M E - 495 Mechanical and Thermal Systems Lab #8 Laser Vibrometry Lab

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San Diego State University *

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495

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Mechanical Engineering

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Apr 3, 2024

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M E - 495 Mechanical and Thermal Systems lab Wednesday Section 3 Lab #8 Laser Vibrometry Lab Group D Department of Mechanical Engineering Professor Hamid Nourollahi Preformed on: February 21st, 2024 Submitted on: February 27th, 2024

Table of Contents Table of Contents 1 The Objective of the Experiment 2 Equipment 4 Experimental Procedure 5 Experimental Results 7 Discussion of Results 11 Lab Questions 12 Conclusion 14 References 15 Table of Figures and Tables Figure 1: PDV 100 Portable Digital Vibrometer Sensor 4 Figure 2: speaker cone 4 Figure 3: Channel tab 5 Figure 4: Experiment 1 data 7 Figure 5: Classical Music Data 8 Figure 6: Rock Music Data 8

The Objective of the Experiment The objective of these experiments is to familiarize students with the process of quantitatively characterizing surface vibrations in a mechanical system. To do so, students will learn to use a Polytec PDV 100 Laser Doppler Vibrometer, which is a tool used to measure the displacement, velocity, and acceleration of mechanical vibrations in a speaker cone when harmonically excited at various frequencies. The final goal for the students is to use the data collected along with empirical data to calculate the damping ratio. The data collected is saved in the form of 4 graphs per type of sound displayed: one graph showing velocity vs time, and the three others showing magnitude vs frequency, so another objective of this experiment is to improve students’ graph interpretation. This experiment also prepares students for real-world situations, for example when bridges are built, a big consideration when doing so is the fact that everything traveling on said bridge creates a vibration, and a similar analysis as the one done in this experiment can be used to test the bridge’s safety. For the first experiment, the speaker is expected to be underdamped because it is old and blown out after years of use. For the second experiment, the rock music will be on the lower end of the frequency spectrum because they have a dominance in bass instruments. These instruments have deep tones that have low frequencies. We expect classical music to have a wider range of frequencies as they have a diverse range of instruments that produce frequencies across the frequency spectrum.

Equations: (Equation 1) ? ? 2 ? ?? 2 + ? ?? ?? + ?? = 𝐹 ? ( ) (Equation 2) ξ = ? ? ??𝑖? (Equation 3) ? ??𝑖? = 2 ?? (Equation 4) β = ?𝑎? −1 [ ξ 1−ξ 2 ] (Equation 5) 𝑃 𝑃 ? = −ξ− ξ 2 −1 2 ξ 2 −1 ? (−ξ+ ξ 2 −1) ω ? ? + −ξ− ξ 2 −1 2 ξ 2 −1 ? (−ξ+ ξ 2 −1) ω ? ? + 1 (Equation 6) 𝐹 ? ( ) = 𝐹 0 ?𝑖?(ω?) (Equation 7) ? ? ( ) = ? ? sin ?𝑖? ω? − ϕ ( ) (Equation 8) ? ? ? ? = 1 1− ω ω ? ( ) 2 ⎡ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎦ 2 + 2ξω ω ? ⎡ ⎢ ⎣ ⎤ ⎥ ⎦ 2 (Equation 9) ? ? = 𝐹 0 ? (Equation 10) ϕ = 2ζω ω ? 1− ω ω ? ( ) 2 ⎡ ⎢ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎥ ⎦ Nomenclature: m = mass (kg) c = damping coefficient k = spring constant F(t) = input force = natural frequency (s -1 ) ω ?? = damping ratio ξ s d = amplitude of the periodic steady-state displacement s s = displacement of the spring ϕ = phase angle

Equipment ● PDV 100 Portable Digital Vibrometer Sensor: It is a device used to measure vibrations. It is equipped with sensors that can detect vibrations and provide data. A laser emerges from its lens and focuses on the area in which vibration analysis is desired. Figure 1: PDV 100 Portable Digital Vibrometer Sensor [1] ● The speaker cone is a part of a speaker that outputs sounds from the computer. Its job is to convert electrical signals into mechanical vibrations, producing sound waves that we can hear. Figure 2: speaker cone [1] ● VibrSoft Software: A data analysis software to analyze vibrations and output the data as graphs. ● Audacity Software: A digital audio editor and recording application.

Experimental Procedure Experiment 1: 1. Open both Vibrsoft and Audacity software 2. On the Vibrsoft applications, locate the top bar menu and select “Acquisitions”. From there click on “Settings” from the drop-down menu. a. A pop-up menu will come up. Click the “Channel” tab and ensure that the settings are the same as the figure below. Figure 3: Channel tab [1] b. Click on the “General” tab and make sure that “peak hold” is selected and set to “3” 3. Make sure that the 'Analyzer 1' window is selected (its top bar should be blue, not gray). 4. Choose Analyzer → Domain → Time to switch the window to the time domain. 5. Repeat steps 4 and select Analyzer±Signal±Velocity 6. Open three windows by selecting Window±New Window 7. Change the domain of these three windows to frequency by selecting Analyzer±Domain±FFT 8. Change one of each window to Displacement, Velocity, and Acceleration 9. Tile the windows either vertically or horizontally. 10. Turn on the cursor by selecting Analyzer±Cursor 11. Change the cursor to 10 seconds on the velocity window and 1kHz on the frequency domain. 12. Open Audacity.

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