Journal

Article title

Content

Title variants

Languages of publication

Abstracts

Discipline

Publisher

Journal

Year

Volume

Pages

1-24

Physical description

Contributors

author

- Applied Mechanics & Design (AMD) Research Group, Department of Mechanical Engineering, Faculty of Engineering, University of Port Harcourt, Port Harcourt, Nigeria

author

author

References

- [1] Big-Alabo, A (2018): Periodic solutions of Duffing-type oscillators using continuous piecewise linearization method, Mechanical Engineering Research, 8(1), 41-52.
- [2] Belendez, A, Hernandez, A, Marquez, A, Belendez, T and Neipp, C (2006): Analytical approximations for the period of a nonlinear pendulum, Eur. Journal of Physics, 27, 539-551.
- [3] Lai, S K, Lim, C W, Lin, Z Zhang, W (2011): Analytical analysis for large-amplitude oscillation of a rotational pendulum system, Applied Mathematics and Computation, 217, 6115-6124.
- [4] Belendez, A, Alvarez, M L, Fernandez, E, Pascual, I (2009): Cubication of conservative nonlinear oscillators, Eur. Journal of Physics, 30(5), 973-981.
- [5] Big-Alabo, A (2019): A simple cubication method for approximate solution of nonlinear Hamiltonian oscillators, International Journal of Mechanical Engineering Education, DOI:10.1177/0306419018822489
- [6] Big-Alabo, A and Ogbodo, C O (2019): Dynamic analysis of crank mechanism with complex trigonometric nonlinearity: a comparative study of approximate analytical methods, Springer Nature Applied Sciences, 1(6), 7 pages.
- [7] Cveticanin, L (2001): Vibrations of a coupled two-degree-of-freedom system, Journal of Sound and Vibration, 242(2), 279-292.
- [8] Lai S K and Lim C W (2007): Nonlinear vibration of a two-mass system with nonlinear stiffnesses, Nonlinear Dynamics, 49, 233-249.
- [9] Big-Alabo, A and Ossia C V (2019): Analysis of the coupled nonlinear vibration of a two-mass system, Journal of Applied and Computational Mechanics, 5(5), 935-950. DOI:10.22055/JACM.2019.28296.1474
- [10] Israr A, Cartmell M P, Manoach E, Trendafilova I, Ostachowicz W M, Krawczuk M, Zak A (2009): Analytical modelling and vibration analysis of partially cracked rectangular plates with different boundary conditions and loading, Journal of Applied Mechanics, 76, 1-9.
- [11] Ismail R and Cartmell M P (2012): An investigation into the vibration analysis of a plate with a surface crack of variable angular orientation, Journal of Sound and Vibration, 331, 2929-2948.
- [12] Hamden M N, Shabaneh N H (1997): On the large amplitude free vibrations of a restrained uniform beam carrying an intermediate lumped mass, Journal of Sound and Vibration, 199(5), 711-736.
- [13] Big-Alabo, A (2018): Continuous piecewise linearization method for approximate periodic solution of the relativistic oscillator, International Journal of Mechanical Engineering Education, DOI:10.1177/0306419018812861
- [14] Beléndez, A, Pascual, C, Méndez, D I, Neipp, C (2008): Solution of the relativistic (an)harmonic oscillator using the harmonic balance method, Journal of Sound and Vibration, 311, 1447-1456.
- [15] Ismail G M, Abul-Ez M, Farea N M, Saad N (2019): Analytical approximations to nonlinear oscillation of nanoelectro-mechanical resonators, Eur. Physical Journal Plus, 134, 47.
- [16] Ghalambaz M, Ghalambaz M, Edalatifar M (2016): Nonlinear oscillation of nanoelectro-mechanical resonators using energy balance method: considering the size effect and the van der Waals force, Appied Nanoscience, 6, 309-317.
- [17] Wu Y and He J H (2018): Homotopy perturbation method for nonlinear oscillators with coordinate-dependent mass, Results in Physics, 10, 270-271.
- [18] Wang Y and An J Y (2019): Amplitude–frequency relationship to a fractional Duffing oscillator arising in microphysics and tsunami motion, Journal of Low Frequency Noise, Vibration and Active Control, Vol. 38(3–4) 1008–1012. DOI:10.1177/1461348418795813
- [19] Cheung Y K, Chen S H, Lau S L (1991): A modified Lindstedt-Poincare method for certain strongly non-linear oscillators, International Journal of Non-Linear Mechanics, 26 (3/4), 367-378.
- [20] He J H (1999): Variational iteration method: a kind of nonlinear analytical technique: some examples, International Journal of Nonlinear Mechanics, 34(4), 699-708.
- [21] He J H (2003): Linearized perturbation technique and its applications to strongly nonlinear oscillators, Computers & Mathematics with Applications, 45(1-3), 1-8.
- [22] Hosen M A, Chowdhury M S H, Ali M Y and Ismail A F (2018): A New Analytical Technique for Solving Nonlinear Non-smooth Oscillators Based on the Rational Harmonic Balance Method in: R Saian and M A Abbas (eds.), Proceedings of the Second International Conference on the Future of ASEAN (ICoFA) 2017 – Volume 2.
- [23] Qian Y H, Pan J L, Chen S P, Yao M H (2017): The Spreading Residue Harmonic Balance Method for Strongly Nonlinear Vibrations of a Restrained Cantilever Beam, Advances in Mathematical Physics, Volume 2017, Article ID 5214616, 8 pages.
- [24] Laio, S K (1994): On the homotopy analysis method for nonlinear problems, Applied Mathematics and Computation, 147(2), 499-513.
- [25] Adomian, G A (1988): Review of the decomposition method in applied mathematics, Journal of Mathematical Analysis and Applications, 135, 501-544.
- [26] He, J H (1999): Homotopy perturbation technique, Computer Methods in Applied Mechanics and Engineering, 178(3/4), 257-262.
- [27] He, J H (2002): Preliminary report on the energy balance for nonlinear oscillations, Mechanics Research Communications, 29, 107-111.
- [28] He J H (2010): Hamiltonian approach to nonlinear oscillators, Physics Letters A, 2312-2314.
- [29] Elıas-Zuniga A and Martınez-Romero O (2013): Accurate solutions of conservative nonlinear oscillators by the enhanced cubication method, Mathematical Problems in Engineering, Article ID 842423, 9 pages.
- [30] He J H (2007): Variational approach for nonlinear oscillators, Chaos, Solitons and Fractals, 34, 1430.
- [31] Big-Alabo A and Ossia C V (2020): Periodic solution of nonlinear conservative systems, IntechOpen, DOI:10.5772/intechopen.90282
- [32] Ansari K A and Khan N U (1986): Nonlinear vibrations of a slider-crank mechanism, Applied Mathematical Modelling, 10, 114-118.
- [33] Chen J S and Haung C L (2000): Dynamic analysis of flexible slider-crank mechanisms with non-linear finite element method, Journal of Sound and Vibration, 246(3), 389-402.
- [34] Chen J S and Chain C H (2001): Effects of Crank Length on the Dynamics Behavior of a Flexible Connecting Rod, Journal of Vibration and Acoustics, 123, 318-323.
- [35] Ha J L, Fung R F, Chen K Y, Hsien S C (2006): Dynamic modeling and identification of a slider-crank mechanism, Journal of Sound and Vibration, 289, 1019-1044.
- [36] Akbari S, Fallahi F, Pirbodaghi T (2016): Dynamic analysis and controller design for a slider-crank mechanism with piezoelectric actuators, Journal of Computational Design and Engineering, 3, 312-321.
- [37] Erkaya S, Su S, Uzmay I (2007): Dynamic analysis of a slider-crank mechanism with eccentric connector and planetary gears, Mechanism and Machine Theory, 42, 393-408.
- [38] Chen J S and Chain C H (2003): On the Nonlinear Response of a Flexible Connecting Rod, Journal of Mechanical Design, 125, 757-763.
- [39] Daniel G B and Cavalca K L (2011): Analysis of the dynamics of a slider-crank mechanism with hydrodynamic lubrication in the connecting rod–slider joint clearance, Mechanism and Machine Theory, 46, 1434-1452.
- [40] Reis V L, Daniel G B, Cavalca K L (2014): Dynamic analysis of a lubricated planar slider-crank mechanism considering friction and Hertz contact effects, Mechanism and Machine Theory, 74, 257-273.
- [41] Fidlin, A (2005): Nonlinear oscillations in Mechanical Engineering, Springer, New York.
- [42] Nayfeh, A H and Mook, D T (1995): Nonlinear oscillations. New York: John Wiley & Sons.
- [43] Big-Alabo, A, Cartmell, M P, Harrison P (2017): On the solution of asymptotic impact problems with significant localised indentation, Proceedings of IMechE Part C: Journal of Mechanical Engineering Sciences, 231(5), 807-822.

Document Type

article

Publication order reference

Identifiers

YADDA identifier

bwmeta1.element.psjd-56ef4e2f-bcad-4895-b736-47231cfd44ec