Modal Analysis & Resonance Testing

Resonance identification, dynamic testing, modal analysis and operating deflection shape analysis, form the basis of our set of expertise in vibration analysis, and are described on this page, in the embedded video below, and in the links above in more detail. This is the heart of vibration testing and key to make confounding vibration issues understandable. Our vibration testing, structural dynamics and modal analysis consulting services have helped push the limits of technologies and cutting edge designs for over 30 years.


Modal and Resonance Testing can provide answers to questions such as:

  • How is the structure deforming physically as it vibrates at a problem resonance?

  • Is the vibration problem caused by excessively large forces, do we have a structural resonance problem, or some of both?

  • How will vibration levels change if we move the force excitation to a new location on the structure, and/or if we change the force axis?

  • Which structural modifications should we expect to reduce vibration levels, and by how much?

These questions are answered using Dynamic Testing, modal testing, and ODS testing, and often, lastly, by Finite Element Analysis (FEA) that has been molded and validated by experimental testing. 

Step back and consider what is Resonance? - Resonance is energy trapped between two different forms of energy storage such as strain in a spring and mass in motion. Resonance is involved in most every thing we hear and feel. Resonant oscillations occur at specific frequencies that are unique to a structure and depend on its mass distribution, the structural stiffness, and damping distribution. A system can be excited to large and problematic amplitudes at resonance (and lead to many unintended and interesting engineering problems).


Mode Shapes - The fascinating thing about resonant oscillations is that each resonance corresponds to a unique deformed shape called a mode shape. Like the ovaling of a bell when struck with a hammer, the cantilevered twang of a diving board, the half-sine shape of the air pressure distribution in a horn, or the twisting of a microscope structure.  The mode shape is the unique deformed shape a structure will take as it oscillates at resonance, and it tells us how the structure will respond with vibration at location A in direction 1 to a force at location B acting in direction 2.


Consider the fact that we can naturally tell the difference between the sound of a block of wood dropping on the floor and that of a steel bar. We characterize the sound by the frequency content of the response to excitation, allowing us to identify thousands of objects in our world. What most people don’t think about as often is what the deformation shape looks like as the system oscillates. We spend much of our time thinking about just that.

Video Sample of Our Work and Modal Analysis Background

The resonant frequency and mode shape are collectively referred to as a mode. A structure will have an infinite number of modes. The modes can be superimposed to approximate the possible deformed motions of the structure. However, usually just a handful of carefully identified mode shape estimates are enough to understand a complex vibration problem. In our work we find the sub-set 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. 


As a vibration consultant we enjoy sharing our knowledge and experience with modal analysis concepts so that we can communicate with our clients and help give the team an appreciation for these important concepts and how they can affect the quality of their designs.


"If you don’t understand the mode shape you can’t fix the resonance problem."


Modal analysis and ODS testing go 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. The mode shapes from modal analysis also give us the physical, geometric, dependence of the structural response to a force at a given location on the structure acting through a specific axis. Sometimes 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 perform 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 (ODS analysis) provides the deformation shape of a structure in response to the forces that are applied to the structure during its operation. Often it is the forced shape during operation that we want to see, as when we characterize an issue with an unstable control system as the ODS shape is often non-linear. Thus, ODS testing alone, however, still allows us to visualize the way the structure deforms due to the forces inherent in operation. This is very valuable and can give us very important clues as to where the structure is weak, where the structure is moving abnormally, and suggesting where we might consider modifications to the structure. We would still like to see the resonant modes that are found using experimental modal analysis but this will often have to wait until there is a scheduled plant shutdown.


Example of project involving Modal, ODS, and strain gage testing - The animation below is a modal analysis representation of the top three floors of 6 story building supporting a multi-ton piece of process equipment located on the 5th floor (represented as the red elements with large exaggerated motions to make the floor system deformations visible, all levels were included in the modal). We performed strain gage testing at critical locations on many of the structural members based on our original ODS Testing. The stain data allowed a structural engineering team to insure that the building was no in danger of structural failure. The floor system vibrated enough, however, that workers were not comfortable in the building and this was a problem for the client. We came up with a suitable design specification for allowable floor vibration levels for worker comfort and safety and went to work engineering solution options for the structural team to meet those specifications.

Modal Analysis of a Building and Process Floor System

We developed an FEA model for this 6 story building which was guided by our on-site experimental modal analysis, many dynamic stiffness tests, and ODS testing. We evaluated structural modifications that included major stiffening members to achieve the desired floor vibration levels. We evaluated custom vibration isolation options for mounting of the vibration source on the 5th floor. The most cost effective solution, however, was the use of tuned reaction masses (TRMs).

Our extensive Client List represents hundreds of projects, some involving days of work, others lasting several months, over the last 30+ years. Descriptions of many of our projects can be found in the left hand links under the various topics that describe our test, analysis, and design work. Our website is put together by our engineers. 

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 Z-Stage Vertical Motion, Chuck and Y-Stage Deflection

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 ans 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.

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. Sometimes 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 perform 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 called 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 Hallway 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 electro-magnetic 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. 

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