The purpose of the thesis is to develop software for determination of normal modes of the vibrating mechanical systems with piecewise constant properties. The resulting software would be demonstrated on the science web page Wolfram.

Fig. 1. Mechanical system with piecewise constant properties

References:

1. S. Abrate, “Vibration of non-uniform rods and beams,” Journal of sound and vibration, 185, 703–716, 1995.
2. B. M. Kumar and R. I. Sujith, “Exact solution for the longitudinal vibration of non-uniform rods,” Journal of sound and vibration, 207, 721–729, 1997.
3. A. I. Fedorchenko, I. Stachiv, A.-B. Wang and W.-C. Wang, “Fundamental frequencies of mechanical systems with piecewise constant properties,” Journal of sound and vibration, 317, 490-495, 2008.
4. A. I. Fedorchenko, I. Stachiv, J. Ho, A.-B. Wang and W.-C. Wang, “On force vibration of the fiber partially immersed in fluid Fundamental frequencies of mechanical systems with piecewise constant properties,” Sensors and actuators A: Physical, 147, 498-503, 2008.