Pakdemirli M.Özkaya E.2024-07-222024-07-2220030022460Xhttp://akademikarsiv.cbu.edu.tr:4000/handle/123456789/20087A general continuous system with an arbitrary cubic non-linearity is considered. The non-linearity is expressed in terms of an arbitrary cubic operator. Three-to-one internal resonance case is considered. A general approximate solution is presented for the system. Amplitude and phase modulation equations are derived. Steady state solutions and their stability are discussed in the general sense. The sufficiency condition for such resonances to occur is derived. Finally the algorithm is applied to a beam resting on a non-linear elastic foundation.EnglishAlgorithmsApproximation theoryAsymptotic stabilityBeams and girdersBoundary conditionsEquations of motionMathematical modelsNonlinear systemsAmplitude modulation equationNonlinear continuous systemPhase modulation equationThree-to-one internal resonanceResonanceArticle10.1016/S0022-460X(03)00364-X