[1] |
H.Aftab, U.Baneen, and A.Israr, Identification and severity estimation of a breathing crack in a plate via nonlinear dynamics, Nonlin. Dyn.104 (2021), no. 3, 1973-1989, DOI 10.1007/s11071‐021‐06275‐9. |
[2] |
R.Ikram and A.Israr, Study of plate vibrating in fluids having part‐through crack at random angles and locations, Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci.235 (2021), no. 22, 6036-6051, DOI 10.1177/09544062211012717. |
[3] |
M.Şimşek, Nonlinear static and free vibration analysis of microbeams based on the nonlinear elastic foundation using modified couple stress theory and He’s variational method, Compos. Struct.112 (2014), 264-272. |
[4] |
G.Sobamowo, Nonlinear vibration analysis of single‐walled carbon nanotube conveying fluid in slip boundary conditions using Variational iterative method, J. Appl. Comput. Mech.2 (2016), no. 4, 208-221, DOI 10.22055/jacm.2016.12527. |
[5] |
P.Valipour, S. E.Ghasemi, M. R.Khosravani, and D. D.Ganji, Theoretical analysis on nonlinear vibration of fluid flow in single‐walled carbon nanotube, J. Theor. Appl. Phys.10 (2016), no. 3, 211-218, DOI 10.1007/s40094‐016‐0217‐9. |
[6] |
A.Big‐Alabo, E. O.Ekpruke, C. V.Ossia, D. O.Jonah, and C. O.Ogbodo, Generalized oscillator model for nonlinear vibration analysis using quasi‐static cubication method, Int. J. Mech. Eng. Educ.49 (2021b), 359-381, DOI 10.1177/0306419019896586. |
[7] |
A.Big‐Alabo and C. V.Ossia, Analysis of the coupled nonlinear vibration of a two‐mass system, J. Appl. Comput. Mech.5 (2019), no. 5, 935-950. |
[8] |
S.Hashemi Kachapi, R. V.Dukkipati, S. G.Hashemi, S. M.Hashemi, S. M.Hashemi, and S. K.Hashemi, Analysis of the nonlinear vibration of a two‐mass-spring system with linear and nonlinear stiffness, Nonlinear Anal.: Real World Appl.11 (2010), no. 3, 1431-1441, DOI 10.1016/j.nonrwa.2009.03.010. · Zbl 1254.70021 |
[9] |
S.Abrate, Modeling of impacts on composite structures, Comput. Struct.51 (2001), 129-138. |
[10] |
G. B.Chai and S.Zhu, A review of low‐velocity impact on sandwich structures, Proc. Inst. Mech. Eng. Part L: J. Mater.: Des. Appl..225 (2011), no. 4, 207-230, DOI 10.1177/1464420711409985. |
[11] |
R. C.Batra, M.Porfiri, and D.Spinello, Vibrations of narrow microbeams predeformed by an electric field, J. Sound Vib.309 (2008), no. 3-5, 600-612, DOI 10.1016/j.jsv.2007.07.030. |
[12] |
E.Esmailzadeh, D.Younesian, and H.Askari, Analytical Methods in Nonlinear Oscillations: Approaches and Applications, Springer, Netherlands, 2019. · Zbl 1439.34002 |
[13] |
A.Elías‐Zúñiga, O.Martínez‐Romero, D.Olvera‐Trejo, and L. M.Palacios‐Pineda, Determination of the frequency‐amplitude response curves of undamped forced Duffing’s oscillators using an ancient Chinese algorithm, Res. Phys.24 (2021), 104085, DOI 10.1016/j.rinp.2021.104085. |
[14] |
L.Cveticanin, M.Zukovic, G.Mester, I.Biro, and J.Sarosi, Oscillators with symmetric and asymmetric quadratic nonlinearity, Acta Mechanica227 (2016), no. 6, 1727-1742, DOI 10.1007/s00707‐016‐1582‐9. · Zbl 1341.34044 |
[15] |
A. H.Salas, J. E.Castillo, and D. J.Mosquera, A new approach for solving the undamped Helmholtz oscillator for the given arbitrary initial conditions and its physical applications, Math. Probl. Eng.2020 (2020), 7876413, DOI 10.1155/2020/7876413. · Zbl 1459.65133 |
[16] |
A.Big‐Alabo and M. P.Cartmell, Vibration analysis of a trimorph plate for optimised damage mitigation, J. Theor. Appl. Mech.49 (2011), no. 3, 641-664. |
[17] |
A.Big‐Alabo and M. P.Cartmell, Vibration analysis of a trimorph plate as a precursor model for smart automotive bodywork, J. Phys.: Conf. Ser.382 (2012), 012010, DOI 10.1088/1742‐6596/382/1/012010. |
[18] |
A. H.Salas and S. A.El‐Tantawy, Analytical Solutions of Some Strong Nonlinear Oscillators. Engineering Problems—Uncertainties, Constraints and Optimization Techniques, IntechOpen, 2022. |
[19] |
H.Hu, Solution of a quadratic nonlinear oscillator by the method of harmonic balance, J. Sound Vib.293 (2006a), no. 1-2, 462-468, DOI 10.1016/j.jsv.2005.10.002. · Zbl 1243.34048 |
[20] |
J. M. T.Thompson, Chaotic phenomena triggering the escape from a potential well, Proc. Royal Soc. A: Math. Phys. Eng. Sci.421 (1989), no. 1861, 195-225, DOI 10.1098/rspa.1989.0009. · Zbl 0674.70035 |
[21] |
C. W.Lim, S. K.Lai, B. S.Wu, W. P.Sun, Y.Yang, and C.Wang, Application of a modified Lindstedt-Poincaré method in coupled TDOF systems with quadratic nonlinearity and a constant external excitation, Arch. Appl. Mech.79 (2009), no. 5, 411-431, DOI 10.1007/s00419‐008‐0234‐5. · Zbl 1168.70302 |
[22] |
W.Jiang, G.Zhang, and L.Chen, Forced response of quadratic nonlinear oscillator: comparison of various approaches, Appl. Math. Mech.36 (2015), no. 11, 1403-1416, DOI 10.1007/s10483‐015‐1991‐7. · Zbl 1331.34054 |
[23] |
I. S.Kang and L. G.Leal, Bubble dynamics in time‐periodic straining flows, J. Fluid Mech.218 (1990), no. −1, 41, DOI 10.1017/s0022112090000921. · Zbl 0706.76126 |
[24] |
A. H.Salas, J. E.Castillo, and L. J.Martınez, Perihelion precessions of inner planets in Einstein’s theory and predicted values for the cosmological constant, Scientific World Journal2022 (2022), 4808065, DOI 10.1155/2022/4808065. |
[25] |
H.Hu, Solutions of a quadratic nonlinear oscillator: iteration procedure, J. Sound Vib.298 (2006b), no. 4-5, 1159-1165, DOI 10.1016/j.jsv.2006.06.005. · Zbl 1243.70030 |
[26] |
H.Hu, Exact solution of a quadratic nonlinear oscillator, J. Sound Vib.295 (2006c), no. 1-2, 450-457, DOI 10.1016/j.jsv.2006.01.013. · Zbl 1243.34001 |
[27] |
L.Cveticanin, Vibrations of the system with quadratic non‐linearity and a constant excitation force, J. Sound Vib.261 (2003), no. 1, 169-176, DOI 10.1016/s0022‐460x(02)01178‐1. · Zbl 1237.70104 |
[28] |
L.Cveticanin, Vibrations of the nonlinear oscillator with quadratic nonlinearity, Phys. A: Stat. Mech. Appl.341 (2004), 123-135, DOI 10.1016/j.physa.2004.04.123. |
[29] |
S. K.Lai and K. W.Chow, Exact solutions for oscillators with quadratic damping and mixed‐parity nonlinearity, Phys. Scripta85 (2012), no. 4, 045006, DOI 10.1088/0031‐8949/85/04/045006. · Zbl 1310.34046 |
[30] |
J.Zhu, A new exact solution of a damped quadratic non‐linear oscillator, App. Math. Model.38 (2014), no. 24, 5986-5993, DOI 10.1016/j.apm.2014.04.065. · Zbl 1449.34003 |
[31] |
A.Beléndez, A.Hernández, T.Beléndez, E.Arribas, and M. L.Álvarez, Closed‐form solutions for the quadratic mixed‐parity nonlinear oscillator, Ind. J. Phys.95 (2020), 1213-1224, DOI 10.1007/s12648‐020‐01796‐2. |
[32] |
A.Beléndez, F. J.Martínez, T.Beléndez, C.Pascual, M. L.Alvarez, E.Gimeno, and E.Arribas, Exact solutions for an oscillator with anti‐symmetric quadratic nonlin earity, Ind. J. Phys.92 (2017), no. 4, 495-506, DOI 10.1007/s12648‐017‐1125‐9. |
[33] |
I. S.Gradshteyn and I. M.Ryzhik, Table of Integrals, Series and Products, 7th ed., Academic Press, Amsterdam, 2007. · Zbl 1208.65001 |
[34] |
A.Mirzabeigy and R.Madoliat, A note on free vibration of a double‐beam system with nonlinear elastic inner layer, J. Appl. Comput. Mech.5 (2019), no. 1, 174-180, DOI 10.22055/jacm.2018.25143.1232. |
[35] |
A.Big‐Alabo and C. V.Ossia, Free vibration of a two‐mass system with coupled cubic‐quintic nonlinear stiffness, Uniport J. Eng. Sci. Res.5 (2020), 28-40. |
[36] |
L.Cveticanin, The motion of a two‐mass system with non‐linear connection, J. Sound Vib.252 (2002), no. 2, 361-369, DOI 10.1006/jsvi.2000.3551. |
[37] |
L.Cveticanin, A solution procedure based on the Ateb function for a two‐degree‐of‐freedom oscillator, J. Sound Vib.346 (2015), 298-313, DOI 10.1016/j.jsv.2015.02.016. |
[38] |
L.Cveticanin, M.KalamiYazdi, H.Askari, and Z.Saadatnia, Vibration of a two‐mass system with non‐integer order nonlinear connection, Mech. Res. Commun.43 (2012), 22-28, DOI 10.1016/j.mechrescom.2012.04.002. |
[39] |
S. S.Ganji, A.Barari, and D. D.Ganji, Approximate analysis of two‐mass-spring systems and buckling of a column, Comput. Math. Appl.61 (2011), no. 4, 1088-1095, DOI 10.1016/j.camwa.2010.12.059. · Zbl 1217.74050 |
[40] |
A.Big‐Alabo, E. O.Ekpruke, and C. V.Ossia, Equivalent oscillator model for the nonlinear vibration of a porter governor, J. King Saud Univ. ‐ Eng. Sci.35 (2021a), 304-309, DOI 10.1016/j.jksues.2021.01.009. |
[41] |
W.Alhejaili, A. H.Salas, and S. A.El‐Tantawy, The Krylov-Bogoliubov-Mitropolsky method for modeling a forced damped quadratic pendulum oscillator, AIP Adv.13 (2023), no. 8, 085029, DOI 10.1063/5.0159852. |