## What is Modal Analysis

**Modal Analysis is the study (analysis) of the dynamic behavior of the piping or pipeline system and used to find the natural frequencies of vibration for the concerned piping or pipeline system. Different modes of vibration (vibration characteristics) of the analyzed piping system is determined using Modal Analysis.**

## Why is Modal Analysis Important

Modal Analysis provides an overview of the limits of the response of a system. All elements of the piping systems like flanges, valves, pipes, etc have an internal frequency at which they vibrate naturally. At this frequency, the components will allow an energy transfer from one form to another with minimal loss. When this frequency reaches towards the “resonant frequency,” the system amplitude increases to infinity and high vibration is observed. Hence, modal analysis is used to find out all such frequencies so that occurrence of resonance can be prevented. Modal analysis is also known as modal and frequency analysis.

Natural frequencies gives us an idea of how fast the piping system is going to vibrate. The term natural means, the system is in free motion without any external forces. So by performing modal analysis the following two points are discovered

- Natural frequency of the piping system and
- the corresponding modes of vibration

## Criteria for Modal Analysis

While performing stress analysis for piping/pipeline systems you might have come across the term two-phase flow. Most of the flowlines are believed to have two-phase flow. Several processes and oil & gas piping systems, too, carry the two-phase flow. Conventionally all two-phase flow lines are believed to be vibration-prone.

The stress analysis basis or flexibility specification of most of the relevant organization informs the stress engineers to perform modal analysis for such systems and properly support these lines using hold-downs, guides, and axial stops to reduce the extent of vibration. It is a standard engineering practice to keep the natural frequency of vibration prone lines in excess of 4 Hz. Now the question is how to calculate the natural frequency or modal frequencies of a complex piping system?

The modal analysis module of Caesar II dynamic analysis is also used to calculate the natural frequency of pipe systems connected to compressors and reciprocating pumps. Harmful vibrations will result when the pipe natural frequency is close to that of connected rotary equipment. In order to avoid resonance and subsequently fatigue failure, many organizations follow the below-mentioned two criteria while modal analysis

- f/fn>1.25 and
- f/fn<0.75

Here, f=excitation frequency of the rotating equipment and fn=piping natural frequency.

## Dynamic Modal Analysis module of Caesar II

**So, here comes the importance of a Caesar II dynamic module called the Modal analysis module. The complex job of calculating the natural frequency of the piping system becomes very easy with the use of this module. The vibration response or dynamic response of any system can be easily determined using modal analysis. In the actual case, Modal analysis breaks up a complex system into a number of modes of vibration, each of which is having a unique vibration response. This article will elaborate on the steps followed for performing the modal analysis using Caesar II.**

## Modal Analysis Steps in Caesar II

To start the modal analysis you must have a stress system. So from the isometric model the system following conventional methods and perform the static analysis and make the system safe in all respect with respect to static analysis. Now follow the below-mentioned steps for dynamic Modal analysis:

## Inputs for Caesar II Modal Analysis

Click on Analysis-Dynamic Analysis as shown in Fig. 1 to open the dynamic module in Caesar II. It will open the window which is shown in Fig. 2.

Now click on Analysis type and select Modal from the drop-down menu. You will get the following window as shown in Fig. 3.

You will get four input spreadsheets as lumped masses, snubbers, control parameters, and advanced.

Click on Control parameters and it will open the window shown in Fig. 4.

Change the frequency cut off to your desired frequency based on your project specification. If you need to arrest all frequencies below 5 Hz and set that value as 5. The stiffness factor for friction can be used up to a value of 100. However, few organizations prefer not to use friction forces in dynamic analysis so use the stiffness factor as zero.

Now select the static load case for which you want to extract the natural frequencies. Normally it is advisable to select the operating temperature case.

## Run the Modal Analysis

Now you are set for analysis, So click on the run button similar to what you do for static analysis. The analysis will extract all the natural frequencies in which the piping system will experience below your cut off frequency values. Fig. 5 shows such a typical modal run screen.

## How to interpret Modal Analysis results

After the analysis run is complete the output screen will open. Select Natural frequencies to check the extracted natural frequencies of the system. Most of the time we check the animation view to get a feel of the actual vibration process. So select Natural frequencies and then click on the animation button as shown in Fig. 6.

In the animation, view check how the system is experiencing vibration. Accordingly, provide support. Normally guide and line stop support with zero gaps will be required to arrest the vibration frequencies. Accordingly, provide support. Sometimes hold down supports will be required. So, each time in the animation view find out the location where the system is vibrating and provide support near to it. In most of the cases, the vibration occurs

- Near rigid bodies (valves, flanges, etc)
- Long unsupported pipe spans
- Long pipe runs where guide support is not provided
- Straight lengths of pipe without line stops

So each time provide support at vibrating places in the piping system and re-run the modal analysis as mentioned above.

As soon as you will provide guide and line stop supports the system will become more rigid and expansion stresses will increase. So each time you change some support type you have to perform static analysis and make the system safe from all considerations and then proceed to the dynamic module.

## Video tutorial on Modal Analysis Basics and related theories

The following video tutorial gives a nice explanation of the modal analysis basics and modal analysis theories.

Few more useful resources for you.

Slug Flow Analysis Using Dynamic Spectrum Method in Caesar II

It’s useful, Thanks for sharing, this website so great. So, can you continue with Harmony Analysis, Spectrum and History response. Thanks very very much.

sir , can you explain how much stiffness factor should we use in our system. As in modal analysis it is dynamic friction stiffness i.e. function of normal force. In that case how much stiffness should we use . As i feel its totally impractical to assume stifness 0 . Guide

If we use snubber to increase natural frequencies of system, how we should estimate snubber axial load to prepare its data sheet and apply for purchase?

Dear Mr. Anup,

I really appreciate your thoughts in sharing knowledge . Thankyou so much!

regards,

vivek

As a retired stress engineer I would help out?