Hong, Jonathan AAJ-7697-2020 0000-0003-0404-8979

Laflamme, Simon AAH-5471-2019 0000-0002-0601-9664

Downey, Austin 0000-0002-5524-2416

Document Type



Engineering systems undergoing extreme and harsh environments can often times experience rapid damaging effects. In order to minimize loss of economic investment and human lives, structural health monitoring (SHM) of these high-rate systems is being researched. An experimental testbed has been developed to validate SHM methods in a controllable and repeatable laboratory environment. This study applies the Euler-Bernoulli beam theory to this testbed to develop analytical solutions of the system. The transverse vibration of a clamped-pinned-free beam with a point mass at the free end is discussed in detail. Results are derived for varying pin locations and mass values. Eigenvalue plots of the first five modes are presented along with their respective mode shapes. The theoretical calculations are experimentally validated and discussed.

Digital Object Identifier (DOI)


©2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (

APA Citation

Hong, J., Dodson, J., Laflamme, S., & Downey, A. (2019). Transverse Vibration of Clamped-Pinned-Free Beam with Mass at Free End. Applied Sciences, 9(15), 2996