# Harmonic Analysis (TABLE) - CAESAR II - Reference Data

## CAESAR II Applications Guide

PPMProduct
CAESAR II
PPMCategory_custom
Reference Data
Version_CAESAR
12

• The problem in this example is taken from the following source:

I. S. Tuba and W. B. Wright, Pressure Vessel and Piping 1972 Computer Programs Verification An Aid To Developers and Users, The American Society of Mechanical Engineers, New York, 1972. Problems 6 and 2.

• Only the input that is germane to the dynamic analysis is discussed.

This example first analyzes the following model for natural frequencies and then for harmonic loads imposed on the top of the structure at nodes 8 and 13.

Enter the model as shown and set the material density on the pipe spreadsheet to be zero. Enter all weights as concentrated masses. Do not enter bends; enter only straight elements.

Member Properties

Pipe Outside Diameter

2.375 in.

Pipe Wall Thickness

0.154 in.

Elastic Modulus

27.9E+06 psi

Poisson's Ratio

0.3

Run the static case, and then click Dynamic Analysis on the CAESAR II toolbar. The software opens the Dynamic Analysis dialog box.

On the Lumped Masses tab, you can add additional masses or delete degrees-of-freedom. In the Eigensolution of larger systems, the deletion of un-needed degrees-of-freedom can be a very important factor in keeping run times reasonable. Usually, masses must neither be added nor deleted. The mass of the piping, fluid, and insulation is automatically calculated and included by CAESAR II. In the current example, the weight of the pipe is zero, and all masses are concentrated and predefined as lumped masses.

Next, use the Control Parameters tab to modify the control parameters as shown below:

Setting Frequency Cutoff (Hz) to zero turns it off, and setting Max. No. Eigenvalues Calculated (0 - Not Used) to 5 guarantees that the first five natural frequencies are included in the results.

Click Run the Analysis . When the Eigensolution is completed, the calculated natural frequencies are printed as shown in the figure below.

Close the Dynamic Output Processor.

Click Output > Animations > Mode Shapes on the main window ribbon to view the animations of the five modes of vibration. The first mode is back and forth along the x-axis, the second mode is transverse along the z-axis and the third mode is a twisting about the y-axis. The next two modes are combinations of the previous three.