Free Vibration of a Cantilever Beam(Continuous System)

4.4 Calculation of Experimental Natural Frequency

To calculate the natural frequency of the cantilever beam experimentally up to third mode, conduct the experiment with the specified cantilever beam specimen. Record the data of time history (Displacement-Time), and FFT plot. The natural frequencies of the system can be obtained directly by observing the FFT plot. The location of peak values corresponds to the natural frequencies of the system. Fig. 4.5 shows a typical FFT plot.


Fig. 4.5: Fast Fourier Transform plot for free vibration of cantilever beam


4.5 Experimental setup

Fig. 4.6: An experimental setup for the free vibration of a cantilever beam


The experimental setup consists of a cantilever beam, transducers (strain gauge, accelerometer, laser vibrometer), a data-acquisition system and a computer with signal display and processing software (Fig. 4.6). Different types of beam materials and its properties are listed in Table 4.1. Different combinations of beam geometries for each of the beam material are summarized in Table 4.2

Accelerometer is a sensing element (transducer) to measure the vibration response (i.e., acceleration, velocity and displacement). Data acquisition system takes vibration signal from the accelerometer, and encodes it in digital form. Computer acts as a data storage and analysis system. It takes encoded data from the data acquisition system and after processing (e.g., FFT), it displays on the computer screen by using analysis software.


Fig. 4.7:  Experimental setup of a cantilever beam


Fig. 4.7 shows an experimental setup of the cantilever beam. It includes a beam specimen of a particular geometry with a fixed end and at the free end an accelerometer is mounted to measure the free vibration response. The fixed end of beam is gripped with the help of clamp. For getting precise free vibration cantilever beam data, it is very important to ensure that clamp is tightened properly; otherwise it may not give fixed end conditions in the free vibration data.


Fig. 4.8 A close view of the fixed end of the cantilever beam


Fig. 4.9: A close view of an accelerometer mounted on the free end of the beam


Accelerometer: It is a time-dependent vibration measuring device. Here, the shown accelerometer is a contacting type of transducer, which converts the acceleration of vibration into equivalent voltage signal, and sends it to data acquisition system.


Fig. 4.10: Data acquisition system


Data acquisition system: It receives voltage signal from the accelerometer, and calibrate the data into equivalent accelerometer scale, and send it to computer where by using a vibration measurement software these data can be analyzed as time history (Displacement-Time) and in frequency domain (i.e., using FFT).


Fig. 4.11: A typical Time-response and FFT plot


When the voltage signal from the accelerometer is sent to the data-acquisition system, it converts the signal to a mechanical vibration data (acceleration) and stores it to the computer. A typical screen-shot of a captured vibration signal by using vibration measurement software is plotted as shown in Fig. 4.11 and can be used for further analysis.