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THE ELLIPTIC MULTIPLE SCALES METHOD FOR A CLASS OF AUTONOMOUS STRONGLY NON-LINEAR OSCILLATORS

✍ Scribed by M. BELHAQ; F. LAKRAD


Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
101 KB
Volume
234
Category
Article
ISSN
0022-460X

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πŸ“œ SIMILAR VOLUMES


PERIODIC SOLUTIONS OF STRONGLY NON-LINEA
✍ F. LAKRAD; M. BELHAQ πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 339 KB

The multiple scales method, developed for the systems with small non-linearities, is extended to the case of strongly non-linear self-excited systems. Two types of nonlinearities are considered: quadratic and cubic. The solutions are expressed in terms of Jacobian elliptic functions. Higher order ap

PERIODIC SOLUTIONS OF STRONGLY QUADRATIC
✍ S.H. Chen; X.M. Yang; Y.K. Cheung πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 228 KB

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

PERIODIC SOLUTIONS OF STRONGLY QUADRATIC
✍ S.H. CHEN; X.M. YANG; Y.K. CHEUNG πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 144 KB

The elliptic Lindstedt}PoincareH method is used/employed to study the periodic solutions of quadratic strongly non-linear oscillators of the form xK #c x# c x" f (x,. xR ), in which the Jacobian elliptic functions are employed instead of the usual circular functions in the classical Lindstedt}Poinc

COMMENTS ON β€œA PERTURBATION-ITERATIVE ME
✍ Dai Decheng πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 125 KB

The new idea of calculation of limit cycles of strongly non-linear systems and its several numerical examples were presented in [1]. It is interesting to study the calculation of limit cycles of non-linear systems further, however some defects have been found in [1].

A perturbation-incremental method for th
✍ Chen, S. H. ;Chan, J. K. H. ;Leung, A. Y. T. πŸ“‚ Article πŸ“… 2000 πŸ› John Wiley and Sons 🌐 English βš– 130 KB πŸ‘ 2 views

The semi-stable limit cycle and bifurcation of strongly non-linear oscillators of the form xK #g(x)" f (x, xR , )xR is studied by the perturbation-incremental method. Firstly, the ordinary di!erential equation is transformed into an integral equation by a non-linear time transformation, then the ini

The Power Spectral Density Of Response F
✍ R. Bouc πŸ“‚ Article πŸ“… 1994 πŸ› Elsevier Science 🌐 English βš– 419 KB

An oscillator with a non-linear restoring force and a small linear damping under wide-band random excitation is considered. A modified Van Der Pol transformation with a suitable amplitude dependent frequency, is used to transform the original system into a first order vector system to which the stoc