## ABSTRACT

Experimental modal analysis is basically a procedure of ‘‘experimental modeling.’’ The primary purpose here is to develop a dynamic model for a mechanical system using experimental data. In this sense, experimental modal analysis (EMA) is similar to ‘‘model identification’’ in control system practice and may utilize somewhat related techniques of ‘‘parameter estimation.’’ It is the nature of the developed model that may distinguish EMA from other conventional procedures of model identification. Specifically, EMA produces a modal model that consists of

1. Natural frequencies

2. Modal damping ratios

3. Mode shape vectors

as the primary result. Once a modal model is known, standard results of modal analysis may be used to extract an inertia (mass) matrix, a damping matrix, and a stiffness matrix, which constitute a complete dynamic model for the experimental system in the time domain. The modal analysis of lumped-parameter systems is covered in Chapter 5 and the analysis of distributed-parameter systems in Chapter 6. Vibration testing and signal analysis are studied in Chapter 4 and Chapter 8 through Chapter 10. These chapters should be reviewed for the necessary background prior to reading this chapter. As EMA produces a modal model (and in some cases a complete time-domain dynamic

model) for a mechanical system from the test data of the system, it can be used extensively. In particular, EMA is useful in

1. Design

2. Diagnosis

3. Control

of mechanical systems, primarily with regard to vibration. In the area of design, the following three approaches that utilize EMA should be mentioned:

1. Component modification

2. Modal response specification

3. Substructuring

add, inertia ness, and damping parameters in a mechanical system and determine the resulting effect on the modal response (natural frequencies, damping ratios, and mode shapes) of the system. In modal response specification, we establish the best changes, from the design point of view, in system parameters (inertia, stiffness, and damping values and their degrees of freedom) in order to give a ‘‘specified’’ (prescribed) change in the modal response. In substructuring, two or more subsystem models are combined using dynamic interfacing components and the overall model is determined. Some of the subsystem models used in this manner could be of analytical origin (e.g., finite-element models). Diagnosis of problems (faults, performance degradation, component deterioration,

impending failure, etc.) of a mechanical system requires condition monitoring of the system, and analysis and evaluation of the monitored information. Often, analysis involves extraction of modal parameters using monitored data. Diagnosis may involve the establishment of changes (both gradual and sudden), patterns, and trends in these system parameters. Control of a mechanical system may be based on modal analysis. Standard and well-

developed techniques of modal control are widely used in mechanical system practice. In particular, vibration control, both active and passive, may use modal control (see Chapter 12). In this approach, the system is first expressed as a modal model. Then control excitations, parameter adaptations, and so on are established, which would result in a specified (derived) behavior in various modes of the system. Of course, techniques of EMA are commonly used here both in obtaining a modal model from test data, and in establishing modal excitations and parameter changes that are needed to realize a prescribed behavior in the system. The standard steps of EMA are:

1. Obtain a suitable (admissible) set of test data consisting of forcing excitations and motion responses for various pairs of degrees of freedom of the test object.