ME495 Lab 08_ Laser Vibrometry

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Laser Vibrometry ME 495: Mechanical and Thermal Systems Lab Section 05: Thursday Group D Authors: Soeung Khanitha, Smith Emilee, Sichantha Jack, Taylor Charles Instructor: Dr. Hamid Nourollahi Wednesday, February 29, 2024

1 Table of Contents Objective of Experiment ( Khanitha Soeung ) ............................................................................................... 2 Equipment ( Khanitha Soeung, Emilee Smith ) ............................................................................................. 2 Experimental Setup ( Khanitha Soeung, Jack Sichantha) .............................................................................. 4 Experimental 02 Procedure ( Khanitha Soeung ) ........................................................................................... 4 Experimental Results ..................................................................................................................................... 5 Discussion of Results (Charles Taylor) .......................................................................................................... 7 Lab Guide Questions (Emilee Smith) ............................................................................................................ 7 Conclusion (Jack Sichantha) .......................................................................................................................... 8 References ( Khanitha Soeung ) ..................................................................................................................... 8 Appendix ( Jack Sichantha) ........................................................................................................................... 9 List of Figures Figure 1: Experimental Setup .................................................................................................................. 4 Figure 2: Harmonic Input ........................................................................................................................ 5 Figure 3: Classical Genre Frequency ....................................................................................................... 6 Figure 4: Hip Hop Genre With Heavy Bass ............................................................................................ 7 List of Tables Table 1: Equations .......................................................................................................................................... 3 Table 2: Constants .......................................................................................................................................... 4

2 Objective of Experiment (Khanitha Soeung) The aim of this experiment is to utilize the Polytec PDV 100 Laser Doppler Vibrometer (LDV) for the quantitative analysis of surface vibrations in a speaker cone. Particularly focusing on measuring displacement, velocity, and acceleration under harmonic excitation at varying frequencies. The empirical data collected will be utilized to ascertain the damping ratio of the speaker cone, providing valuable insights into the mechanical limitations of the system. The team hypothesized that the measured vibrations in the speaker cone will exhibit varying characteristics based on the frequency of harmonic excitation and that as the speaker gets old and worn, it will lose strength to counter the vibrations properly. Furthermore, it is expected that an increase in frequency will lead to changes in displacement, velocity, and acceleration profiles, reflecting the dynamic response of the system. Additionally, the damping ratio is anticipated to influence the rate of vibration decay, with higher damping ratios resulting in quicker attenuation of oscillations. It is hypothesized that the damping ratio will be close to critically damped because the speaker is calibrated to critical damping of oscillations for the best quality of sound. Equipment (Khanitha Soeung, Emilee Smith) ● PDV 100 Portable Digital Vibrometer ○ Main tool for measuring vibrations ● Sensor ○ The vibration sensor that connects to the PDV 100 ○ This captures the vibrations in the system and sends the data to the vibrometer for measurement and analysis ● BNC Cable ○ This is used to connect the sensor to the PDV 100 ○ Transmits signals in various applications due to their reliability and durability ● USB Polytec Hardlock ○ Hardware key provided by Polytec, the manufacturer of the PDV 100.

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3 ○ Used for software licensing ● PDV 100 Portable Digital Vibrometer Power supply ○ Provides power to the PDV 100 ● ArtDio Portable Computer Speaker ○ Used for audio output from the system ○ Vibrations can be converted into audible signals for analysis ● USB Cable ○ Connects the PDV 100 to the computer for data transfer ● Polytec VIB - E - 220 Data Acquisition System ○ Another component for data analysis ● Audacity Software ○ Audio editing and recording software ○ Used for processing of the data collected by the vibrometer ● Tripod ○ Used to stabilize the sensor ● Computer ○ Used for running software applications, analyzing data, and storing measurement results Table 1: Equations Equation 1: Second Order System ? ? 2 ? ?? 2 + ? ?? ?? + 𝑘? = 𝐹(?) Equation 2: Damping Ratio ξ = ? ? ??𝑖? Equation 3: Damping Coefficient ? ??𝑖? = 2 𝑘? Equation 4: Harmonic Input 𝐹(?) = 𝐹 0 ?𝑖?(ω?)

4 Equation 5: Phase Angle ϕ = ?𝑎? −1 2ξω/ω ? 1−(ω/ω ? ) 2 ⎡ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎦ Table 2: Constants Constant Value Spring Constant 𝑘 = 618 𝑁/? Mass of Speaker Cone ? = 7 ?? = 7 * 10 −6 𝑘? Experimental Setup (Khanitha Soeung, Jack Sichantha)

5 Figure 1: Experimental Setup Experimental 02 Procedure (Khanitha Soeung) In experiment 02, the frequency contents of two sound courses , classical music and hip hop music, were investigated in the frequency domain to derive the qualitative observations regarding the frequency ranges correlated with melody and bass. Firstly, a classical music piece was selected from Youtube, and it was played for approximately 20 seconds using the same procedures as outlined in experiment 01. Following the playback, a screenshot of the data was taken to capture the frequency spectrum. Subsequently, a music piece from Future was chosen from Youtube. This was also played for roughly 20 seconds using the same steps mentioned above. After the playback, another screenshot of the data was captured to analyze the frequency spectrum. Through this process qualitative data was collected to delve deeper into the distribution of frequencies associated with melody and bass in both classical and hip hop genres.

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6 Experimental Results (Emilee Smith) Figure 2: Harmonic Input

7 Figure 3: Classical Genre Frequency

8 Figure 4: Hip Hop Genre With Heavy Bass Table 3: Experimental Data Sample Calculations: ω ? = 𝑘 ? = 618 𝑁/? 7*10 −6 𝑘? = 9396. 04 ω = 2π? = 2π * 1𝑘𝐻𝑧 = 6283 ? ? 2 ? ?? 2 + ? ?? ?? + 𝑘? = 𝐹(?) 𝐹 0 ?𝑖?(ω?) = 0

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9 → ? = 0. 142 ? ??𝑖? = 2 𝑘? = 2 618 𝑁? * 7 * 10 −6 𝑘? = 0. 132 ξ = ? ? ??𝑖? = 0.142 0.132 = 1. 076 ϕ = ?𝑎? −1 2ξω/ω ? 1−(ω/ω ? ) 2 ⎡ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎦ = ?𝑎? −1 2*1.076*6283/9396.04 1−(6283/9396.04) 2 ⎡ ⎢ ⎣ ⎤ ⎥ ⎦ = 1. 204 ?𝑎?𝑖𝑎?? Discussion of Results (Charles Taylor) Figure 2: Harmonic Input depicts the relationship between the magnitude of the vibrations vs the frequency in regard to each acceleration, velocity and position. The figure represents the plotted data from experiment 1. The graph in the top left of this figure depicts the magnitude of velocity shown in the time domain. This data is then Laplace Transformed into the frequency domain to produce what is shown in the other 3 plots. As shown in the magnitude vs. time plot the peak amplitude is highest around the time when the frequency reaches the input value. This verifies that our equipment and equations are operational. Shown in the calculations section of the results section above, the damping ratio for the vibrations in experiment 1 is equal to 1.076. The damping ratio represents the damping of the system, where, >1 is over damped, <1 is under damped, and =1 is critically damped. Because the damping ratio is 1.076, the system is slightly overdamped. Figures 3 and 4 depict a similar set of information to figure 2, which is vibration magnitude vs time transformed into magnitude vs. frequency. The difference in this figure is that it represents the vibrations from a classical music piece and a hip hop genre music (with a heavy bass), as opposed to the harmonic input of sounds from experiment 1. This figure represents the vibration vs time and frequency data from experiment 2. It would not be possible to solve for the damping ratio of experiment 2’s plots because we do not know F(t) for the music. The damping ratio is a measure for oscillatory functions, therefore neither of the musics would have a damping ratio. This said, the primary purpose of comparing the two different music styles is to see the effect that different sound types can have on vibrations, namely the effect of bass. As shown in table 3, the magnitude of acceleration, velocity and displacement of the vibrations are all greater when heavy bass is introduced to the music sample. There are several possible sources of error in this experiment. Error would generally be most

10 clearly depicted in the damping ratio of experiment 1 and visibly via looking at the plots. Error is expected to be relatively small for this dataset because the damping ratio is very close to showing critical damping, which is what it is set to. A couple possible sources of error may be slight misalignment of the laser vibrometer and wear of the speaker or vibrometer. These would both likely cause systematic error, however, depending on the form of ware on the equipment, durability could possibly engender random errors in the data. The team’s hypothesis was proven true in that the damping ratio was very close to 1, representing critical damping of the harmonic function. It was also shown to be true that a higher bass will cause frequency to increase. Lab Guide Questions (Emilee Smith) 1. Determine the phase angle for the data from the first experiment. ω ? = 𝑘 ? = 618 𝑁/? 7*10 −6 𝑘? = 9396. 04 ω = 2π? = 2π * 1𝑘𝐻𝑧 = 6283 ? ? 2 ? ?? 2 + ? ?? ?? + 𝑘? = 𝐹(?) 𝐹 0 ?𝑖?(ω?) = 0 → ? = 0. 142 ? ??𝑖? = 2 𝑘? = 2 618 𝑁? * 7 * 10 −6 𝑘? = 0. 132 ξ = ? ? ??𝑖? = 0.142 0.132 = 1. 076 ϕ = ?𝑎? −1 2ξω/ω ? 1−(ω/ω ? ) 2 ⎡ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎦ = ?𝑎? −1 2*1.076*6283/9396.04 1−(6283/9396.04) 2 ⎡ ⎢ ⎣ ⎤ ⎥ ⎦ = 1. 204 ?𝑎?𝑖𝑎?? 2. Find c when the system is critically damped. Critically damped: , → ξ = 1 ξ = ? ? ??𝑖? 1 = ? 0.132 = 0. 132 3. What can you say about the frequency contents of the two music pieces in Experiment 2? We predicted that for a high pitch (classical music) the frequency would be higher and for a low pitch (bass-heavy) the pitch would be lower. The frequency contents that came from experiment 2 confirmed this. The lower the bass, the lower the frequency, meaning the resulting wavelengths are longer and

11 slower than those of the high pitch, high frequency sounds that came from the classical music we evaluated. 4. How is ‘bass’ of music related to frequency? ‘Bass’ is just another definition for low frequency, ranging from 16 to 250 Hz. Conclusion (Jack Sichantha) In conclusion, the results of the experiments shed light on the dynamic relationship between sound vibrations and their effects on physical systems. Through analysis and comparison, the team has gained valuable insight in the behavior of vibrations in response to various types of music stimuli. Experiment 02 delved into the impact of music genres on vibration characteristics. Primarily focusing on the influence of bass frequencies. The team's observations revealed that the heavy bass, as exemplified by hip-hop music, resulted in amplified magnitudes of acceleration, velocity, and displacement compared to classical music. This suggests a correlation between bass intensity and vibrational energy. However it is important to note that there are a few limitations of our study. Experiment 02 presented challenges in quantifying dampening due to the variability in musical compositions. The primary aim of this comparison was to explain the qualitative differences in vibration responses rather than quantifying precise dampening ratios. Potential sources of error, such as misalignment of equipment or wear on the speaker and vibrometer, were acknowledged. While these factors may introduce systematic errors, the rigours experimental design mitigated their impact to ensure the reliability of the teams findings. In summary, this experiment provides valuable insight into the complex relationship between sound vibrations and physical systems. By explaining the influence of music genres on vibrations characteristics, as a result the team was able to contribute a deeper understanding of the relationship between sound and motion. References ( Khanitha Soeung ) [1] Nourollahi, A. (2024). ME-495 Laboratory Exercise – Number 8 –Laser Vibrometry In

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12 ME Dept, SDSU – Nourollahi. SDSU Publishing [2] Nourollahi, A. (2024). ME-495 Course Introduction_and Syllabus Spring 2024-1. In ME Dept, SDSU – Nourollahi. SDSU Publishing Appendix N/A