Modal deposition of shock energy
Proposed for publication in Earthquake Engineering and Structural Dynamics.
A relatively new concept in the field of mechanical shock analysis has been introduced whereby an analysis is made on the work done on structures by the excitation force. The energy imparted to a structure by the excitation can then be divided into various storage and loss mechanisms within the structure. These energies can be used to both evaluate shock response severity and characterize the underlying excitation. Previous work has illustrated the many advantages of the energy methods over traditional shock response spectrum techniques. This work will show that the energy delivered to a MDOF system is uncoupled between modes. Therefore, the total deformational energy delivered to a MDOF system is a weighted sum of the uncoupled modal contributions. This leads to the ability to compute input energy on a modal basis using uncoupled, SDOF calculations. Further, the internal storage and loss energies are also uncoupled. When the input excitation is broadband, the energy input into a MDOF structure by ground motion is dominated by that mode with the largest fraction of participating mass, often the fundamental mode of the system. This leads to the justification for treating complex structures as SDOF oscillators when using energy methods to evaluate both the underlying excitation and the structural response.