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
THE ELLIPTIC MULTIPLE SCALES METHOD FOR A CLASS OF AUTONOMOUS STRONGLY NON-LINEAR OSCILLATORS
β 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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π SIMILAR VOLUMES
The elliptic perturbation method is applied to the study of the periodic solutions of strongly quadratic non-linear oscillators of the form xΒ¨+ c1 x + c2 x 2 = ef(x, xΛ), in which the Jacobian elliptic functions are employed. The generalized Van der Pol equation with f(x, xΛ) = m0 + m1 x -m2 x 2 is
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
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].
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
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