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An Elementary Solution to a Duffing Equation [PDF]
The Scientific World Journal, 2022 In this work, we study the Duffing equation. Analytical solution for undamped and unforced case is provided for any given arbitrary initial conditions.
Alvaro H. Salas
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Analytical Solution to the Generalized Complex Duffing Equation [PDF]
The Scientific World Journal, 2022 Future scientific and technological evolution in many areas of applied mathematics and modern physics will necessarily depend on dealing with complex systems.
Alvaro H. Salas S +2 more
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Solution to a Damped Duffing Equation Using He’s Frequency Approach [PDF]
The Scientific World Journal, 2022 In this paper, we generalize He’s frequency approach for solving the damped Duffing equation by introducing a time varying amplitude. We also solve this equation by means of the homotopy method and the Lindstedt–Poincaré method.
Alvaro H. S. Salas +2 more
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Advances in Mathematical Physics, 2021 Based on the study of the feature extraction algorithm based on the multiple empirical mode decomposition of the Duffing equation, this paper proposes a corresponding improved algorithm, completes the identification and analysis of the psychological ...
Min Chai, Lei Ba
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Applied Mathematics in Science and Engineering, 2023 The type of symmetry exhibited by a travelling wave can have important implications for its behaviour and properties, such as its polarization, dispersion, and interactions with other waves or boundaries.
Mahdi Rakah +4 more
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Results in Physics, 2021 Because the Duffing equation is very sensitive to weak signals and noise immunity, the modified Duffing detection system is applied to detect the weak nonlinear signal in nonlinear ultrasonic experiment.
Yuhua Zhang, Silong Quan, Guoquan Liu
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Analytical Solution for the Cubic-Quintic Duffing Oscillator Equation with Physics Applications
Complexity, 2022 The nonlinear differential equation governing the periodic motion of the one-dimensional, undamped, and unforced cubic-quintic Duffing oscillator is solved exactly by obtaining the period and the solution.
Alvaro H. Salas +2 more
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The bistable Duffing oscillator in discrete time
Физика волновых процессов и радиотехнические системы, 2020 The dynamics of an oscillatory system with a soft cubic-nonlinear return force a bistable Duffing oscillator, in discrete time are consider. The mathematical analysis is based on a continuous-time model in the form of the Duffing equation.
V.V. Zaitsev
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Journal of Low Frequency Noise, Vibration and Active Control, 2022 The Duffing oscillator equation is one of important equations that model several nonlinear phenomena in science and engineering. The differential transform method (DTM) is applied to obtain the solutions of homogeneous and non-homogeneous Duffing ...
Noufe H Aljahdaly, Maram A Alharbi
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Detection the nonlinear ultrasonic signals based on modified Duffing equations
Results in Physics, 2017 The nonlinear ultrasonic signals, like second harmonic generation (SHG) signals, could reflect the nonlinearity of material induced by fatigue damage in nonlinear ultrasonic technique which are weak nonlinear signals and usually submerged by strong ...
Yuhua Zhang +3 more
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