Response variations of a cantilever beam–tip mass system with nonlinear and linearized boundary conditions

Vamsi C. Meesala, Muhammad R. Hajj

Research output: Contribution to journalReview articlepeer-review

8 Scopus citations

Abstract

The distributed parameter governing equations of a cantilever beam with a tip mass subjected to principal parametric excitation are developed using a generalized Hamilton's principle. Using a Galerkin's discretization scheme, the discretized equation for the first mode is developed for simpler representation assuming linear and nonlinear boundary conditions. The discretized governing equation considering the nonlinear boundary conditions assumes a simpler form. We solve the distributed parameter and discretized equations separately using the method of multiple scales. Through comparison with the direct approach, we show that accounting for the nonlinear boundary conditions boundary conditions is important for accurate prediction in terms of type of bifurcation and response amplitude.

Original languageEnglish
Pages (from-to)485-496
Number of pages12
JournalJVC/Journal of Vibration and Control
Volume25
Issue number3
DOIs
StatePublished - 1 Feb 2019

Keywords

  • Parametric excitation
  • boundary conditions
  • cantilever beam–mass systems
  • method of multiple scales
  • perturbation methods

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