Abstract
Supposing the upper end of a mass-loaded string is subjected to an axial harmonic displacement excitation, the parametrically-excited transverse vibration of the string due to dynamic coupling between axial and transverse directions is investigated in this paper. If only the first order transverse vibration mode is retained, it is found that the motion of the mass-loaded string can be described by Mathieu’s Equation. Based on the stability criterion for the solution to Mathieu’s Equation, an analytical formula is derived, which can be used to calculate the critical excitation amplitude causing parametric resonance at different excitation frequencies. This formulation is verified by some numerical simulation work.
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Zhang, C., Zhang, S. (2011). Critical Condition for Parametric Resonance of Axially Mass-Loaded String. In: Lin, S., Huang, X. (eds) Advances in Computer Science, Environment, Ecoinformatics, and Education. CSEE 2011. Communications in Computer and Information Science, vol 217. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23339-5_6
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DOI: https://doi.org/10.1007/978-3-642-23339-5_6
Publisher Name: Springer, Berlin, Heidelberg
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