Signs of the "one-mode" response forces in linear spectral method: comparison of conventional and standard approaches

Abstract

Two variants of linear-spectral method (LSM) are compared in the paper: the conventional one, prescribed in several foreign standards, and "Standard" one prescribed in the Russian Standard SP 14.13330. "One-component one-mode" responses, obtained by static analysis in the conventional LSM are combined twice: first for different modes but for each single excitation component, then for different excitation components. In the "standard" alternative LSM variant first one chooses the "most dangerous" direction of the one-component excitation for each mode, then one obtains the "one-mode" response for this excitation, and finally these responses are combined. In both cases the combination is performed using the complete quadratic combination (CQC) rule, accounting for the correlation between one-mode responses. "Standard" variant leaves some uncertainty: the "dangerous" direction can be changed for the opposite one. Such a change leads to the sign change in the one-mode response. This is of no importance for the non-correlated responses, which are combined using the SRSS rule. However, for the correlated responses as it is shown in the paper using sample problem the uncertainty in the signs can lead to the incorrect results, and the error can be significant.