Dunkeley Formula
Transverse Vibration of Beam Lab Report
Introduction
This experiment aimed to study the forced damped transverse vibration of a beam and verify Dunkerley’s empirical formula.
According to Dunkerley’s empirical formula,
1f2=1fb2+1fω2 where f referring to the natural frequency of heavy beam with central load fb referring to the natural frequency of heavy beam only fω referring to the natural frequency of light beam with central load M
By using the results of light damping, Dunkerley’s empirical formula would be studied and verified by comparing the calculated resonant frequency f of the whole system and the experimental value.
Apparatus 1. Beam vibration apparatus which consists of : (1) A rectangular bar-length
Cross section
Mass
Young’s modulus E Motor and rotor assembly – mass Mass of one plate 2. DC power supply 3. B & K accelerometer 4369 with magnetic support and cable holder – mass = 66.7gm 4. B & K charge amplifier 2635 5. Oscilloscope
Procedure
1. The charge amplifier was set to the following (1) Transducer Sensitivity range switch 1-11 (2) Transducer Sensitivity conditioning knobs (221) (3) mV/unit output switch 100 (4) Upper frequency limit 0.1kHz (5) Accel-Vel-displ switch 1mm (1Hz) 2. The oscilloscope was set to: (1) Sweep Time/cm (20~50) ms (2) Gain (5~50) mV/cm 3. The output was connected from the charge amplifier to channel 1 or 2 of the oscilloscope. 4. The accelerometer was attached by means of magnetic support to the steel plate of the motor assembly. 5. With light damping, the motor by was started increasing the voltage supply of the DC power supply from 20 volt to 40 volt in step of 1 volt. 6. Te frequency was recorded and amplitude of vibration from
Introduction
This experiment aimed to study the forced damped transverse vibration of a beam and verify Dunkerley’s empirical formula.
According to Dunkerley’s empirical formula,
1f2=1fb2+1fω2 where f referring to the natural frequency of heavy beam with central load fb referring to the natural frequency of heavy beam only fω referring to the natural frequency of light beam with central load M
By using the results of light damping, Dunkerley’s empirical formula would be studied and verified by comparing the calculated resonant frequency f of the whole system and the experimental value.
Apparatus 1. Beam vibration apparatus which consists of : (1) A rectangular bar-length
Cross section
Mass
Young’s modulus E Motor and rotor assembly – mass Mass of one plate 2. DC power supply 3. B & K accelerometer 4369 with magnetic support and cable holder – mass = 66.7gm 4. B & K charge amplifier 2635 5. Oscilloscope
Procedure
1. The charge amplifier was set to the following (1) Transducer Sensitivity range switch 1-11 (2) Transducer Sensitivity conditioning knobs (221) (3) mV/unit output switch 100 (4) Upper frequency limit 0.1kHz (5) Accel-Vel-displ switch 1mm (1Hz) 2. The oscilloscope was set to: (1) Sweep Time/cm (20~50) ms (2) Gain (5~50) mV/cm 3. The output was connected from the charge amplifier to channel 1 or 2 of the oscilloscope. 4. The accelerometer was attached by means of magnetic support to the steel plate of the motor assembly. 5. With light damping, the motor by was started increasing the voltage supply of the DC power supply from 20 volt to 40 volt in step of 1 volt. 6. Te frequency was recorded and amplitude of vibration from