An analytical solution for excited pile vibrations with variable section impedance in the time domain and its engineering application

Abstract Through pile defect generalization, a definite solution to the problem of longitudinal vibrations in a finite pile lying on an elastic stratum with variable section impedance is established using the δ function. By separating variables and applying the boundary and continuity conditions of the pile–soil system, the characteristic equation for the problem is derived, and the corresponding eigenvalues are determined through numerical calculations. Then, the analytical solution for a pile subjected to steady sinusoidal excitation in the time domain is derived. The amplitude–frequency curves are analysed, and conclusions are drawn. An analytical solution for a pile subjected to transient excitation in the time domain is obtained using the principle of superposition. Then, a parametric study is conducted to investigate the characteristics of signals reflected from a defect, yielding several conclusions that are important for guiding practical defect detection. Finally, two engineering projects are described, and the theoretical and measured curves are compared.

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