Free Vibration of Cantilever Beam with Lumped Mass at Free End

2.7 Virtual experimentation

Virtual experimentation provides the interface, which gives facility to perform experiments virtually. It provides different options for material selection, instruments, and specimen dimensions. After making desired selection and running the program, it gives the result from a storage database for a particular configuration selected by the user. Fig. 2.15 shows an overall flowchart for a virtual laboratory in which several experiments can be performed through the internet by users remotely with the help of already stored measured data.


Fig. 2.15: Overview of measurement based virtual experiments


2.8 Steps in virtual experimentation and its programming

The program of free vibration is divided in many sections. The step by step description of program is given as follows.

1. Title page -
This is the first page of the virtual experiment of the free vibration of a cantilever beam. It includes the title of experiment, and a photo of the experimental setup (see Fig. 2.16).

Fig. 2.16: Title Page

2.Introduction - This section contains aim of experiment, some important definitions related to free vibration, damping ratio etc.

Fig. 2.17: Introduction page (some basic definitions)

3. Input section
- This section contains various input options for the user to choose about the experiment configuration, i.e. the beam material, beam dimensions, and the transducer for the vibration measurement etc. User has to select proper input to proceed for the virtual experiment. When user enters the input configuration, each parameter generates a specific number and form a set of numbers. Based on the input configuration the virtual program takes the particular stored measured vibration data, which are related to that particular configuration, from the database. For each experiment, the database contains 10 set of files, which are chosen by the program randomly.

Fig. 2.18: User information and selecting materials with different specifications


4.Experiment -
The data from the files are read and are plotted in a particular sequence. First the response-time graph is plotted then its FFT is plotted. The data from the file is taken as an array, and it is plotted in the loop one-by–one by using a script (computer code) inside the loop.


Fig. 2.19: Response- Time graph

5.Theoretical calculations
- Theoretical calculations are done based on the input configuration chosen by the user to compare with experiment results. Program decodes the input, and generates the related parameter like the Young’s modulus, the density and dimensions of the beam. By using these values the theoretical calculation are done with the help of formula provided in this report. Refer section 2.3 for the theoretical formulations and calculations.

Fig. 2.20: Theoretical Calculation of natural frequency for the chosen configuration in


6.Experimental calculations
- The experimental calculations are done by using the data taken from already stored measurement data files. A waveform peak detector is used to get peak values and its time locations from the freely decaying response. By using these peak locations, the damped natural frequency is calculated; and by using the sets of peak values, the damping ratio is obtained by using the logarithmic decrement. The natural frequency and the damping ratio are calculated at different peaks, and then calculate the average damped natural frequency. The natural frequency can also be obtained by using the FFT plot. Again a waveform peak detector is used to get the peak location of FFT plot. The peak location is itself the damped natural frequency of the system. The undamped natural frequency can be calculated by using a formula given in equation 2.17. Refer section 2.9 and 2.10 for formulae and the procedure for experimental calculation of the undamped natural frequency and the damping ratio.

Fig. 2.21: Experimental calculation of natural frequency


7. Results
The result compares of theoretical and experimental results.

Fig. 2.22: comparison of theoretical and experimental results


8. TESTS OF USERS FOR ASSESSMENT OF THEIR LEARNING - After the successful completion of the experiment, the computer program offers a test. User has to go through it, and it is basically a student performance evaluation technique about his/her learning and understanding of the subject.

Fig. 2.23: Evaluation test page


An exercise page with sets of further questions, which are based on the basic theoretical concepts of the experiment for further evaluation of the user, is given.

Fig. 2.24: Exercise page (small test to the users)


10. FEEDBACK - At the end of the program, there is a feedback section which asks for the quick feedback about the performance and usefulness of the overall experiments, learning, navigational aspect, feel of performing aspect, testing, etc.

Fig. 2.25: Feed back page and end of the experiment


The total procedure is described as a flow chart in Fig. 2.26

Fig. 2.26: A flow chart for virtual the vibration lab and its program execution


Fig. 2.26 describes virtual vibration laboratory and the flow of execution of the program. Virtual vibration lab has number of experiment and user has to select one of them at a time. Once a particular experiment is selected, first of all he/she will go through the lab manual and then only starts the virtual program for performing the virtual experiment. At the beginning of the experiment, after the brief introduction, the virtual program offers a simple pre-experiment test to the user. If user qualifies the test he can procecd further otherwise program will be terminated and user needs to go through manual again. After qualifying the pre-experiment test, program gives input options related to the experiment, the user selects a combination of input configuration and proceed to the experiment for that configuration of the experiment. The virtual experiment leads the display of experimental results and its analysis. The experimental results are then compared with the theoretical analysis results. The user can repeat the experiment with different set of input configurations. It leads to the comparison with respect to different configurations chosen by the user so as to analyze effects of chosen parameters on the results. At the end the virtual program, it offers the student an evaluation test. Finally, it takes the feedback regarding the program execution, control, navigation, ease of use, learning, feel of performing experiment, and all other related components. This user feedback is very important for the further improvement of the existing virtual experiments and overall laboratory.


Fig. 2.27: A flow chart for the virtual experiment and its virtualization


Fig. 2.27 explains the actual experiment, its virtualization and application by using the internet. The experiment is performed with the help of input configuration and sensing instruments. For this, actual experiments need to be performed with all possible input configurations and all the data are stored in the database by using the measurement technique and measurement software. A virtual programming is done in a sequence which follows the same sequence as in case of actual experiment. This developed graphical computer program is published into the internet by using the internet publishing tools of the virtualization software. This allows the virtual experiments to be accessible by the remote users through the internet.