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Non-perturbative stability analysis of periodic responses in driven non-linear oscillators

✍ Scribed by K.-E. Thylwe; E. Gravador

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
495 KB
Volume
182
Category
Article
ISSN
0022-460X

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✦ Synopsis

A linear stability theory for non-linear periodic solutions is presented in which higher order phase-integral asymptotic approximations are used. The stability matrix is derived in an exact formalism which combines Floquet and phase-integral theory. The periodic responses are assumed given in analytic forms which are accurate in the strongly non-linear regime of system parameters.

πŸ“œ SIMILAR VOLUMES

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The method of equivalent linearization has been extended to obtain periodic responses of harmonically excited, piecewise non-linear oscillators. A dual representation of the solution is used to enhance greatly the algebraic simplicity. The stability analysis of the solutions so obtained is carried o

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The elliptic perturbation method is applied to the study of the periodic solutions of strongly quadratic non-linear oscillators of the form x¨+ c1 x + c2 x 2 = ef(x, x˙), in which the Jacobian elliptic functions are employed. The generalized Van der Pol equation with f(x, x˙) = m0 + m1 x -m2 x 2 is