Impulse Response of an Elastic Rod with a Mass-damper-spring Termination
DOI:
https://doi.org/10.5890/JVTSD.2023.06.005Abstract
This paper investigates the impulse response of a longitudinally vibrating rod with a mass-damper-spring termination. The equations of motion of the system are derived using Lagrange's method. The vibration of the rod consists of rigid-body and elastic motions. The impulse response is predicted with a particular solution method which constructs the response as the summation of the solution satisfying homogeneous boundary conditions and a particular solution dealing with non-homogeneous boundary conditions. The particular solution method transforms the original partial differential equation to discrete dynamic systems represented in a state-space form. The transient and total impulse responses at selected locations on the rod are studied in detail. The vibration reduction of the rod by tuning the mass-damper-spring system is discussed with the help of root locus with respect to the mass, damping and stiffness parameters. The tuning of the mass-damper-spring system can change coupling between the rigid-body and elastic motions, which in turn can significantly affect the response of the rod. The method of particular solution is validated through the error analysis and response comparison of a rod with free-free boundary conditions.References
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