(34) VIBRATION ANALYSIS:

a) Modal Analysis:

In order to do modal analysis, the model must be broken up into pieces so that each pipe run can be analyzed individually. Isolate a single run of pipe and provide anchors with thermal movements entered from the respective load case. The flow chart below shows the basic process.

Ensure the specific gravity of the fluid medium is entered in the pipe properties as it will affect the modal analysis.

Click on “Load > Dynamic Analysis”. On the “Modal” tab, set the maximum number of modes to 6. Leave Fluid density factor at the default value. Use a minimum cutoff frequency of 90 Hz. For the “Hot modulus case”, choose the thermal case with the highest temperatures. Set the “Pressure stiffening case” to the pressure case that corresponds with the temperature case chosen for the “Hot modulus

case”. Make sure “include contents” is checked. To mitigate eigen frequencies add additional mass for the insulation at the piping center of gravity.

b) Harmonic Analysis:

Prior to starting harmonic analysis, the modal analysis must be set up. Refer to section 34a for modal analysis. In harmonic analysis, the cutoff frequency must be set to 1.5 times the forcing function frequency.

Click on “Load> Harmonic”. Create a new file name. Only one file name is necessary to input many forcing functions. Based on the forcing function data available, choose the appropriate input. Set the damping coefficient to a value no greater than 0.1. Set the frequency drop down to “Sum” and direction to “Resultant”. For each node which is an “equipment excitation interface”, enter the data into the grid table. Below is an example of the Harmonic Load screen with information filled out.

Next, go to “Load > Dynamic Analysis” and navigate to the Harmonic tab. Create a new dynamic load case and select the data set created previously. Use the combination RMS. Make sure ZPA and Missing Mass are checked. Click Apply and run the analysis. Make sure the harmonic box is checked as shown in the picture below. The harmonic analysis is used to check the stress level of the piping under the forcing function in the load case “Sustained + H1”.

(35) MODELING PRESSURE BALANCED EXPANSION JOINTS: Pressure balanced expansion joints can be modeled in Auto Pipe using the following procedure.

Create a pipe run in the direction of flow long enough to include the universal bellows. (This can be connected to an existing pipe run, or an anchor with movements specified.)

Create a new segment at the end of the pipe run created previously.

Create a second new pipe run in the direction of flow that will accommodate the size of the satellite bellows.

Next, create a new pipe run at the point in between the two existing runs – where the new segment was created – and specify the tee as a “Welding” tee. This pipe run will go in the direction of the equipment and/or existing piping connection. The picture below shows the current progress of the pressure balanced expansion joint.

Click on “Insert > Beam Section Properties” and create a new custom beam as shown in the picture below.

Insert beams on both ends of the expansion joint using the previously created Section ID, perpendicular to the radial movement of the pipe. The beams must be longer than the radius of the pipe. Be sure to name the beam nodes uniquely. The picture below on the left shows beams being inserted at the ends of the expansion joint. Once these two beams are in place, tie the free ends of the beams together by placing a “Tie/Link” type support at the end of one beam and specifying the opposite beam node in the field titled “Connected to:”. This can be seen in the picture below and to the right.

Repeat these steps for the opposite side of the pipe. In this example, both input and output connections will be modeled as anchors with movements specified. The result should look like the picture below.

Insert a small run of pipe downstream of the input connection to provide a node at which to insert the Flexible Joint. Place a Flexible Joint at the just-created node (this is the universal bellows) with the appropriate length and stiffness values. Place another Flexible Joint (satellite bellows) at the node at opposite end of the expansion joint making sure to specify BEFORE the node so that the Flexible Joint is on the pipe. Again, define the appropriate stiffness and length of the joint. The completed pressure balanced joint should look like the picture below.