[1] S.S. Rathore, V.R. Kar, Sanjay, Large-amplitude vibration of rotating functionally graded blades including geometrical nonlinearity and stress stiffening effects, Mechanics based design of structures and machines, 52(6) (2024) 3135-3159.
[2] D. Huang, W. Zhang, Y. Zhang, A. Amer, Nonlinear dynamics of graphene-reinforced aluminum matrix composite aero-engine blade in thermal environment, Composite Structures, 331 (2024) 117900.
[3] H. Guo, X. Ouyang, K.K. Żur, X. Wu, T. Yang, A.J. Ferreira, On the large-amplitude vibration of rotating pre-twisted graphene nanocomposite blades in a thermal environment, Composite Structures, 282 (2022) 115129.
[4] W. Zhang, X. Gu, Y. Zhang, New modeling on vibrations and bifurcations of FGGP reinforced pretwisted composite rotating blade under axial aerodynamic force: Theoretical and numerical researches, Thin-Walled Structures, 184 (2023) 110523.
[5] Y. Wang, J. Chen, Nonlinear free vibration of rotating functionally graded graphene platelets reinforced blades with variable cross-sections, Engineering Analysis with Boundary Elements, 144 (2022) 262-278.
[6] M. Amabili, Nonlinear vibrations of rectangular plates with different boundary conditions: theory and experiments, Computers & structures, 82(31-32) (2004) 2587-2605.
[7] M. Amabili, Do we need to satisfy natural boundary conditions in energy approach to nonlinear vibrations of rectangular plates?, Mechanical Systems and Signal Processing, 189 (2023) 110119.
[8] R. Gholami, R. Ansari, M.K. Hassanzadeh-Aghdam, S. Sahmani, Geometrically nonlinear higher-order shear deformable model of TiO2/GNP/polymer nanocomposite rectangular plates: A numerical study on mechanical properties and nonlinear primary resonance features, International Journal of Non-Linear Mechanics, (2025) 105209.
[9] H. Ovesy, P. Khaneh Masjedi, Investigation of the effects of constitutive equations on the free vibration behavior of single-celled thin-walled composite beams, Mechanics of Advanced Materials and Structures, 21(10) (2014) 836-852.
[10] G. Zuo, L. Hou, R. Lin, S. Ren, Y. Chen, Combination resonance and primary resonance characteristics of a dual-rotor system under the condition of the synchronous impact of the inter-shaft bearing, Scientific reports, 13(1) (2023) 1153.
[11] M.S. Taima, M.B. Shehab, T.A. El-Sayed, M.I. Friswell, Comparative study on free vibration analysis of rotating bi-directional functionally graded beams using multiple beam theories with uncertainty considerations, Scientific Reports, 13(1) (2023) 17917.
[12] W. Zhang, Structural design and dynamic characteristics analysis of braided composite two-stage gear transmission system, Scientific Reports, 14(1) (2024) 5584.
[13] M. Naghinejad, H.R. Ovesy, Free vibration characteristics of nanoscaled beams based on nonlocal integral elasticity theory, Journal of Vibration and Control, 24(17) (2018) 3974-3988.
[14] M. Naghinejad, H.R. Ovesy, Viscoelastic free vibration behavior of nano-scaled beams via finite element nonlocal integral elasticity approach, Journal of Vibration and Control, 25(2) (2019) 445-459.
[15] M. Naghinejad, H.R. Ovesy, Free vibration characteristics of nonlocal viscoelastic nano‐scaled plates with rectangular cutout and surface effects, ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, 101(5) (2021) e201900294.
[16] J. Yang, J. Xie, T. Wang, F. Yang, J. Chen, The vibration response mechanism of a blade disk rotor system under the coupling effects of cracks and aerodynamic forces, Scientific reports, 12(1) (2022) 1520.
[17] M. Yao, L. Ma, W. Zhang, Nonlinear Dynamics of the High‐Speed Rotating Plate, International Journal of Aerospace Engineering, 2018(1) (2018) 5610915.
[18] N. Chandiramani, L. Librescu, C. Shete, On the free-vibration of rotating composite beams using a higher-order shear formulation, Aerospace Science and Technology, 6(8) (2002) 545-561.
[19] X. Gu, W. Zhang, Y. Zhang, A novel dynamic model on nonlinear vibrations of functionally graded graphene platelet reinforced rotating pretwisted composite blade considering subsonic airflow excitation and blade-casing rubbing, Composite Structures, 315 (2023) 116936.
[20] J. Chen, P. Cui, Q.-S. Li, Free vibrations of functionally graded graphene-reinforced composite blades with varying cross-sections, International Journal of Structural Stability and Dynamics, 20(14) (2020) 2043006.
[21] Y. Niu, M. Yao, Q. Wu, Resonance in dangerous mode and chaotic dynamics of a rotating pre-twisted graphene reinforced composite blade with variable thickness, Composite Structures, 288 (2022) 115422.
[22] Y.-J. Kee, S.-J. Shin, Structural dynamic modeling for rotating blades using three dimensional finite elements, Journal of Mechanical Science and Technology, 29 (2015) 1607-1618.
[23] K.K. Żur, J. Yuan, H. Guo, Z. Cheng, B. Bartoszewicz, On the vibration of hybrid turbine blades with an interaction between surface discontinuities and twist angle variation, Aerospace Science and Technology, (2025) 110035.
[24] S. Sina, H. Haddadpour, Axial–torsional vibrations of rotating pretwisted thin walled composite beams, International Journal of Mechanical Sciences, 80 (2014) 93-101.
[25] W. Zhang, G. Liu, B. Siriguleng, Saturation phenomena and nonlinear resonances of rotating pretwisted laminated composite blade under subsonic air flow excitation, Journal of Sound and Vibration, 478 (2020) 115353.
[26] M.M.H. Pour, H.R. Ovesy, Nonlinear dynamic buckling analysis of imperfect viscoelastic composite laminated plates, Struct. Eng. Mech, 79(5) (2021) 653-663.
[27] Z.-Z. Pan, X. Chen, L.-W. Zhang, Modeling large amplitude vibration of pretwisted hybrid composite blades containing CNTRC layers and matrix cracked FRC layers, Applied Mathematical Modelling, 83 (2020) 640-659.
[28] J. Poojary, V. Rajamohan, Nonlinear free vibration analysis of internal thickness-tapered multi-layered composite rectangular plates undergoing moderately large deflections, Journal of Sound and Vibration, 572 (2024) 118159.
[29] G. Liu, G. Chen, F. Cui, A. Xi, Nonlinear vibration analysis of composite blade with variable rotating speed using Chebyshev polynomials, European Journal of Mechanics-A/Solids, 82 (2020) 103976.
[30] Z.-M. Li, T. Liu, H. Kang, J. Tian, J. Jing, D. Wang, Theoretical and experimental investigations on steady-state responses of rotor-blade systems with varying rotating speeds based on a new nonlinear dynamic model, Mechanical Systems and Signal Processing, 184 (2023) 109692.
[31] E. Ansari, A. Setoodeh, T. Rabczuk, Isogeometric-stepwise vibrational behavior of rotating functionally graded blades with variable thickness at an arbitrary stagger angle subjected to thermal environment, Composite Structures, 244 (2020) 112281.
[32] X. Gu, Y. Zhang, W. Zhang, Q. Bi, Nonlinear analysis of a rotating pre-twisted composite blade reinforced with functionally graded graphene platelets under axial and transverse excitations, Nonlinear Dynamics, 111(14) (2023) 12947-12972.
[33] Y. Zhang, Y. Niu, W. Zhang, Nonlinear and chaotic vibrations of rotating functionally graded GPL reinforced composite pre-twisted blade subjected to aerodynamic force, Thin-Walled Structures, 181 (2022) 110135.
[34] X. Gu, W. Zhang, Y. Zhang, Nonlinear vibrations of rotating pretwisted composite blade reinforced by functionally graded graphene platelets under combined aerodynamic load and airflow in tip clearance, Nonlinear dynamics, 105(2) (2021) 1503-1532.
[35] P.-F. Dang, Z.-X. Yang, Y.-Y. Yan, Q.-K. Han, Z.-H. Jin, Nonlinear vibration characteristics of rotating composite blade considering the temperature-dependent graded material properties, Composite Structures, 258 (2021) 113419.
[36] M.-Y. Fan, J. Chen, Nonlinear dynamics of rotating functionally graded graphene platelets/titanium alloy trapezoid plates under 1: 3 internal resonance, Nonlinear Dynamics, 112(23) (2024) 20793-20812.
[37] H. Arvin, F. Bakhtiari-Nejad, Nonlinear free vibration analysis of rotating composite Timoshenko beams, Composite Structures, 96 (2013) 29-43.
[38] M.Y. Fan, J. Chen, Large amplitude vibration of rotating graphene reinforced titanium alloy dovetailed blades with general boundary conditions, Thin-Walled Structures, 208 (2025) 112801.
[39] M. Salehian, H.R. Ovesy, H. Dabiryan, Free vibration optimization of 2D tri-axial braided composite fan blade with ANN-Anal-FEM-GA integrated model, Scientific Reports, 14(1) (2024) 28819.
[40] Y. Niu, H. Ji, C. Tao, C. Zhang, Y. Wu, J. Qiu, Design of trailing edge flap based on MFC and prediction of deformation and aerodynamic performance using BP neural network, Journal of Intelligent Material Systems and Structures, (2025) 1045389X241305660.
[41] A.S. Azizi, M. Razbin, S.M. Mousavi, M. Li, A.A.R. Darzi, Enhancing thermal efficiency in twisted tri-lobe double pipe heat exchangers via integrated CFD and AI approaches, International Journal of Thermal Sciences, 206 (2024) 109331.
[42] A.A.R. Darzi, S.M. Mousavi, M. Razbin, M. Li, Utilizing neural networks and genetic algorithms in AI-assisted CFD for optimizing PCM-based thermal energy storage units with extended surfaces, Thermal Science and Engineering Progress, 54 (2024) 102795.
[43] S.M. Mousavi, A.S. Azizi, M. Razbin, A.A.R. Darzi, M. Li, Optimized design of helical-finned double pipe heat exchangers via numerical simulation and artificial intelligence, Applied Thermal Engineering, 258 (2025) 124605.
[44] M. Razbin, A.A. Gharehaghaji, M. Salehian, Y. Zhu, M.H. Kish, N.H. Kouchehbaghi, Artificial neural network-assisted theoretical model to predict the viscoelastic–plastic tensile behavior of polyamide-6 multi-ply yarns, Neural Computing and Applications, 36(29) (2024) 18107-18123.
[45] M. Razbin, M. Salehian, A.A. Gharehaghaji, A viscoelastic-plastic model for the core of various close-packings of multifilament polyamide-6 yarns, Scientific Reports, 14(1) (2024) 23800.
[46] F. Shahmoradi Ghaheh, M. Razbin, M. Tehrani, L. Zolfipour Aghdam Vayghan, M. Sadrjahani, Modeling and optimization of dyeing process of polyamide 6 and woolen fabrics with plum-tree leaves using artificial intelligence, Scientific Reports, 14(1) (2024) 15067.
[47] C. Zhang, W.K. Binienda, L.W. Kohlman, Analytical model and numerical analysis of the elastic behavior of triaxial braided composites, Journal of Aerospace Engineering, 27(3) (2014) 473-483.
[48] J.N. Reddy, Mechanics of laminated composite plates and shells: theory and analysis, CRC press, 2003.
[49] M.C. Da Silva, Non-linear flexural-flexural-torsional-extensional dynamics of beams—II. Response analysis, International Journal of Solids and Structures, 24(12) (1988) 1235-1242.
[50] M. Amabili, M.P. Paı¨ doussis, Review of studies on geometrically nonlinear vibrations and dynamics of circular cylindrical shells and panels, with and without fluid-structure interaction, Appl. Mech. Rev., 56(4) (2003) 349-381.
[51] A. Saood, A.H. Khan, M.I. Equbal, K.K. Saxena, C. Prakash, N.I. Vatin, S. Dixit, Influence of fiber angle on steady-state response of laminated composite rectangular plates, Materials, 15(16) (2022) 5559.
[52] X. Liu, Backbone Curve Analysis of Nonlinear Mechanical Systems, University of Sheffield, 2018.
[53] T. Detroux, L. Renson, L. Masset, G. Kerschen, The harmonic balance method for bifurcation analysis of large-scale nonlinear mechanical systems, Computer Methods in Applied Mechanics and Engineering, 296 (2015) 18-38.
[54] K. Worden, Nonlinearity in structural dynamics: detection, identification and modelling, CRC Press, 2019.
[55] P. Ribeiro, M. Petyt, Non-linear free vibration of isotropic plates with internal resonance, International journal of non-linear mechanics, 35(2) (2000) 263-278.
[56] R.E. Mickens, Truly nonlinear oscillations: harmonic balance, parameter expansions, iteration, and averaging methods, World Scientific, 2010.
[57] C. VanDamme, M. Allen, A. Madrid, Using the harmonic balance method to directly compute NNMs of geometrically nonlinear finite element models, in: Proceedings of the International Conference on Noise and Vibration Engineering (ISMA), Leuven, Belgium, 2018.
[58] M. Petyt, P. Ribeiro, Geometrical non-linear periodic vibration of plates, in: ASME International Mechanical Engineering Congress and Exposition, American Society of Mechanical Engineers, 2000, pp. 61-72.
[59] P. Ribeiro, M. Petyt, Nonlinear vibration of plates by the hierarchical finite element and continuation methods, International Journal of Mechanical Sciences, 41(4-5) (1999) 437-459.
[60] R. Lewandowski, On beams membranes and plates vibration backbone curves in cases of internal resonance, Meccanica, 31(3) (1996) 323-346.