On the Analytical Solutions of the Forced Damping Duffing Equation in the Form of Weierstrass Elliptic Function and its Applications

El-Tantawy S. A.; Salas Alvaro H.; Alharthi M. R.

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On the Analytical Solutions of the Forced Damping Duffing Equation in the Form of Weierstrass Elliptic Function and its Applications

机译：On the Analytical Solutions of the Forced Damping Duffing Equation in the Form of Weierstrass Elliptic Function and its Applications

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In this study, a novel analytical solution to the integrable undamping Duffing equation with constant forced term is obtained. Also, a new approximate analytical (semianalytical) solution for the nonintegrable linear damping Duffing oscillator with constant forced term is reported. The analytical solution is given in terms of the Weierstrass elliptic function with arbitrary initial conditions. With respect to it, the semianalytical solution is constructed depending on a new ansatz and the exact solution of the standard Duffing equation (in the absence of both damping and forced terms). A comparison between the obtained solutions and the Runge-Kutta fourth-order (RK4) is carried out. Moreover, some complicated oscillator equations such as the constant forced damping pendulum equation, forced damping cubic-quintic Duffing equation, and constant forced damping Helmholtz-Duffing equation are reduced to the forced damping Duffing oscillator, in which its solution is known. As a practical application, the proposed techniques are applied to investigate the characteristics behavior of the signal oscillations arising in the RLC circuit with externally applied voltage.

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《Mathematical Problems in Engineering: Theory, Methods and Applications》 |2021年第7期|6678102.1-6678102.9|共9页
作者
El-Tantawy S. A.; Salas Alvaro H.; Alharthi M. R.;
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作者单位

Port Said Univ, Dept Phys, Fac Sci, Port Said 42521, Egypt|Al Baha Univ, Fac Sci & Arts, Dept Phys, Res Ctr Phys RCP, Al Mikhwah, Saudi Arabia;

Univ Nacl Colombia, Dept Math, Dept Math & Stat, FIZMAKO Res Grp, Univ Nacl Colombia Nubia Campus, Bogota, Colombia;

Taif Univ, Dept Math & Stat, Coll Sci, POB 11099, At Taif 21944, Saudi Arabia;

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On the Analytical Solutions of the Forced Damping Duffing Equation in the Form of Weierstrass Elliptic Function and its Applications

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