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This paper details the mathematical modelling of vibratory pile driving systems using a linear model with the objective of obtaining a closed form solution to estimate either the power requirement of the machine, the torque requirement of the motor driving the eccentrics, or both. It begins by reviewing the system model for the system without a suspension, which is used to enable connection of the vibrating machine with a crane, a mast of a dedicated machine, or an excavator. It proceeds to solve the equations of motion for a system with a suspension, using Laplace transforms and solving the inverse transform using residues and complex integration. The model indicates that, under certain conditions, both the amplitude and the power consumption of the system increase with a suspension, but the results make the practical implications of the result uncertain. Finally a simple set of equations is developed for actual vibratory design which results in the suspension being ignored and the necessary torque of the driving motor computed. |
