Problem 1: Design of a large-scale musical instrument
The purpose of this project is to design a large-scale musical instrument using metallic plates installed in an 8m x 16m room, as shown in Figure 1-1. These plates act as parabolic reflectors (Figure 1-2), causing reflected sound waves to converge at the focal point. Small nibbled slots or multiple small drilled holes should be designed to influence the natural frequencies and responses of the plates. The plates should be designed to possess different fundamental frequencies within the audible range of 50 to 8.5kHz (the region of musical sounds). It's important to note that musical sounds can be obtained when the frequencies of the plates are multiples of each other.
Figure 1-1: Geometry of the room with metallic plates installed in it.
Figure 1-2 Geometry of the metallic plates.
The following assumptions can be made:
· The material is 70/30 brass.
· The thickness is 3mm.
· The other dimensions of the plates can be varied to obtain the desired frequencies.
Suggested steps:
1) Conduct a brief literature survey on large scale musical instruments and their frequencies of resonance.
2) Construct a model that predicts the frequencies and modes of vibration and their variations with respect to geometry and material properties.
3) Explore how frequencies can be tuned with geometrical cuts into the plates.
4) Explore practical loading scenario to operate the proposed instrument.
5) Justify your choices
Remark: make the assumptions that you believe are necessary to solve the problem.
References for Problem 1
[1] Lee, H.P., Lim, S.P., Chow, S.T., 1990. Prediction of natural frequencies of rectangular plates with rectangular cutouts. Computers & Structures 36, 861-869, https://doi.org/10.1016/0045-7949(90)90157-W.
[2] Prasshanth, C.V., Anish Kumar, U., Badri Narayanan, S., Bhaskara Rao, L., 2024. Vibration analysis of perforated functionally graded circular plates. Materials Today: Proceedings, 1-7. https://doi.org/10.1016/j.matpr.2024.04.100
[3] Leissa, A.W., 1969 Vibration of Plates, Office of Technology Utilization, National Aeronautics and Space Administration, https://ntrs.nasa.gov/citations/19700009156
[4] Zhou, Q., Sariola, V., Latifi, K., Liimatainen, V., 2016. Controlling the motion of multiple objects on a Chladni plate. Nature Communications 7, 12764-1-10, 10.1038/ncomms12764