Mathematical modelling for a micro-tunnelling machine

We study a model of stochastic hyperbolic equation with free boundary. This model is motivated by a micro tunnelling machine which is used for the conduit installation for communication cables. By using this tunnelling machine, a flexible pilot pipe is thrust into ground and hence the total length of the inserted pipe becomes a function of time. Furthermore, the thrust force generated by a hydraulic pump is stochastically perturbed. The transverse displacement of the inserted pipe is firstly shown to be governed by a hyperbolic equation with free boundary by using the Hamilton principle. Secondly, the existence of a solution of this equation is studied and two digital simulation examples are demonstrated for checking the buckling phenomena to the inserted pipe.