Free Transverse Vibration due to a Point Load on a Simply:

Supported Shaft

In this kind of vibration, all of the particles vibrate along paths perpendicular to the shaft axis. The shaft might be having single to various supports. It might be carrying its own load, a single point load or various point loads come in this category. These cases are now to be dealt with separately.

Assume a very light shaft AB of length carrying a point load 'W' at a distance 'a' from the support A and at distance 'b' from the support B.

                                                                    a + b = l                      ----(28)

and the deflection

δ =        W a² b²/3E I i                                                               ------- (29)

The natural circular for equation is following

where  δ = W/ k                              ----------(30)

                      ----------(31)

 The mass of the beam was neglected for resolve of the natural frequency.