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ISSN: 2475-4811 (print)
ISSN: 2475-482X (online)
Journal of Vibration Testing and System Dynamics

C. Steve Suh (editor), Pawel Olejnik (editor),

Xianguo Tuo (editor)

Pawel Olejnik (editor)

Lodz University of Technology, Poland

Email: pawel.olejnik@p.lodz.pl

C. Steve Suh (editor)

Texas A&M University, USA

Email: ssuh@tamu.edu

Xiangguo Tuo (editor)

Sichuan University of Science and Engineering, China

Email: tuoxianguo@suse.edu.cn

Impulse Response of an Elastic Rod with a Mass-damper-spring Termination

Journal of Vibration Testing and System Dynamics 7(2) (2023) 169--186 | DOI:10.5890/JVTSD.2023.06.005

Siyuan Xing$^1$, Jian-Qiao Sun$^2$

$^1$ Department of Mechanical Engineering, California Polytechnic State University, San Luis Obispo, CA 93047, USA

$^2$ Department of Mechanical Engineering, School of Engineering, University of California, Merced, California, 95343, USA

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Abstract

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.

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