Retaining the influence of crucial local effects in mixed Guyan and modal reduction

Abstract

For the modal frequency and transient response analysis of moderate to large-sized structures, as well as residual structures that consist of synthesized, component mode-reduced sub-models with common boundaries, the structural model is most effectively reduced by the mixed Guyan and modal reduction. A strategy for the correct reduction of such systems which necessarily retains the crucial degrees of freedom in the reduced system is presented. A detailed set of practical guidelines for the appropriate selection of such degrees of freedom is given. To obtain the transformation to modal subspace, this reduction is followed by an eigensolution and the transformation is performed without shedding any degrees of freedom of the reduced model. This procedure automatically includes the high-frequency “quasi-static” mode shapes that are necessary to retain the influence of crucial local effects in the reduced system. Example problems that include important elements such as a stiff spring, a nonlinear stopper mechanism, and a concentrated excitation force, are presented to demonstrate the strength of the method in the solution of practical industrial applications. These example problems may also serve as reference problems for future developments in modal dynamic analysis techniques.