Modal Analysis
Modal testing, also called Experimental Modal Analysis, is used to determine the mode shapes associated with problem resonances on real world structures.
Why is experimental modal analysis such a useful tool?

First, being able to visualize the deformation that takes place at the problem resonance is one of our most powerful tools. Often the deformation is concentrated in a few critical locations and the modal analysis will make these locations apparent, explain coupling between elements, show where stiffness is needed, where and how damping is best applied, or where compliance may be used to create vibration isolation.

Secondly, the mode shape gives us the physical and geometric dependence of the structural response to a force at a given location on the structure acting through a specific axis.
Modal Analysis of AFM Tool for Semiconductor Inspection, deformation Dominated by Course ZStage Vertical Motion, Chuck and YStage Deflection
In our work we find the subset of modes that are sufficient to characterize and gain a full understanding of a vibration and/or acoustic problem. The most fundamental concept we use in all of our work is the concept of structural modes.
If you don’t understand the mode shape you can’t fix the resonance problem.
Example, Prototype Wing  In creating a prototype wing section it is important to check that the first bending mode is not closely coupled to a twisting mode, possibly resulting in catastrophic flutter. Experimental modal analysis is helpful in showing these modes. When we create a computer model of the wing we also want to verify that we have the wing simulated with sufficient accuracy. We compare the wing simulation to the experimental modal analysis testing and check that all the important resonances are about where they should be in the simulation, that the simulated mode shapes match the experimentally determined shapes, and that stiffness values match. If the simulated dynamic parameters match the experimental modal and dynamic testing results then we have more confidence in using the computer model for further R&D, which may include various load configurations or structural modifications.
Experimental modal analysis of a physical system that has problematic structural dynamics will often be used to "mold" a Finite Element Model (FEA) to represent the important dynamics aspects of the actual physical system. It is very important to note that creating an FEA model to represent a physical system without modal testing is dangerous because the FEA model will always look "good" but will likely radically misrepresent the most important dynamics of the system. This is because actual physical boundary conditions are so hard to determine without modal and dynamics testing. It is also the case that it is hard work for the FEA modeler to put in the detail of the important boundary conditions necessary to getting realistic results.
Performing a modal analysis and dynamics testing first is a wise choice because this testing can tell the experienced FEA modeler how to start the modeling process and where to pay attention to which boundary conditions. This will save considerable effort and valuable time. Again, getting it right the 1st time is very cost effective in fast paced engineering cycles.
Example, Engine/Generator Set  Below are a pair of animations representing a engine/generator/skid system. The upper image is from a finite element analysis of the system. The lower trace is the actual mode shape representation from the original experimental modal analysis. We used modal analysis and dynamics testing to finely tune and then validate our FEA model. The details of how we joined the generator to the skid were very important and took considerable effort. The modal and dynamic testing, however, showed that this was necessary. See Fatigue Cracks on Engine/Gen Set
Comparison of the Mode Shape Derived From the Physical System using Modal Analysis Testing, with the FEA model that was "Tuned" to Match the Modal Test Data
Using our modal and dynamic testing, we created an FEA simulation of the physical system that was accurate in its simulated dynamic response. Note this is NOT the same as matching dimensions in a CAD model. We used this FEA model to find an optimal, cost effective, and practical set of modifications to the frame of the engine/gen set. After installation of these modifications we found that the modified system matched our FEA predictions, shifted the frame resonances away from the operating speed, changed the mode shape to drastically reduce the stress concentration on the frame, and solved the fatigue issue. The system has been running for years now with no problems. We got the fix it right the 1st time.
Background on Modal Analysis and ODS testing  Using modal analysis, the movement of the large masses and the response of the supporting structural elements will suddenly make sense and the effort of fixing the problems of the structure becomes much more intuitive when the deformation is visible.
Additionally, a modal analysis will serve the very valuable role of aligning the engineering team on a solution path by allowing all engineers to see the issue much more easily.
Modal analysis and ODS testing goes hand in hand to create the full picture of the forced response of a system with structural resonances below and near the operating frequency. These resonances amplify motion at some frequencies and attenuate it at others. Some times the force levels are perfectly reasonable but the resonances have changed to become problematic making modal testing very important. Unfortunately, quite often we cannot shut down the vibrating structure to preform high quality modal testing to characterize the structural resonances because shutting the equipment in questing means shutting down the whole factory. This is costly (although sometimes we perform limited modal tests with the structure in operation). Operating deflection shape analysis gives us the deformed shape under the inherent force associated with operation of the system.
Modal analysis testing involves a set of dynamic testing measurements call frequency response functions. Each measurement is of the response at a given point on a structure to a known input force at another point. The ratio of the response to the input force as a function of frequency is called the Transfer Function, or the Frequency Response Function (FRF).
A modal analysis uses the frequency response functions measured at multiple points on the structure to determine the shape of the structure as it deforms at a particular resonance. The triaxial acceleration (or velocity, displacement, strain, etc) is measured at each point on the structure per unit force applied to the structure. The frequency response (magnitude and phase) is measured at each point (in each of 3 axes) of the response per unit applied force. The vibration is measured at sometimes hundreds of locations on the structure. The transfer functions are then analyzed to extract the modal parameters.
The mode shapes of the structure are displayed by connecting the measurement points in the software by lines. The motion of each point is based upon its normalized X,Y, and Z displacements and relative phases from the actual measurements made on the structure.
From the animated mode shapes we can see which elements of the structure move relative to other elements and thereby identify areas of concentrated compliance that reduce the rigidity of the structure. The amplitude of deformation changes with location on the structure. The ability to excite the structural mode shape is directly related by the relative amplitude of the structure at that location in that axis. The operating room floor mode shown below shows that the floor system is much more responsive to a unit force at the center bay location than on the right edge where the hallway is located. The relative amplitudes of the FRFs used in the modal can be used to predict excitation levels at the center of the operating room to forces applied by foot fall in the hallway. The image shows at a glance how the floor will deform the most and where it is and isn't easily excited.
Modal Analysis of a Hospital Floor System Showing How a Section of Hollway is Coupled to the Center of the Operating Room
Note that for linear systems, the mode shape does not depend on the amplitude of excitation. Therefore, we can arbitrarily scale the mode shape to high amplitudes for ease of viewing.
We often use an instrumented impulse hammer to apply a measured impulse to the structure, or an electromagnetic shaker to apply random excitation, while measuring the response at various locations to get an initial survey of the dynamics of the structure.
We often start an investigation into the dynamics of a structure by taping at various locations we can quickly get a larger picture of the structural dynamics, causes of resonant amplification, and the nature of the disturbance transmission path. With this understanding we can often quickly narrow down on the possible nature and scope of the problem and a solution path to the vibration problem can be designed quickly and efficiently. Sometimes a full and detailed modal will be necessary, but sometimes a very simple modal analysis is all that is needed.
Whether making a few dynamics measurements, or a full modal analysis, we use the concepts of modal analysis to understand dynamic problems.
We have performed many hundreds of modal analyses and know the pitfalls and details that must be considered to gather meaningful data. Getting good modal data is not easy. Analyzing the data involves sorting out bad data, knowing when you have good data, and sufficient concentration of measurement points to really know how a structure is deforming. Our analysis of the modal data will often broaden the scope of understanding of the structural dynamics of the engineering team and make future designs much more robust.