Application of the proper orthogonal decomposition for linear and nonlinear structures under transient excitations

Model reduction has become very important in order to save calculation time. In particular, in structural dynamics, computations become very time-consuming when the critical time step of explicit integrators becomes very small. The main focus of this paper is on the application of the Proper Orthogonal Decomposition (POD) method to a structure subjected to transient earthquake loading. It is shown that based on the information of only a small portion of the transient excitation and the structure ("snapshots"), it is possible to assemble a reduced-order model, which yields a very accurate and time-saving approximation of the response to the entire earthquake. The POD reduction method is applied not only to linear, but also to nonlinear structures under earthquake loading. In the linear case, the POD results can be compared to those obtained by the classical method of modal truncation. In the nonlinear case, base isolation systems (friction pendulum systems) are integrated in the structure. Error estimations are applied in order to assess the solution of the POD-reduced system of the linear and the nonlinear systems. The POD can be applied successfully if the snapshots within the chosen time interval describe the main behavior of the system well. In both the linear and nonlinear cases, the approximation of the system as reduced by the POD is very accurate even if only a few POD modes are used. The advantage over the method of Modal Truncation is not only the optimality of the POD modes concerning their associated energy, but also its applicability to nonlinear systems.