Nonlinear free vibration of a beam on Winkler foundation with consideration of soil mass motion of finite depth

Abstract

Nonlinear free vibration characteristics of a beam on elastic foundation are investigated. Considering the effect of soil–structure interaction on the nonlinear dynamic response of the beam and using the expression of subgrade reaction obtained from the equation of motion of Winkler foundation, the nonlinear equation of motion of the beam on Winkler foundation with the soil mass motion of finite depth is derived. Then, using the eigenvalue analysis method and the method of multiple scales, the linear and nonlinear natural frequencies and mode shapes of the beam are obtained. Finally, by means of numerical calculation and parameter analysis, the effects of Winkler foundation mass, stiffness and damping on the dynamic characteristics of the beam are explored.