TRIFLEX? Windows Chapter 9

Chapter 9

9.0 TRIFLEX WINDOWS Dynamic Capabilities __________________________ 2

9.1 Modal Analysis Methodology_____________________________________ 2 9.1.1 Modeling Considerations _____________________________________ 3

9.2 Modal Analysis________________________________________________ 4 9.2.1 TRIFLEX Input for Modal Analysis_____________________________ 4 9.2.2 TRIFLEX Output for Modal Analysis_______________________________ 5

9.3. Modal Analysis Program Verification ____________________________ 10 9.3.1 Benchmark Problem____________________________________________ 10

Figures FIGURE 9.1 CASE DEFINITION DATA ......................................................................... 4 FIGURE 9.2 DYNAMIC DATA ENTRY.......................................................................... 5 FIGURE 9.3 MODAL FREQUENCIES ............................................................................ 6 FIGURE 9.4 SYSTEM MOVEMENTS............................................................................. 7 FIGURE 9.5 SYSTEM FORCES AND MOMENTS......................................................... 8 FIGURE 9.6 SYSTEM STRESSES ................................................................................... 9 FIGURE 9.7 MAXIMUM SYSTEM VALUES................................................................. 9

TRIFLEX? Windows Chapter 9

9.0 TRIFLEX WINDOWS Dynamic Capabilities The TRIFLEX WINDOWS program was developed by PIPINGSOLUTIONS INC. to aid the piping engineer and analyst in the design of complex piping systems incorporating the effects of dynamic phenomena. TRIFLEX predicts the 1) Mechanical resonant frequencies and mode shapes of the piping system, 2) Response spectrum analysis – Not on this license 3) Time history analysis – Not on this license This brief guide has the following purposes: ? Explanation of input data preparation for users familiar with TRIFLEX ? Explanation of output results ? Modeling suggestions, precautions for the piping engineer ? Verification based on industry benchmark problem

9.1 Modal Analysis Methodology TRIFLEX Dynamics is based on recent work done by mechanical engineering experts in university research laboratories in the past decades. The formulation has a sound Finite Element basis with a stiffness method, which lends itself to dynamic analyses. The nodes generated by the pre-processor are efficiently renumbered so that: (a) larger piping systems can be handled, and (b) the computations required for convergence to a free vibration solution are

minimized. Since the solution of the eigenvalue (frequencies) problem consumes more time than the corresponding static problem, the number of dynamic degrees of freedom is reduced by neglecting rotational inertia of every node. Even the translational masses (or inertia) are lumped and distributed equally at the two nodes of a run and this has been found satisfactory. Extensive care has been taken in the formulation of element stiffness matrices, assemblage to form the global matrix for the piping system and the iterative solution technique so that: (a) available core memory in the computer is utilized to the maximum extent

TRIFLEX? Windows Chapter 9 (b) I/O to disk storage, and hence overhead to the job, are minimized. 9.1.1 Modeling Considerations ? TRIFLEX uses the latest available techniques and automatically tries to optimize

the nodes to minimize solution time, improve accuracy of results and minimize use of memory.

? All weight data are converted to mass input data and external loads are ignored. ? Modal analysis can handle any linear restraints features coded by the user for a static

run. In order to eliminate the need to retype or edit an existing input file, which has non-linear boundary restraints, TRIFLEX has the following conventions:

- 1-D Restraints are treated as rigid two way restraints - Limit stops with positive and negative gaps will be treated as FREE - Limit stops with the same signs will be treated as RIGID - Limit stops with zero dimension gaps will be treated as RIGID - Friction coded at data points is ignored - Requested Spring Hangers sizing will abort the job. Users are advised to

replace this request for a spring hanger size with the resultant spring hanger previously sized in a static analysis

- Dampers are treated as rigid restraints - All initial movements are set to zero

? Modal analysis should be performed with more CAUTION than static analysis.

Solution algorithms are very sensitive to poor coding, e.g., sudden variations of stiffnesses between two adjacent pipe elements. The practice of coding very short runs or bends (i.e., less than 0.1") should be avoided in the context of dynamic analysis.

? The user should use the “Maximum spacing with respect to diameter” for automatic

intermediate point generation between two data points when encountering long runs. A minimum of one intermediate points should be placed between two consecutive restrained points, and two consecutive elbows or bends.

? TRIFLEX has been extensively benchmarked both for accuracy and speed against

the published results of the NRC (Nuclear Regulatory Commission, Washington, D.C.).

TRIFLEX? Windows Chapter 9

9.2 Modal Analysis 9.2.1 TRIFLEX Input for Modal Analysis Modal Analysis is carried out in order to extract the natural frequencies and the associated mode shapes. A piping system consists of elastic components (pipes, fittings, flexible restraints) and distributed masses (pipes, fittings, rigid components). Once displaced from static equilibrium, the system will oscillate at a combination of the mode shapes, each vibrating at the associated frequency. Frequencies and mode-shapes are instrumental in the linear prediction and analysis of time-varying phenomena. To run a Modal Analysis, the user must:

1. Check the box for “Mode Shapes and Frequencies” for the Load case 1 in the “Load case“ dialog

Figure 9.1 Case Definition Data

TRIFLEX? Windows Chapter 9 2. Complete the top line of the DYNAMICS DATA ENTRY SCREEN; that is, specify

the number of mode shapes derived and the maximum allowable natural frequency. No. of Mode Shapes: Specify the number of modes or frequencies to be calculated. The default value is 10. If calculations occurs in “demo Mode” the number of Mode Shapes need to be reset to two. Max. Freq.: Specify the cut-off frequency (default value = 100 Hz.) for the analysis in Hertz or cycles/sec. Only those frequencies with the corresponding mode shape from among the required number of modes that are below the specified number for Hertz will be retained.

Figure 9.2 Dynamic Data Entry

To run the model the user has two options. He can do a left mouse click on the green arrow from the top of the Main Screen or he can select “Basic Calculation” option from “Calculate” command of the Main Screen. 9.2.2 TRIFLEX Output for Modal Analysis Following the normal system description reports the program also reports the following reports for a modal analysis. MODAL FREQUENCIES Natural frequencies are printed in ascending order. Frequencies (RAD/SEC as well as CYCLES/SEC) and Period are listed for each mode. To obtain this report in spreadsheet format selecting “Output” and “View Analysis Results” dialog from “Main Screen”. The name of the report is “Modal Frequencies” (Fig. 9.3) To obtain this report select “print Preview” or “Print” option from “Output” dialog of “Main Screen” and select the check box for “Modal Frequencies”

TRIFLEX? Windows Chapter 9 MODE SHAPE Mode shapes, i.e., deflections and rotations, are printed with the maximum value of the displacement normalized to 100. The KEY here is "shape" and not the actual value of deflection or rotation. In order to emphasize this subtle point, the deflections are printed as non-dimensional and the rotations are DIMENSIONAL, e.g., deg./100 inch. A report with deflections and rotations can be display for each calculated frequencies. To obtain this report select “print Preview” or “Print” option from “Output” dialog of “Main Screen” and select the check box for “System Deflections & Rotations” A similar report can be obtained in spreadsheet format selecting “Output” and “View Results” dialog from “Main Screen”. The name of the report is “System Movements” (Fig. 9.4)

Figure 9.3 Modal Frequencies

TRIFLEX? Windows Chapter 9 FORCES AND STRESSES The force report and the stress report generated for each mode correspond to a maximum deflection of 1 in. (25.4 mm) whereas the nondimensional 100 is used in the mode shape report.

Figure 9.4 System movements

To obtain this report select “print Preview” or “Print” option from “Output” dialog of “Main Screen” and select the check box for “System Forces & Moments” and/or “System Stresses” A similar report can be obtained in spreadsheet format selecting “Output” and “View Results” dialog from “Main Screen”. The names of the reports are “System Forces & Moments” and “System Stresses” MAXIMUM SUMMARY The maxims of deflections, rotations, forces, moments, stresses, and the corresponding data points are printed for each frequencies.

TRIFLEX? Windows Chapter 9 To obtain this report select “print Preview” or “Print” option from “Output” dialog of “Main Screen” and select the check box for “Sum. Max. Sys. Values”. The same things can be obtained in spreadsheet format selecting “Output” and “View Description” dialog from “Main Screen”. The names of the reports are “Maximum System Values”

Figure 9.5 System Forces and Moments

TRIFLEX? Windows Chapter 9

Figure 9.6 System Stresses

Figure 9.7 Maximum System values

TRIFLEX? Windows Chapter 9

9.3. Modal Analysis Program Verification This section presents a comparison of the program generated solution with a known solution of a selected benchmark problem. This provides a confirmation of the adequacy of the program for modal analysis of piping systems. 9.3.1 Benchmark Problem The benchmark problem is stored under the file name NRC.dta in the folder “Samples” under the folder where TRIFLEX WINDOWS was installed. It simulates a 3-1/2 inch diameter water line extending between two elevations. It is a simple configuration joining two anchors and having numerous intermediate supports. The geometric and material properties of the pipe elements are given below.

Pipe outside diameter = 3.5 in Pipe wall thickness = 0.216 in Pipe density = 0.403 lb/in3 Young's Modulus of Elasticity = 25,800,000 psi Poisson's Ratio = 0.3

Mode number Frequency NRC Frequency TRIFLEX Difference

1 6.04 6.03 -0.16% 2 6.26 6.24 -0.32%

3 7.76 7.94 2.32% 4 8.94 8.86 -0.89% 5 12.44 12.42 -0.16% 6 12.83 12.81 -0.16% 7 14.30 13.92 -2.66% 8 15.49 15.42 -0.45% 9 16.37 16.18 -1.16%

10 18.54 18.35 -1.02% Comparison of Natural Frequencies of Benchmark Problem

This sample problem used is published in Bezler, P., Subudhi, M. and Hartzman, M., "Piping Benchmark Problems", Dynamic Analysis independent Support Motion Response Spectrum,” Regulatory Commission, NUREG/CR-1677, Vol. 2, August 1985. Load the example job NRC.dta from the “Samples” folder. Keep the “by default” setting for number of made shapes and for maximum frequencies

TRIFLEX? Windows Chapter 9 where 10 vibration modes and the associated natural frequencies, bounded by a cut-off frequency of 100 Hz. are required. Perform the analysis. The following table reflects the modal frequencies, and a comparison of the modal frequencies to those found in the above mention book.