 239, 112047. https://doi.org/10.1016/j.compstruct.2020.112047.   DOI
112 Wu, W. (2021), "Adaptive momentum-based optimization to train deep neural network for computer simulation of hygro-thermomechanical vibration performance of laminated plates", Mech. Based Des. Struct., 1-24. https://doi.org/10.1080/15397734.2021.1883442.   DOI
113 Xu, G.D., Zeng, T., Cheng, S., Wang, X.H. and Zhang, K. (2019), "Free vibration of composite sandwich beam with graded corrugated lattice core", Compos. Struct., 229, 111466. https://doi.org/10.1016/j.compstruct.2019.111466.   DOI
114 Cai, X., Shi, K., Zhong, S. and Pang, X. (2021b), "Dissipative sampled-data control for high-speed train systems with quantized measurements", IEEE T Intell. Transp. https://doi.org/10.1109/TITS.2021.3052940.   DOI
115 Ni, T., Liu, D., Xu, Q., Huang, Z., Liang, H. and Yan, A. (2020a), "Architecture of cobweb-based redundant TSV for clustered faults", IEEE T Very Large Scale Integration (VLSI) Syst., 28(7), 1736-1739. https://doi.org/10.1109/TVLSI.2020.2995094.   DOI
116 Khosravi, F. and Hosseini, S.A. (2020), "On the viscoelastic carbon nanotube mass nanosensor using torsional forced vibration and Eringen's nonlocal model", Mech. Based Des. Struct., 1-24. https://doi.org/10.1080/15397734.2020.1744001.   DOI
117 Khosravi, F., Hosseini, S.A. and Tounsi, A. (2020), "Torsional dynamic response of viscoelastic SWCNT subjected to linear and harmonic torques with general boundary conditions via Eringen's nonlocal differential model", Eur. Phys. J. Plus., 135(2), 183. https://doi.org/10.1016/j.measurement.2020.108026.   DOI
118 Allam, O., Draiche, K., Bousahla, A.A., Bourada, F., Tounsi, A., Benrahou, K.H., Mahmoud, S., Adda Bedia, E. and Tounsi, A. (2020), "A generalized 4-unknown refined theory for bending and free vibration analysis of laminated composite and sandwich plates and shells", Comput. Concrete, 26(2), 185-201. http://doi.org/10.12989/cac.2020.26.2.185.   DOI
119 Bourada, F., Bousahla, A.A., Tounsi, A., Bedia, E., Mahmoud, S., Benrahou, K.H. and Tounsi, A. (2020), "Stability and dynamic analyses of SW-CNT reinforced concrete beam resting on elastic-foundation", Comput. Concrete, 25(6), 485-495, https://doi.org/10.12989/cac.2020.25.6.485.   DOI
120 Cai, X., Zhong, S., Wang, J. and Shi, K. (2020), "Robust H∞ control for uncertain delayed TS fuzzy systems with stochastic packet dropouts", Appl. Math. Comput., 385, 125432. https://doi.org/10.1016/j.amc.2020.125432   DOI
121 Zine, A., Bousahla, A.A., Bourada, F., Benrahou, K.H., Tounsi, A., Adda Bedia, E., Mahmoud, S. and Tounsi, A. (2020), "Bending analysis of functionally graded porous plates via a refined shear deformation theory", Comput. Concrete, 26(1), 63-74, http://doi.org/10.12989/cac.2020.26.1.063.   DOI
122 Gong, C., Hu, Y., Gao, J., Wang, Y. and Yan, L. (2019), "An improved delay-suppressed sliding-mode observer for sensorless vector-controlled PMSM", IEEE T Ind. Electron., 67(7), 5913-5923. https://doi.org/10.1109/TIE.2019.2952824.   DOI
123 Gunasekaran, V., Pitchaimani, J. and Chinnapandi, L.B.M. (2020), "Analytical investigation on free vibration frequencies of polymer nano composite plate: Effect of graphene grading and non-uniform edge loading", Mater. Today Commun., 24, 100910. https://doi.org/10.1016/j.mtcomm.2020.100910.   DOI
124 Shariati, M., Azar, S.M., Arjomand, M.-A., Tehrani, H.S., Daei, M. and Safa, M. (2020d), "Evaluating the impacts of using piles and geosynthetics in reducing the settlement of fine-grained soils under static load", Geomech. Eng., 20(2), 87-101. https://doi.org/10.12989/gae.2020.20.2.087.   DOI
125 Shariati, M., Ghorbani, M., Naghipour, M., Alinejad, N. and Toghroli, A. (2020e), "The effect of RBS connection on energy absorption in tall buildings with braced tube frame system", Steel Compos. Struct., 34(3), 393-407. https://doi.org/10.12989/scs.2020.34.3.393.   DOI
126 Li, B., Xiao, G., Lu, R., Deng, R. and Bao, H. (2019), "On feasibility and limitations of detecting false data injection attacks on power grid state estimation using D-FACTS devices", IEEE T. Ind. Inform., 16(2), 854-864. https://doi.org/10.1109/ACCESS.2020.2999585.   DOI
127 Li, B., Wu, Y., Song, J., Lu, R., Li, T. and Zhao, L. (2020), "DeepFed: Federated Deep Learning for Intrusion Detection in Industrial Cyber-Physical Systems", IEEE T. Ind. Inform., 17(8), 5615-5624. https://doi.org/10.1109/TII.2020.3023430.   DOI
128 Alipour, M., Torabi, M.A., Sareban, M., Lashini, H., Sadeghi, E., Fazaeli, A., Habibi, M. and Hashemi, R. (2020), "Finite element and experimental method for analyzing the effects of martensite morphologies on the formability of DP steels", Mech. Based Des. Struct., 48(5), 525-541. https://doi.org/10.1080/15397734.2019.1633343.   DOI
129 Ansari, R. and Torabi, J. (2019), "Semi-analytical postbuckling analysis of polymer nanocomposite cylindrical shells reinforced with functionally graded graphene platelets", Thin Wall. Struct., 144, 106248. https://doi.org/10.1016/j.tws.2019.106248.   DOI
130 Zhang, Z.J., Han, B., Zhang, Q.C. and Jin, F. (2017), "Free vibration analysis of sandwich beams with honeycomb-corrugation hybrid cores", Compos. Struct., 171, 335-344. https://doi.org/10.1016/j.compstruct.2017.03.045.   DOI
131 Liu, C., Deng, F., Heng, Q., Cai, X., Zhu, R. and Liserre, M. (2020a), "Crossing thyristor branches based hybrid modular multilevel converters for DC line faults", IEEE T Ind. Electron., 68(10). https://doi.org/10.1109/TIE.2020.3026277.   DOI
132 Li, B., Liang, R., Zhou, W., Yin, H., Gao, H. and Cai, K. (2021a), "LBS meets blockchain: an efficient method with security preserving trust in SAGIN", IEEE Internet Thing J. https://doi.org/10.1109/JIOT.2021.3064357   DOI
133 Li, X., Dong, Z.Q., Yu, P., Wang, L.P., Niu, X.D., Yamaguchi, H. and Li, D.C. (2021b), "Effect of self-assembly on fluorescence in magnetic multiphase flows and its application on the novel detection for COVID-19", Phys. Fluid., 33(4), 042004. https://doi.org/10.1063/5.0048123.   DOI
134 Liu, D., Li, Z., Kitipornchai, S. and Yang, J. (2019), "Three-dimensional free vibration and bending analyses of functionally graded graphene nanoplatelets-reinforced nanocomposite annular plates", Compos. Struct., 229, 111453. https://doi.org/10.1016/j.compstruct.2019.111453.   DOI
135 Habibi, M., Ghazanfari, A., Assempour, A., Naghdabadi, R. and Hashemi, R. (2017), "Determination of forming limit diagram using two modified finite element models", Mech Eng. 48(4), 141-144. https://doi.org/10.22060/MEJ.2016.664.   DOI
136 Cao, Y., Miraba, S., Rafiei, S., Ghabussi, A., Bokaei, F., Baharom, S., Haramipour, P. and Assilzadeh, H. (2020), "Economic application of structural health monitoring and internet of things in efficiency of building information modeling", Smart Struct. Syst., 26(5), 559-573, https://doi.org/10.12989/sss.2020.26.5.559.   DOI
137 Cai, K., Chen, H., Ai, W., Miao, X., Lin, Q. and Feng, Q. (2021a), "Feedback convolutional network for intelligent data fusion based on near-infrared collaborative IoT technology", IEEE T. Ind. Inform., 18(2). https://doi.org/10.1109/TII.2021.3076513.   DOI
138 Zhang, L., Zheng, H., Wan, T., Shi, D., Lyu, L. and Cai, G. (2021a), "An integrated control algorithm of power distribution for islanded microgrid based on improved virtual synchronous generator", IET Renew. Power Gener., 15(12),2674-2685. https://doi.org/10.1109/TSG.2016.2521405   DOI
139 Zhao, H., Wang, L., Issakhov, A. and Safarpour, H. (2021a), "Poroelasticity framework for stress/strain responses of the multi-phase circular/annular systems resting on various types of elastic foundations", Eur. Phys. J. Plus, 136(8), 1-44. https://doi.org/10.1140/epjp/s13360-021-01761-w.   DOI
140 Habibi, M., Hashemi, R., Sadeghi, E., Fazaeli, A., Ghazanfari, A. and Lashini, H. (2016), "Enhancing the mechanical properties and formability of low carbon steel with dual-phase microstructures", J. Mater. Eng. Perform., 25(2), 382-389. https://doi.org/10.1007/s11665-016-1882-1.   DOI
141 Habibi, M., Hashemi, R., Tafti, M.F. and Assempour, A. (2018b), "Experimental investigation of mechanical properties, formability and forming limit diagrams for tailor-welded blanks produced by friction stir welding", J. Manuf. Proc., 31, 310-- 323. https://doi.org/10.1016/j.jmapro.2017.11.009.   DOI
142 Habibi, M., Hashemabadi, D. and Safarpour, H. (2019a), "Vibration analysis of a high-speed rotating GPLRC nano-structure coupled with a piezoelectric actuator", Eur. Phys. J. Plus, 134(6), 307. https://doi.org/10.1140/epjp/i2019-12742-7.   DOI
143 Habibi, M., Mohammadgholiha, M. and Safarpour, H. (2019b), "Wave propagation characteristics of the electrically GNP-reinforced nanocomposite cylindrical shell", J. Braz. Soc. Mech. Sci. Eng., 41(5), 221. https://doi.org/10.1007/s40430-019-1715-x.   DOI
144 Zhou, C., Zhao, Y., Zhang, J., Fang, Y. and Habibi, M. (2020), "Vibrational characteristics of multi-phase nanocomposite reinforced circular/annular system", Adv. Nano Res., 9(4), 295-307. https://doi.org/10.12989/anr.2020.9.4.295.   DOI
145 Zhang, W., Liu, Z., Liang, Z., Oslub, K. and Safarpour, H. (2021b), "A comprehensive computer simulation of the size-dependent sector or complete microsystem via two-dimensional generalized differential quadrature method", Eng. Comput., 1-17. https://doi.org/10.1007/s00366-021-01440-5.   DOI
146 Zhang, Y., Wang, Z., Tazeddinova, D., Ebrahimi, F., Habibi, M. and Safarpour, H. (2021c), "Enhancing active vibration control performances in a smart rotary sandwich thick nanostructure conveying viscous fluid flow by a PD controller", Wave. Random Complex, 1-24. https://doi.org/10.1080/17455030.2021.1948627.   DOI
147 Zhao, Y., Moradi, Z., Davoudi, M. and Zhuang, J. (2021b), "Bending and stress responses of the hybrid axisymmetric system via state-space method and 3D-elasticity theory", Eng. Comput., 1-23. https://doi.org/10.1007/s00366-020-01242-1.   DOI
148 Dai, Z., Jiang, Z., Zhang, L. and Habibi, M. (2021), "Frequency characteristics and sensitivity analysis of a size-dependent laminated nanoshell", Adv. Nano Res., 10(2), 175-189. https://doi.org/10.12989/anr.2021.10.2.175.   DOI
149 Cai, X., Shi, K., Zhong, S., Wang, J. and Tang, Y. (2021c), "Dissipative analysis for high speed train systems via looped-functional and relaxed condition methods", Appl. Math. Model., 96, 570-583. https://doi.org/10.1016/j.apm.2021.03.042.   DOI
150 Dai, H. and Safarpour, H. (2021), "Frequency and thermal buckling information of laminated composite doubly curved open nanoshell", Adv. Nano Res., 10(1), 1-14, https://doi.org/10.12989/anr.2021.10.1.001.   DOI
151 Oyarhossein, M.A., Alizadeh, A.A., Habibi, M., Makkiabadi, M., Daman, M., Safarpour, H. and Jung, D.W. (2020), "Dynamic response of the nonlocal strain-stress gradient in laminated polymer composites microtubes", Sci. Rep., 10(1), 1-19. https://doi.org/10.1038/s41598-020-61855-w.   DOI
152 Habibi, M., Mohammadi, A., Safarpour, H., Shavalipour, A. and Ghadiri, M. (2019d), "Wave propagation analysis of the laminated cylindrical nanoshell coupled with a piezoelectric actuator", Mech. Based Des. Struct., 1-19, https://doi.org/10.1080/15397734.2019.1697932.   DOI
153 Ghazanfari, A., Soleimani, S.S., Keshavarzzadeh, M., Habibi, M., Assempuor, A. and Hashemi, R. (2020), "Prediction of FLD for sheet metal by considering through-thickness shear stresses", Mech. Based Des. Struct., 48(6), 755-772. https://doi.org/10.1080/15397734.2019.1662310.   DOI
154 Mou, B., Bai, Y. and Patel, V. (2020), "Post-local buckling failure of slender and over-design circular CFT columns with high-strength materials", Eng. Struct., 210, 110197. https://doi.org/10.1016/j.engstruct.2020.110197.   DOI
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156 Ni, T., Yang, Z., Chang, H., Zhang, X., Lu, L., Yan, A., Huang, Z. and Wen, X. (2020b), "A novel TDMA-based fault tolerance technique for the TSVs in 3D-ICs using honeycomb topology", IEEE T Emerg. Topic Comput., 9(2), 724-734. https://doi.org/10.1109/TETC.2020.2969237   DOI