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Mathematica Solution of Rayleigh Equation in Non-Linear Vibration
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| Organization: | Universidade Federal do Rio de Janeiro |
| Department: | Mechanical Engineering Dept. - EE/COPPE/UFRJ |
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| Communications in Numerical Methods in Engineering |
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The stable periodic motion, described by Rayleigh differential equation, is solved by using the Mathematica software system. We define rules computing the periods T, the magnitude A, the displacement u(t), and the velocity v(t) for prescribed perturbation parameter (epsilon) and circular frequency (omega). These rules have been explored to find the period T, the magnitude A, and the reducing factor of the circular frequency (alpha)=2(pi)/T with 10 correct digits after decimal point for (omega) equal to 1 and the values of (epsilon) in the range from 0.1 to 100. The displacement and the velocity are plotted for (epsilon) equal to 0.1, 1, 10, and 100.
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stable periodic motion, non-linear ordinary differential equations, Mathematica
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