Improved Modal Truncation Methods for the Dynamic Analysis of Non-Classically Damped Systems

Mode superposition method is one of the important approaches for dynamic analysis of structures. Damped or complex modes are normally needed to decouple the equations of motion of non-classically damped systems. To reduce the computation scale, several low modes are commonly considered in the analysis. Similar to the undamped or real mode superposition method, the issue of correction for the modal truncation also exists in the complex mode superposition method. In the study, the conventional correction methods for the non-classically damped systems using the undamped modes are discussed first. A new complex modal acceleration method is then derived, in which the contribution of the truncated high modes is approximated by the static response with respect to the external load. To take into account the effect of the loading frequency contents on the correction, a generalized complex modal acceleration method is further developed by using the technique of shifting frequency. It should be noted that the aforementioned methods are static or quasi-static correction. In order to include dynamic characteristics of the high modes under the external load, “pseudomodes” are constructed to replace the unknown higher modes, and it is called the complex modal truncation augmentation method herein. Finally, a numerical example is used to illustrate the effectiveness of the proposed generalized complex modal acceleration method and the complex modal truncation augmentation method.