Modal Analyses: Efficient Design Modifications using HyperWorks

Leonardo Rosa_20310
Leonardo Rosa_20310 New Altair Community Member
edited December 2021 in Altair HyperWorks

INTRODUCTION

There are two techniques for solving the equations of motion of a frequency or transient response analysis:

  • Direct Integration
  • Modal Superposition

Direct Integration has less limitations, but it consumes a lot of computational resources, because it must solve all Degrees of Freedom (DOF) of the Finite Element Model (FEM), for each frequency or time step.

Conversely, the Modal Superposition technique allows you to find an approximation of the motion, by using less DOFs. Therefore, it consumes less computational resources, making this technique popular.

In a FEM, each node has several DOFs. The Direct Integration technique will solve the equation of motion of each one of those DOFs. Using Modal Superposition, each natural mode represents one DOF. This leads to the question: how many natural modes are required, to obtain a good approximation of the motion, on a frequency or transient response analysis?

Before answering that, let’s understand the concept of modal base.

IMPORTANT: This article uses, as examples, constrained modal analyses of a Body-in-White. It's merely for illustrative purposes.


MODAL BASE

A modal base is the set of natural modes that will be used on a frequency or transient response. It’s very common to hear engineers mention they will, first, build a modal base, before solving their frequency or transient response simulation.

In OptiStruct, two methods are very popular to extract natural modes out of a FEM: the Lanczos and the Automated Multilevel Sub-Structuring (AMLS).

Lanczos is represented by the bulk data entry EIGRL. It’s the most popular method to extract natural modes out of a FEM. Lanczos is used for the examples in this article.

AMLS is represented by the bulk data entry called EIGRA. It is less precise than the Lanczos method, but it consumes less computational resources. Therefore, AMLS is recommended for problems that require the extraction of a large number of natural modes.

Another advantage of Modal Superposition is that engineers can build and save their modal base to use it in as many simulations as they need, saving computational resources. For example: one engineer can generate the modal base that will be distributed to an entire team. Then, each team member will perform different frequency and transient response simulations. In OptiStruct, this can be achieved by using the subcase information entries EIGVRETRIEVE and EIGVSAVE.


EFFECTIVE MASS

If the structure is constrained, the effective mass can be used to evaluate the importance of each natural mode. It’s one of the most popular ways to check the quality of a modal base.

The effective mass is an indirect way of measuring the kinetic energy of each natural mode. It’s the quantity of mass moving in each direction, for a given natural mode. As a consequence, effective mass values are in units of mass or units of inertial moments.

To request the effective mass using OptiStruct, the following two lines are added to the solver deck:


OUTPUT,HGEFFMASS: writes the effective mass as an HyperGraph plot file. PARAM,EFFMAS,YES: writes the modal participation factor and effective mass inside the OUT file.


Below is an example of what is written to the OUT file when EFFMAS is requested:


 image


As can be seen, OptiStruct offers the effective mass sum of all natural modes extracted in a certain rigid body DOF. Engineers will compare each sum with the total mass and total inertial moment of the model. A good practice is to consider that 80% of effective mass in all DOFs will lead to a good approximation of the motion. In this example, 12 natural modes are extracted:


image


 To obtain 80% of effective mass in all DOFs, 120 natural modes must be extracted. Follow the resume:


image


For most DOFs, more than 50% of the effective mass is concentrated in the first 12 natural modes. The exception is only the X-TRANS. Therefore, let’s continue showing only the first 12 natural modes. Follow the table below:


image

  

As mass and inertial moments have different units, many engineers like to use percentages. This way, the amount of effective mass in all DOFs can be visualized together. See the below example:


 image


Values highlighted in orange designate natural modes with the highest effective mass of each DOF. They can be considered the principal modes for that specific DOF. Values highlighted in yellow are natural modes that also have a high effective mass for a given DOF. They are important modes.

Using the values highlighted in orange and yellow, the following resume can be built:


 image

  

Design modifications targeting principal and important modes have a high impact on the dynamic response of the structure. In the next section, I’ll show you an efficient way of doing design modifications.

Normally, engineers format the table of effective mass - in percentage using spreadsheet software to make it look more attractive. For example, I like to use 3D bar plots to quickly flag important natural modes. See the below image:


image


HyperGraph offers similar capabilities. However, the effective mass sum of all natural modes extracted for each DOF is considered to be 100%. By using HGEFFMASS, a MASS.MVW file is created. Below is a plot generated for this example:


image

 

DESIGN MODIFICATIONS

Design modifications are often needed in order to increase or reduce the frequency or the response of a natural mode. In complex assemblies, the most efficient way to work is by using kinetic and strain energy. Basically, engineers will sum energy values per part or component, to flag where the most efficient modification can be done.

Using OptiStruct, the following outputs are requested, to obtain kinetic and strain energies:


EKE: requests the kinetic energy for each element. ESE: requests the strain energy for each element.


The following video shows how to create the summation of kinetic and strain energy, by part or component, using HyperView: 




Now that we already have the sum of strain and kinetic energy, let’s suppose I want to increase the frequency of the lowest natural mode. The first step will be to flag what part or component has the highest strain and kinetic energy sum:


image


To raise the frequency of a natural mode, I can increase the stiffness of parts with high strain energy or reduce the mass of parts with the highest kinetic energy. In this example, I can increase the stiffness of the side body (CH-CBN-OUTER-L and CH-CBN-OUTER-R) or reduce the mass of the roof (CH-ROOF). Let’s perform both modifications and compare frequencies:


image


As can be seen, reducing the mass of the roof produces the best result.

This strategy can be done for other natural modes. Remember, modifications on principal or important modes have a higher impact on the dynamic response of the structure.


CONCLUSION

This article explains that:

  • A modal base is a collection of natural modes and it will be used in a posterior transient or frequency response.
  • A practical rule - in order to achieve a good approximation of the motion - is to have, at least, 80% of effective mass in all DOFs.
  • The higher the effective mass, the higher the contribution for the dynamic response.
  • The sum of strain and kinetic energy, by part or component, help making efficient design modifications.


Stay tuned! Soon, I will speak about frequency and transient response.





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