Method for Improving Incomplete Modal Coupling

Abstract

The writers are concerned with the free vibration of discrete undamped linear dynamic systems commonly designed in structural engineering. The primary purpose is to present a rational method for improving the natural modes and frequencies computed by incomplete modal coupling, without increasing the order of the resultant eigenvalue problem. Improvement is accomplished through use of a candidate table in an iterative process that introduces significant modes into sequential modal analyses. The error trend and sensitivity analysis due to modal truncation is evaluated by computation of a scalar number called significance index which represents an approximation to the error in a certain eigenvalue due to omission of a certain mode shape. This information forms the basis of the candidate table, which serves as a guide for the optimal automated selection of modes for modal substitution. The method of analysis is demonstrated for a discrete model containing 378 degrees‐of‐freedom.