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Mathematica Solution of Rayleigh Equation in Non-Linear Vibration

M. D. Mikhailov
Organization: Universidade Federal do Rio de Janeiro
Department: Mechanical Engineering Dept. - EE/COPPE/UFRJ
Journal / Anthology

Communications in Numerical Methods in Engineering
Year: 2003
Volume: 19
Page range: 401-6

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.

*Mathematics > Calculus and Analysis > Differential Equations

stable periodic motion, non-linear ordinary differential equations, Mathematica