Republic of the PhilippinesPOLYTECHNIC UNIVERSITY OF THE PHILIPPINES

College of EngineeringMECHANICAL ENGINEERING DEPARTMENT

NDC Compound, Pureza St., Sta. Mesa, Manila

FORCED VIBRATION

WRITTEN REPORT ON VIBRATION ENGINEERING

Submitted by:

AROMIN, ALBERT S.JARILLO, DARWIN JAY T.LIBAO, MARC RUSSELL

BSME 5-1

Submitted to:Engr. Armingol Morales

Professor

VIBRATION ENGINEERINGFORCED VIBRATION

Forced vibrations occur when the object is forced to vibrate at a particular frequency by a periodic input of force.

Objects which are free to vibrate will have one or more natural frequency at which they vibrate,

If an object is being forced to vibrate at its natural frequency, resonance will occur and you will observe large amplitude vibrations. The resonant frequency is fo.

The phase relationship between the driving oscillation and the oscillation of the object being driven is different at different frequencies.

Below resonance they are in phase with each other. At resonance the phase relationship is 90o or pi/2

rad.

Above resonance the phase relationship is 180o or pi rad.

 In engineering practice, we are almost invariably interested in predicting the response of a structure or mechanical system to external forcing.  For example, we may need to predict the response of a bridge or tall building to wind loading, earthquakes, or ground vibrations due to traffic.

Equation of Motion for External Forcing We have no problem setting up and solving equations of motion by now. First draw a free body diagram for the system

Newton’s law of motion gives Rearrange and substituted for F(t)

our equation can be reduced to the form

Equation of Motion for Base Excitation

Equation of Motion for

The equation reduces to the standard form

Equation of motion for Rotor Excitation Finally, we will derive the equation of motion for the third

case.  Free body diagrams are shown below for both the rotor and the mass