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Modeling and Probabilistic Investigation of Out-of-Plane Vibrations of Spinning Discs With Reliability Approach

Nouri, Hossein | 2024

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 57244 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineering
  6. Advisor(s): Mofid, Masoud; Foyouzat, Mohammad Ali
  7. Abstract:
  8. The primary objective of this research is to develop a suitable method for solving the out-of-plane vibration equation of spinning disks, and to investigate the system's response probabilistically while analyzing its reliability. Spinning disks have extensive applications in various industries and engineering fields, including computer disk-drive systems, electronic components, and rotating machinery. These disks experience severe vibrations at certain speeds due to resonance phenomena, which affect their performance and may lead to system failure. Initially, this research solves the governing equation of the motion of rotating disks deterministically using an analytical method. A thin air layer beneath the disk is modeled as an elastic foundation with variable modulus, and its impact on the system's frequencies is examined. Subsequently, a comprehensive parametric study is conducted to investigate the effects of variations in angular speed, outer radius, and thickness on the natural frequencies of the system. It is noteworthy that in all previous studies, parameters have been considered deterministically, without probabilistic analysis. Therefore, in this research, probabilistic analyses are conducted by assigning appropriate probability distributions to the geometric and mechanical parameters using reliability methods. Thus, the innovations of this research include providing a defined framework for solving the equations and conducting reliability analysis while accounting for the uncertainties in critical parameters such as angular speed, outer radius, thickness, and modulus of elasticity. The natural frequencies computed using this method were validated against existing literature data, demonstrating that the presence of the elastic foundation increases the system's natural frequency. Additionally, it was observed that the elastic foundation's influence is more significant in the lower modes than in the higher modes. Furthermore, it was determined that the natural frequency related to the (1,0) mode defines the critical speed, which is slightly higher than the disk's angular speed. Finally, it was found that as the angular speed increases, the reliability index decreases linearly, becoming very small near the critical speed. Therefore, to design rotating disks safely, the maximum allowable speed should be slightly below the critical speed. Additionally, the changes in the reliability index against the coefficient of variation of the outer radius, thickness, and modulus of elasticity were examined, which can help provide an appropriate framework for reliability-based design of rotating disks
  9. Keywords:
  10. Spinning Disk ; Out of Plane Vibration ; Elastic Foundation ; Angular Velocity ; Reliability Analysis

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