Dynamic Analysis of Nonclassically Damped Systems with Linear Behavior Using Load-Dependent Ritz Vectors

In the present paper, a practical superposition method is proposed for complex load-dependent Ritz (CLDR) vectors for use in the dynamic analysis of nonclassically damped systems. In particular, an algorithm for CLDR vector generation is developed and the CLDR vectors are calculated in the physical space, instead of the state space, to reduce the computational effort and storage space, while improving the stability of the algorithm. Moreover, single CLDR vector (i.e. using only one starting vector) and block CLDR vector (i.e. using multi-starting vectors) generation procedures are introduced for the uni and multidirectional loading patterns respectively, and the latter is applied to the system with repeated natural frequencies. In addition, a criterion, which is based on the spatial load distribution, is proposed to determine a proper number of the CLDR vectors prior to their use in the dynamic analysis. Two numerical examples are provided to illustrate the accuracy and efficiency of the proposed method. Also, the performance of the cut-off criterion is presented and 10% error or less in the participation loading distribution is recommended for practical applications.