Nonlinear free vibration of a beam on Winkler foundation with a consideration of soil mass effect

Based on the Winkler model, Euler beam theory, and the motion equation of elastic foundation, the nonlinear dynamics model of a finite-length beam on Winkler foundation with a consideration of the effect of soil mass is obtained. Applying the eigenvalue analysis and the method of multiple scales, the linear and nonlinear natural frequencies and mode shapes of the beam are obtained. By means of the numerical calculation, the effect of soil mass on the linear and nonlinear free vibrations of the finite-length beam on Winkler foundation are explored. The numerical results show that:the natural frequencies of beam decrease, when the effect of soil mass on the dynamic response of the beam is included in the nonlinear dynamic model of the finite-length beam on Winkler foundation. Moreover, it is significant for the effect of soil mass on the high-order nonlinear mode shapes of the beam.