Interpretation & Importance of Mass Participation in Modal Analysis

We often come across the dynamics or vibration problems in most of the product development across all industries.  We have gained enough knowledge through the degree of Bachelors or Masters, with an example of the famous engineer disastrous design of “Tacoma Narrows Bridge-1940”, that considering the dynamics effects in design is quite critical.  Generally, a dynamics problem is categorized into linear or nonlinear dynamics. This blog is related to the linear dynamics and nonlinear dynamics will be discussed in length in another blog. The most commonly heard terminology which we stumble upon in the design of such vibrating products is “natural frequencies“, “resonance“, “eigenmodes” etc. We have many linear dynamics simulation techniques such as “Harmonic Analysis“, “Random Vibration“, “Response Spectrum“, “Transient Analysis“, “Acoustic Analysis“, etc based on the loading it undergoes and also on the output we are interested in. But all these dynamics simulations start with the first step called “Modal Analysis“.

Modal Analysis

What makes something unique is an identity of its own, right? What if I say natural frequency is the identity of a body? Let’s see why. Assume you are imparting energy (striking) to a body. What will happen is obvious, the body will start to vibrate. But the vibrational frequency will be in its natural frequencies. It doesn’t matter how much or where you give the energy it will always vibrate in its natural frequencies, period.  This is why the base of any dynamic analysis is said to be modal analysis as it shows its identity or behavior.

The modal analysis calculates natural frequencies and mode shapes of the designed model. It’s the only analysis that doesn’t require any input excitation or loads, which also makes sense, as mentioned before natural frequencies are independent of the excitation loads. Natural frequency depends only on two things mass and stiffness.

Why do we need to do the modal analysis?

Yes, we can find natural frequencies, and mode shapes through modal analysis but why to do it? Let me explain that through an example, when you ride a motorcycle, sometimes you might have experienced vibration in your handle. Some bikes have too much vibration that, you can’t even use your rear mirror. This is because the handle’s natural frequency is matching with engines RPM.

Structure borne noise: A structure makes peak noise when it’s vibrating in its natural frequency.

Whirling of shafts: To find the critical RPM of a shaft so that, crossing the critical speed will be done with precautions to avoid resonance.

Avoiding resonance is always preferred, thus shifting or modifying natural frequency can help to control, above mentioned issue. Natural frequency depends on only two parameters, modifying them will help to design a dynamic body part.

As an engineer, I always go in search of the physical meaning rather than proving by an equation. But at times equations are unavoidable.

Now let us see how we can get the natural frequency of a system.

Excitation force Equation of any dynamic system can be represented as

Every natural frequency is associated with each mode shape and mode shape represents the displacement behavior. There is enough material on the internet which explains mode shape. Right now, let’s concentrate on the “Mass Participation Factor” other important information from modal analysis, which would assist us in the simulation of other linear dynamic simulations.  What is mass participation in general? Consider a 3 massed system as shown below.

The figure shown above is a mode of the system. Here masses participating in the X direction are M1 and M2  and thus total mass participation is M1 +M2.  The only difference in FEA is that instead of lumped masses, the system will be discretized by elements.

Now let’s see ANSYS modal Analysis. Here I’m taking a cantilever beam, with 0.8478 kg. Having a cross-section of 3*60*600.

As you can see from the participation factor calculation. I have solved the first 12 natural frequencies. In this table, ANSYS solver calculates only frequency and Participation factor ie 1st and 4th column. Every other column is calculated from these two values. Let’s look at the most important column one by one.

As you can see this ratio is in direct comparison with total mass, which gives a better clarity on how much of the total mass participation is extracted. In other words, the sum of the effective masses in each direction should equal the total mass of the structure. But clearly, this depends on the number of extracted modes.

The same logic is for rotational mass participation. But here you might get ratios bigger than 1. Then, there can be confusion as mass participating is more than the total mass of the system? The answer is, participation factors for rotational DOFs are calculated about the global origin (0,0,0). The calculated effective mass essentially contains a moment arm (effective mass multiplied by the distance from centroid). Thus, the effective mass for the rotational DOFs can be greater than the actual mass and the participation factors can be greater than 1.0.

Ideally, the ratio of effective mass to total mass can be useful for determining whether or not a sufficient number of modes have been extracted for the “Mode Superposition” for further analysis. Modal superposition is a solution technique for all linear dynamic analyses. Any dynamic response can be calculated as the sum of the mode shapes, that are weighted with some scaling factor (modal coefficient). Also, the time step of the transient simulation is calculated based on the most influential mode in the modal analysis.

Modal analysis is usually done without considering any force or working environment. This assumption is taken by considering mass and stiffness to be constant. But at times this doesn’t work, like a pressurized vessel or pipe. As compressive or tensile force changes the stiffness. In such cases, we have to do a prestressed Modal Analysis.

In some cases, like rotating shafts with motors, turbines, the natural frequency will not match with the working condition. This is because, for different RPM, stiffness also changes,(Centrifugal force changes). In these cases, we need to consider the rotational speed of the shaft. In ANSYS Modal Analysis (Rotodynamic Analysis) rotational speed with Coriolis effect can be directly given to find the critical speed of the shaft.

Modal analysis is a prerequisite for all linear dynamics analyses like Harmonic, Random vibration, and Response spectrum analysis. Hence Modal Analysis plays a huge role wherever you are trying to find out vibration characteristics of a design. Thereby it is relevant for most industries like Rotating machines, construction, automobile, Machine tool, agricultural equipment, and Mining.

Engineering Simulation opens up a huge range of possibilities. Since CAEsimulation requires more than just software, we at CADFEM help our customers to adopt simulation for success in every phase of product development, thereby enabling them to realize their product promise.

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Author Bio:

Mr. Vineesh Vijayan, Application Engineer


Mr. Vineesh Vijayan has done his Master of Technology in Machine Design. With good expertise in Structural Simulation currently, he is contributing his efforts to CADFEM India as an Application Engineer.

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ANSYS 18.0 – The latest release is here!

Banner for ANSYS 18.0 software release

The day has arrived!! Most of our customers would’ve received announcement of the latest release – ANSYS 18. It’s time to rejoice and celebrate this new release.

ANSYS 18.0 ushers in the era of pervasive engineering simulation – an era where all types of engineers use simulation throughout the entire product lifecycle. While simulation was once the primary domain of experts and used mainly for verification, it is now moving upfront in the development process to quickly evaluate changes in design. At the same time, it’s also moving downstream of the product lifecycle process to analyze real-time operational data from connected machines in the industrial internet.

By incorporating simulation into all segments of a product’s lifecycle, ANSYS 18.0 adds tremendous value by spurring innovation, reducing development and operational costs, and improving time to market. Whether your field is structures, fluids, electromagnetics, semiconductors, systems, embedded software or some multiphysics combination of these areas, ANSYS 18.0 is the simulation platform to achieve your engineering and business goals.

Digital Launch Event

To learn more about pervasive engineering simulation and ANSYS 18.0, we invite you to the digital launch event on January 31. During this event, the ANSYS CEO, Ajei Gopal, and numerous technology leaders from industry will talk about this exciting new release from ANSYS. Here’s the line-up of the speakers from ANSYS:

  • Ajei Gopal, President and CEO, ANSYS, Inc.
  • Andre Bakker, Senior Director Fluids Development, ANSYS, Inc.
  • Dale Ostergaard, Senior Director Software Development, ANSYS, Inc.
  • Larry Williams, Senior Director Electronics Products, ANSYS, Inc.
  • Sergey Polstyanko, Senior Director, Research and Development, ANSYS, Inc.
  • Eric Bantegnie, Vice President and GM Systems Business Unit, ANSYS, Inc.

In addition, you can also learn more about ANSYS 18.0 by visiting the “What’s New” section of the Customer Portal.

Current Customers – Next Steps

Current customers can download ANSYS 18.0 from the Download Center on the ANSYS customer portal.

You need a license manager upgrade to run ANSYS 18.0 products. Your current license keys will continue to function with the new 18.0 license manager. Support for operating systems, graphics cards, third-party CAD products and more is available on the Platform Support page.

If you need any support, please feel free to contact us.

Together with ANSYS, we are excited to bring you this latest release. This comes as the result of countless hours of work by 1,000+ professionals in the research and development organization. We believe it will exceed your expectations and provide considerable value in your engineering processes and product lifecycle.

May the force always be with you! 🙂

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