Objective: (3 sentences)
The goal of this experiment is to study the vibrational characteristics of a cantilever beam subjected to dynamic excitation. Students will use a shaker to excite the beam and a laser system to monitor its displacement, allowing them to analyze the beam's response at various frequencies. This will include identifying resonance frequencies, mode shapes, and understanding how the beam behaves under vibrational forces.
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1. Theory Overview
Vibration Analysis:
Vibration analysis is a critical aspect of mechanical engineering, focusing on how structures and materials respond to dynamic forces. In mechanical systems, vibration refers to the oscillatory motion of an object around an equilibrium position. This motion can be caused by various forces, such as external impacts, rotational imbalances, or periodic excitations. When analyzing vibrations, it is essential to understand the concept of vibration modes. Vibration modes describe the specific patterns in which a structure deforms or oscillates when subjected to vibrational forces. Each structure, whether a beam, plate, or complex mechanical system, has a set of natural frequencies at which it tends to vibrate most easily. These natural frequencies correspond to specific vibration modes, often termed as mode shapes.
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Rao, Singiresu S. "Mechanical vibrations." (1995).
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2. Pre-Lab Quiz
Quiz Date: xxxxxx
The quiz will cover the theory of vibrations, modal analysis, and cantilever beam behavior.
Review resonance frequencies, vibration modes, and laser monitoring principles.
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3. Experimental Procedure
Step-by-Step Instructions:
Set up the cantilever beam and shaker system.
Make sure the amplifier is connected and the amplitude gain is at zero before opening.
Check the stability of the cantilever beam with the shaker.
Adjust the amplifier gains and the wave properties from the waveform generator.
Excite the beam at various frequencies.
Use the laser system to measure displacement and amplitude.
Identify resonance frequencies and vibration modes.
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4. Data Collection
During the lab, collect the following:
Frequency and amplitude data
Resonance frequency observations
Mode shapes of the cantilever beam
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5. Post-Lab Report
Due Date: xxxxxx
The report for this part is expected to include:
· Abstract and Introduction
· Procedures and Steps
· Experiment Related (Plots & Calculations)
· Discussion and Conclusion
Submit a report analyzing:
Resonance frequencies and mode shapes.
The vibrational response of the beam at different excitation frequencies.
Comparison of experimental data with theoretical predictions.
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[Video Tutorial on Vibration Analysis] (Link)
[Sample Report Format] (Link)
Responsible TAs:
TA Name, emailGürdeniz Neşer, gneser18@ku.edu.tr