Derivation of Transfer Function of a Two-Degree-of-Freedom Damped System with Base Excitation

Derivation of Transfer Function of a Two-Degree-of-Freedom Damped System with Base Excitation

Utah State University, Logan, UT

The derivation of a closed-form expression for the acceleration transfer function of a two-degree-of-freedom (2DOF) spring-damper system with a base excitation vibration input is presented in this paper. An analytical example was solved with a finite element model to verify the closed-form expression. In the current small satellite industry, dynamic coupling between the launch vehicle and the deployer/satellite assembly is that of interest. This coupling can amplify the launch loads into the deployer/satellite assembly. In this paper, analytical method is used to derive the two-degree-of-freedom system response of a mass, spring, and damper system to a base excitation. After achieving the analytical response of each degree of freedom response, one can calculate the transfer function (an input multiplier to get the output) as a function of two-degree-of-freedom system parameters m (mass), k (stiffness) and c (damping).