| Título: | Analytical approximate solutions for the cubic-quintic Duffing oscillator in terms of elementary functions |
| Autores: |
Beléndez Vázquez, Augusto Álvarez López, Mariela Lázara Francés Monllor, Jorge Bleda Pérez, Sergio Beléndez Vázquez, Tarsicio Nájera López, Alberto Arribas Garde, Enrique |
| Fecha: |
2012-10-15 2012-10-15 2012-06-28 2012-09-30 |
| Publicador: | RUA Docencia |
| Fuente: |
 |
| Tipo: | info:eu-repo/semantics/article |
| Tema: |
Nonlinear oscillators Approximate analytical solution Rational harmonic balance method Chebyshev polynomials Cubic-quintic Duffing oscillator Física Aplicada Matemática Aplicada |
| Descripción: |
Accurate approximate closed-form solutions for the cubic-quintic Duffing oscillator are obtained in terms of elementary functions. To do this, we use the previous results obtained using a cubication method in which the restoring force is expanded in Chebyshev polynomials and the original nonlinear differential equation is approximated by a cubic Duffing equation. Explicit approximate solutions are then expressed as a function of the complete elliptic integral of the first kind and the Jacobi elliptic function cn. Then we obtain other approximate expressions for these solutions, which are expressed in terms of elementary functions. To do this, the relationship between the complete elliptic integral of the first kind and the arithmetic-geometric mean is used and the rational harmonic balance method is applied to obtain the periodic solution of the original nonlinear oscillator. This work was supported by the “Generalitat Valenciana” of Spain, under Project PROMETEO/2011/021, and by the “Vicerrectorado de Tecnología e Innovación Educativa” of the University of Alicante, Spain, under Project GITE-09006-UA. |
| Idioma: | Inglés |
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