Year: 2025
Type: article
Abstract: The vibrations of a string-mass system are considered. A heavy mass is suspended from a string, and the system is subjected to axial rotation. The partial differential equation modeling the system’s dynamics is first derived. For uniform axial rotation, exact analytical solutions are given. For harmonically fluctuating rotation speeds, an approximate solution is found using the method of multiple scales to analyze the system’s principal parametric resonances. The stability of the system is examined both analytically and numerically. The analytically derived stability boundaries qualitatively match the behavior observed in numerical simulations. With some transformations, the system can also be reduced to a standard Mathieu equation. Keywords: string-mass; perturbation; rotation; principal parametric resonances; stability; Mathieu equation
Source: Engineering Transactions
Author: Pakdemirli, Mehmet
Institution: Manisa Celal Bayar University
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W6964020245
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