where i is used to make a difference between control rod and control rod guide tube; [rho] is the density; V is the volume; [m.sub.a] is the added mass; t is the time; u(t) is the transverse deflection of the structure at time t; c is the damping coefficient; [c.sub.a] is the added damping coefficient; k is the stiffness coefficient; p(t) is the external excitation at time t; F(t) is the impact force at time i.
where [F.sub.c] is the collision force; [k.sub.h] is the Hertz model stiffness parameters; [delta] is the normal relative plunge depth along the contact surface between the control rod guide tube and the control rod; n is Hertz model coefficient, with n usually taken as 3/2; [lambda] is the damping coefficient; e is the recovery coefficient; [[delta].sub.0] is the normal relative velocity along the contact surface when the collision occurs; [m.sub.1] is the quality of the guide tube part of the collision that occurred; [m.sub.2] is the quality of the control rod part of the collision that occurred.
It also ignores the collision between control rod assembly and control rod guide tubes. Dou et al.
where [mu] is the fluid viscosity coefficient; B is the control rod diameter; h is the size of the gap between the control rod guide tubes and the control rod; L is the control rod length; [lambda] is the dimensionless correction factor; [C.sub.d] is the equivalent linear damping coefficient; [rho] is the density of the liquid; [for all] is the control rod volume; [K.sub.a] is the added mass coefficient.
We use the model Hertzdamp  to describe the collision between control rod assembly and the control rod guide tubes.