Parameter sensitivity of cantilever beam with tip mass to parametric excitation

  • Vamsi C. MeesalaEmail author
  • Muhammad R. Hajj
Original Paper


The sensitivity of the response of a parametrically excited cantilever beam with a tip mass to small variations in elasticity (stiffness) and the tip mass is performed. The governing equation of the first mode is derived, and method of multiple scales is used to determine the approximate solution based on the order of the expected variations. We demonstrate that the system can be designed so that small variations in either stiffness or tip mass can alter the type of bifurcation. Notably, we show that the response of a system designed for a supercritical bifurcation can change to yield a subcritical bifurcation with small variations in the parameters. Although such a trend is usually undesired, we argue that it can be used to detect small variations induced by fatigue or small mass depositions in sensing applications.


Parametric excitation Cantilever beam-mass systems Sensitivity analysis Uncertainty quantification Mass/gas sensing Damage detection 



The authors would like to thank Dr. Mohammad Younis for sharing his expertise and providing valuable suggestions. The first author would also like to thank Dr. Ayoub Boroujeni for providing useful insights on carbon fiber/epoxy resin composites.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Biomedical Engineering and MechanicsVirginia TechBlacksburgUSA
  2. 2.Department of Civil, Environmental and Ocean EngineeringStevens Institute of TechnologyHobokenUSA

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