Karhunen-Loeve decomposition of the transient dynamics of a multibay truss

We compute the transient dynamics of an impulsively loaded multibay truss. In computing the transient responses, we avoid numerical instabilities due to exponential dichotomy of the bay transfer matrices by employing the direct global matrix approach. This method eliminates the need of transfer matrix multiplications that are prone to numerical instabilities and, instead, requires a numerically stable inversion of a global transfer matrix of large dimension. The transient responses at multiple points of the truss are used to perform system identification of the dynamics using Karhunen-Loeve (K-L) decomposition. This analysis computes dominant coherent structures (proper orthogonal modes) of the truss under specific transient excitations, together with the energy of each identified coherent structure. The identified K-L modes can be used to develop accurate low-order models of the truss dynamics for control or substructure synthesis purposes.