Abstract
Based on the nonlinear equation of motion of the beam on the Winkler foundation with the consideration of finite-depth soil mass motion, the nonlinear forced vibrations of the beam were investigated. Applying the Galerkin method and the method of multiple scales, the frequency-response equation and the second-order approximate solution of the primary resonance of the beam were obtained. Then, by means of the numerical calculation and parameter analysis, the effects of parameters about the soil mass motion on the frequency-response curves of the beam on the Winkler foundation were explored, such as foundation depth, soil mass, and Winkler foundation stiffness. The results show that the effect of the soil mass motion on the nonlinear forced vibration of the beam on the Winkler foundation is significant. When the effect of soil mass motion is introduced into the equation of motion of the beam, the range and the softening behavior of primary harmonic resonance of the system are reduced.
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