Interpolation-based condensation of algebraic semi-discrete models with frequency response application

Abstract

Condensation model reduction theory, a method of degree-of-freedom-elimination for semi-discrete system models with response-prediction fidelity in the retained degrees-of-freedom (DOF), is applied to algebraic semi-discrete models. The condensation process makes use of an interpolation over a user-chosen subset, denoted as a “window,” of the set of continuous-independent-variable values. The window's “size” and “location,” as well as the accuracy of the method within the window, are hence controllable by the user. (There is a computational-cost versus accuracy/windowsize tradeoff for a given DOF reduction, as would be expected.) One target of this capability is the DOF reduction of spatially-discrete, continuous-time-transformed (Fourier, Laplace, etc.) linear system models, for which the resulting semi-discrete model has frequency as the continuous independent variable. The window would then correspond to a selected frequency range, (a region of the complex frequency plane in the most general case). Another target of this capability is the DOF reduction of nonlinear, path-independent static or quasistatic models, for which the window corresponds to a region of the reduced-DOF-model solution space itself. As a demonstration, the method is applied to the frequency response of a non-periodic linear elastic laminate over a rectangular window in the complex frequency plane. It is seen that the frequency-response predicted by the reduced-DOF model at each of various values within the window, as well as the eigenvalues predicted by the reduced-DOF model within the window, agree well with the corresponding predictions of the original, full-DOF model.