Analytical solution in frequency domain of dynamic response of thin-wall pipe piles with variable wave impedance under low strain transient concentrated load

Dynamic response of pipe piles under low strain transient concentrated load is a three dimensional wave problem. Based on the three dimensional wave theory, the computational model and wave equation of dynamic response of thin-wall pipe piles with variable wave impedance are established. Combined the initial and boundary conditions, the analytical solution of wave equation in frequency domain is obtained by Laplace transformation method. The time domain response is obtained by Fourier inverse transformation. By comparing the results of analytical solution with that of 3D finite element method, the following conclusions are achieved: the wave crest of the results of analytical solution can well meet that of the 3D-FEM results; and the displacement responses of them have little difference. The dynamic responses at different points on top of the pile and the high-frequency interference problem are also researched. The characteristics of dynamic responses of variable modulus piles and variable section piles are studied.