On the Dynamic Simulation of Large Nonlinear Mechanical Systems. Part 2: The Time Integration Technique and Time Response Loop

Part 2 presents a time integration technique for nonlinear differential equations and illustrates its use in the time response loop of the simulation technique outlined in Part 1. The time integration method for nonlinear differential equations is based upon the repetitive analytical (modal) solution of a set of equations linearized about the current operating position. This linearized set of equations may include viscous damping. The method incorporates a variable time step suited to the degree of nonlinearity and as shown in an example problem, gives comparable agreement in results with a Runge-Kutta numerical technique. The time response loop of the simulation technique uniquely combines the concepts of substructuring, system synthesis, and frequency reduction discussed in Part 1 with the time integration method presented here to form the overall simulation technique.