Nonlinear transverse free vibrations of piles

The nonlinear partial differential equation governing the nonlinear transverse vibration of pile was derived under the assumption of that both the materials of pile and soil obey nonlinear elastic and linear viscoelastic constitutive relations. The approximate expressions of the nth-order main frequency and the response of the nonlinear vibration of pile with ends hinged have been obtained by the complex mode method and multiple time scales method. Results point out that the main frequency of the nonlinear system is related to not only the natural frequency of linear vibration system, but also the amplitude, damping and nonlinearity of materials. There are high-order harmonic waves with twice the main frequency, and the main frequency of three times as well as the sum and/or difference of 2 or 3 main frequencies besides the harmonic wave with the main frequency in the response of the nonlinear system. Numerical examples were given and the effect of parameters was considered in detail.