Class: BE-309
Group: T1
Members: Soe Y Ahn, Bethany Gallagher, Robert Pierson, Zack Shinar, Alexander Taich
Date: Fall 1998
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Abstract:
This experiment gave a thorough analysis of a system under a sinusoidal force. Using light plastic bars of various materials (Acrylic, Polystyrene, HMWPE) and sound waves, resonance phenomena was demonstrated. Two different transducers, piezoelectric accelerometer and electret condenser microphone, were used to record the vibration of materials. Initially, the impulse hammer was used to find the experimental fundamental frequencies of the materials, but due to low Young’s moduli of the bars, they vibrated in low frequencies in addition to their natural frequencies. This created excessive noise in the signal that interfered the determination of the fundamental frequencies. Expected fundamental natural frequency for each bar was calculated. For accelerometer the expected values for Acrylic, Polystyrene, HMWPE1, and HMWPE2 were 12.52, 3.79, 5.91, and 6.36 (HZ) respectively. With the microphone these values changed to 16.73, 6.52, 8.16, and 8.32 (Hz) as a result of lighter weight of the transducer. Resonant frequencies were determined through plotting power vs. input frequency. When the input frequency approached the resonant frequencies, the power of the vibration increased dramatically. The accelerometer graphs displayed sharp peaks at resonant frequencies, but with the microphone, continuous increase in power was observed. This is due to the fact that the omnidirectional microphone recorded the sound waves from the speaker as well as the vibration of the bars. Experimental resonant frequencies were found to be much greater than the expected values. Therefore, they were attributed to harmonics of the system. Due to low power in low frequency region, the transducers were not able to detect the fundamental frequencies. The experimental values correlated with harmonics of the expected fundamental frequencies. Deviations from the theoretical harmonics were greater for the accelerometer due to its heavy mass. The average percent deviation for the accelerometer ranged from 14.99 to 34.43% and for the microphone it ranged from 5.98 to 20.19 %. The HMWPE bars with different widths were expected to have increase in natural frequency with increase in width. However, the trend was unclear because of difficulty in determining which harmonics were recorded. Finally, a glass slide cover with an expected fundamental frequency of 1.697KHz was subjected to input frequency with high amplitude that was varied around the expected value in attempt to shatter the glass slide cover. However, not enough energy was transferred to break it.