Time domain approach toward the calculation of the compliance function of flexible motion systems

For high-performance distributed parameter motion systems, the dynamics introduced by structural flexibilities need to be considered. Especially at the low frequency region, where most of the energy of the commonly used reference setpoint is concentrated. The contribution of non-rigid body modes at low frequencies is called the compliance function of the system. It is representative for the quasi-static behaviour of the whole non-rigid body modes. This work proposes a new method for the calculation of the compliance function. It is based on employing the differential equation representation
for the flexible structure. The approach is validated for a standard damped second order ODE and a one dimensional flexible model, i.e., the Euler-Bernoulli beam. We show that we get a major reduction in calculation in comparison with the zero frequency response calculation. The extension of this approach to the general PDE’s will be the scope of the future works.