Nonlinear forced vibrations of thin structures with tuned eigenfrequencies: the cases of 1:2:4 and 1:2:2 internal resonances

作者：Monteil Melodie; Touze Cyril^*; Thomas Olivier; Benacchio Simon

来源：Nonlinear Dynamics, 2014, 75(1-2): 175-200.

DOI：10.1007/s11071-013-1057-7

• Internal resonance
• Nonlinear oscillations
• Multiple scales

This paper is devoted to the analysis of nonlinear forced vibrations of two particular three degrees-of-freedom (dofs) systems exhibiting second-order internal resonances resulting from a harmonic tuning of their natural frequencies.
The first model considers three modes with eigenfrequencies omega (1), omega (2), and omega (3) such that omega (3)a parts per thousand integral 2 omega (2)a parts per thousand integral 4 omega (1), thus displaying a 1:2:4 internal resonance. The second system exhibits a 1:2:2 internal resonance, so that the frequency relationship reads omega (3)a parts per thousand integral omega (2)a parts per thousand integral 2 omega (1). Multiple scales method is used to solve analytically the forced oscillations for the two models excited on each degree of freedom at primary resonance. A thorough analytical study is proposed, with a particular emphasis on the stability of the solutions. Parametric investigations allow to get a complete picture of the dynamics of the two systems. Results are systematically compared to the classical 1:2 resonance, in order to understand how the presence of a third oscillator modifies the nonlinear dynamics and favors the presence of unstable periodic orbits.

• 出版日期2014-1