V. Natural Frequency of Beam on Springs

Find the period of free vibration for a beam supported on two springs with a point mass.

Reference

Timoshenko, S., Young, D., and Weaver, W., Vibration Problems in Engineering, John Wiley & Sons, 4th edition, 1974. page 11, problem 1.1-3.

Problem

A simple beam is supported by two spring as shown in the figure. Neglecting the distributed mass of the beam, calculate the period of free vibration of the beam subjected to a load of W.

 EI = 30,000.0 ksi

 A = 7.0 ft

 B = 3.0 ft.

 W = 1,000 lbfK = 300.0 lb/in.

Comparison

Table 1. Comparison of results
Period (sec) 0.533 0.53317 negligible

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\08 Dynamic Analysis\Natural Frequency of Beam on Springs.STD is typically installed with the program.

``````STAAD PLANE : NATURAL FREQUENCY OF BEAM ON SPRINGS
START JOB INFORMATION
ENGINEER DATE 14-Sep-18
END JOB INFORMATION
*
*  REFERENCE 'VIBRATION PROBLEMS IN ENGINEERING' BY
*  TIMOSHENKO,YOUNG,WEAVER. (4TH EDITION, PAGE 11, PROB 1.1-3)
*  THE ANSWER IN THE BOOK IS T = 0.533 sec., viz., F = 1.876 CPS
*
UNIT FEET POUND
JOINT COORDINATES
1 0 0 0; 2 7 0 0; 3 10 0 0;
MEMBER INCIDENCES
1 1 2; 2 2 3;
UNIT INCHES POUND
SUPPORTS
1 3 FIXED BUT MZ KFY 300
MEMBER PROPERTY AMERICAN
1 2 PRIS AX 1 IZ 1
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 3e+07
POISSON 0.3
END DEFINE MATERIAL
CONSTANTS
MATERIAL MATERIAL1 ALL
CUT OFF MODE SHAPE 1
2 FY -1000
MODAL CALCULATION REQUESTED
PERFORM ANALYSIS
FINISH
``````

```               CALCULATED FREQUENCIES FOR LOAD CASE       1