Detection the nonlinear ultrasonic signals based on modified Duffing equations
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DOI: 10.1016/j.rinp.2017.08.054
Abstract: Abstract 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… read more here.
Keywords: shg signals; nonlinear ultrasonic; duffing equations; duffing equation ... See more keywords
An Elementary Solution to a Duffing Equation
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DOI: 10.1155/2022/2357258
Abstract: In this work, we study the Duffing equation. Analytical solution for undamped and unforced case is provided for any given arbitrary initial conditions. An approximate analytical solution is given for the damped or trigonometrically forced… read more here.
Keywords: solution duffing; duffing equation; equation; elementary solution ... See more keywords
On Hyers–Ulam Mittag-Leffler stability of discrete fractional Duffing equation with application on inverted pendulum
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DOI: 10.1186/s13662-020-02920-6
Abstract: A human being standing upright with his feet as the pivot is the most popular example of the stabilized inverted pendulum. Achieving stability of the inverted pendulum has become common challenge for engineers. In this… read more here.
Keywords: discrete fractional; inverted pendulum; duffing equation; hyers ulam ... See more keywords