Quasiperiodic forced vibrations of a beam interacting with a nonlinear spring

Summary A simply supported beam with fixed ends and an attached strongly nonlinear spring is considered. As the forced bending vibrations of the beam have moderate amplitudes, the stretching force is a nonlinear function of the deflection. The vibrations are presented as a series with respect to the modes of the beam without attachment. Applying the Bubnov-Galerkin procedure, an infinite system of ordinary differential equations is derived. Using the multiple scales method, the quasiperiodic vibrations in the region of the combination resonance are analyzed in the paper. The system vibrations, when the nonlinear spring is attached in different points, are analyzed. Applicability of the nonlinear spring for mitigation of a combination resonance is discussed.