# V. Rayleigh Natural Frequency of a Cantilever Beam

To calculate the Natural frequency of vibration using the Rayleigh method for a light cantilever beam with a mass at the free end.

## Reference

Thomson, W.T., Vibration Theory and Applications, Prentice-Hall, Inc., 1965.

## Problem

Find the natural frequency of vibration, f, of a mass, m, attached to the end of a light cantilever beam of length, L, and flexural stiffness, EI.

### Model for dynamic beam no. 2

 E = 30,000 ksi

 I = 1.3333 in4

 m = 0.1 lb-sec2/in

 L = 30 in

## Comparison

Table 1. Comparison of results
Frequency, f (Hz) 33.553 33.5365 none

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

``````STAAD PLANE NATURAL FREQUENCY OF A CANTILEVERED MASS
START JOB INFORMATION
ENGINEER DATE 14-Sep-18
END JOB INFORMATION
*
*  REFERENCE:  THOMSON, W.T., "VIBRATION THEORY AND APPLICATIONS",
*      PRENTICE HALL INC., ENGLEWOODS, NEW JERSEY, 1965
*
INPUT WIDTH 72
UNIT INCHES POUND
JOINT COORDINATES
1 0 0 0; 2 30 0 0;
MEMBER INCIDENCES
1 1 2;
MEMBER PROPERTY AMERICAN
1 PRIS IZ 1.33333
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 3e+07
POISSON 0.290909
END DEFINE MATERIAL
CONSTANTS
MATERIAL MATERIAL1 ALL
SUPPORTS
1 FIXED
2 FY -38.64
CALCULATE RAYLEIGH FREQUENCY
PERFORM ANALYSIS
PRINT JOINT DISPLACEMENTS
FINISH
``````

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