3.4 Experimental setup

Fig. 3.4: An experimental setup for the forced vibration of a cantilever beam

The schematic of the experimental setup is shown in Fig. 3.4, which consists of a cantilever beam, an exciter, controller/amplifier, two transducers (e.g., accelerometer and laser vibrometer), a data-acquisition system, and a computer with signal display and processing software. Different types of beam materials and its properties are listed in Table 3.1. Different combinations of beam geometries for each of the beam material are summarized in Table 3.2.

Accelerometer (transducer) is a sensing element 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 data acquisition system and after processing (e.g., FFT, etc.), it displays on the computer screen by using analysis software.

When we perform the experiment, the exciter keeps the excitation force in such a way that the displacement increases almost linearly with time Fig. 3.10 (b). Because of this reason, we get continuously increasing displacement-frequency graph Fig.3.11 (a) but the force-time graph Fig.3.10 (a) decreases up to the resonance then it increases. The controller of the exciter minimizes the force amplitude so that at resonance large oscillations do not take place.

 

Table 3.1  Material properties of various beams

 

Material	Density (kg/m 3 )	Young’s Modulus (N/m 2 )
Steel	7850	2.1×10 11
Copper	8933	1.2×10 11
Aluminum	2700	0.69×10 11

 

Table 3.2  Different geometries of the beam

Length,L,(m)	Breadth,b,(m	Depth,h,(m)
0.45	0.02	0.003
0.65	0.04	0.003

 

3.5 Photos of Experimental setup

 

Fig. 3.5: Experimental setup of a cantilever beam for forced vibration.

 

Fig. 3.5 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 vibration response. The fixed end of the beam is gripped with the help of clamp. For getting precise vibration response of the cantilever beam, it is very important to ensure that clamp is tightened properly, otherwise it may not give fixed end conditions and relative sliding may take place.

 

Fig. 3.6: Exciter

 

Exciter is used to give desired excitation to the beam. The power is given to the exciter by controller which is connected with a computer to select the excitation parameter. The different types of excitation can be generated by exciter e.g. sine, swept sine, rectangular, triangular etc. In case of forced vibration we use swept sine force signal, in which user have to select the initial and final frequency, and the sweep rate.

 

Fig. 3.7: A close view of the fixed end of the cantilever beam

 

Fig. 3.8: A close view of an accelerometer mounted on the beam at the free end

 

An accelerometer (Fig. 3.8) is a time-dependent (dynamic) vibration measuring device. It is a contacting type of transducer. It is a transducer, which converts the acceleration of vibration into equivalent voltage signal, and sends it to the data acquisition system (Fig. 3.9).

 

Fig. 3.9: Data acquisition system

 

Data acquisition system receives voltage signal from the accelerometer, and calibrate the data into equivalent accelerometer scale through its sensitivity and send it to computer where by using a software these data can be analyzed in time history (displacement-time) and frequency domain (i.e., using FFT).

 

Fig. 3.10: Time-force and time-response graph

  (a): Excitation force against Time

(b): Response against Time  

 

When the voltage signal from the accelerometer is sent to the data-acquisition system, it calibrates it into mechanical vibration data and send it to computer where by using the vibration measurement software, it can be plotted as shown in above Figure and can be used for further analysis.