Designing a modal test plan based on finite element method results

Abstract

This chapter introduces some principles and methods for designing modal test plans based on finite element method (FEM) results. The number of points in FEM is closed, generally in the thousands. From the FEM results, many orders of modal frequencies and vibration shapes can be obtained. However, in a modal test, only the foremost orders are concerned; thus, the number of measured points is limited, generally in the tens. There are 2–4 exciting points for a multi input multi output (MIMO) test, whereas 1 exciting point is practical for a single input single output (SIMO) test when the modes are not closed. When the number of foremost orders and measured points are fixed, it is not practical to automatically compute the position of the total measured points from the FEM results for several reasons. First, the computing work is very complex and time-consuming. Second, for the best mathematical results, some key points may be lost and some points that cannot be measured are included. Most importantly, none of these point are able to construct a regular plane, so the result is unacceptable aesthetically. The practical approach is to design an initial plan in which the position is measured manually according to common experience and the space is evenly distributed. By computing the maximum value of the un-diagonal elements of the modal assurance criterion (MAC) matrix and observing the modal shape animation of the simplified results, some measured positions can be modified. If some points need to be deleted in the initial base, this task can be completed automatically by dividing all measured positions into two groups: points that are allowed to be deleted and points that cannot be deleted. After the positions of all measurements are fixed, the number of exciting points and their positions can be obtained automatically according to the exciting energy distribution of different orders in each position.