18.1 Introduction

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Experimental modal analysis (EMA) 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, 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, which may

distinguish EMA from other conventional procedures of model identification. Specifically, EMA

produces a modal model as the primary result, which consists of:

1. Natural frequencies

2. Modal damping ratios

3. Mode shape vectors

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. Since EMA produces a modal model (and in some cases a

complete time-domain dynamic model) for a mechanical system from test data of the system, its uses can be

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© 2005 by Taylor & Francis Group, LLC

extensive. In particular, EMA is useful in mechanical systems, primarily with regard to vibration, in:

1. Design

2. Diagnosis

3. Control

In the area of design, the following three approaches that utilize EMA should be mentioned:

1. Component modification

2. Modal response specification

3. Substructuring

In component modification, we modify (i.e., add, remove, or vary) inertia (mass), stiffness, 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 (DoF), 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 can 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, can use modal control. In this approach, the system is first expressed as a

modal model, then control excitations, parameter adaptations, and so on are established that 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 as follows:

1. Obtain a suitable (admissible) set of test data, consisting of forcing excitations and motion

responses for various pairs of DoF of the test object.

2. Compute the frequency transfer functions (the frequency response functions) of the pairs of test

data, using Fourier analysis. Digital Fourier analysis using Fast Fourier Transform (FFT) is the

standard way of accomplishing this. Either software-based (computer) equipment or hardwarebased

instrumentation may be used.

3. Curve fit analytical transfer functions to the computed transfer functions. Determine natural

frequencies, damping ratios, and residues for various modes in each transfer function.

4. Compute mode shape vectors.

5. Compute inertia (mass) matrix M, stiffness matrix K, and damping matrix C.

Some variations of these steps is possible in practice, and Step 5 is omitted in some situations. In

the present chapter, we will study some standard techniques and procedures associated with the

process of EMA.

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