The forced vibration and boundary control of pretwisted timoshenko beams with general time dependent elastic boundary conditions

S. M. Lin, S. Y. Lee

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)

Abstract

The governing differential equations and the general time-dependent elastic boundary conditions for the coupled bending-bending forced vibration of a pretwisted non-uniform Timoshenko beam are derived by Hamilton's principle. By introducing a general change of dependent variable with shifting functions, the original system is transformed into a system composed of four non-homogeneous governing differential equations and eight homogeneous boundary conditions. The transformed system is proved to be self-adjoint. Consequently, the method of separation of variables can be used to solve the transformed problem. The physical meanings of these shifting functions are explored. The orthogonality condition for the eigenfunctions of a pretwisted non-uniform beam with elastic boundary conditions is also derived. The relation between the shifting functions and the stiffness matrix is derived. The boundary control of a pretwist Timoshenko beam is studied. The effects of the total pretwist angle, the position of loading and the boundary spring constants on the energy required to control the performance of a pretwisted beam are investigated.

Original languageEnglish
Pages (from-to)69-90
Number of pages22
JournalJournal of Sound and Vibration
Volume254
Issue number1
DOIs
Publication statusPublished - 2002 Jun 27

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Acoustics and Ultrasonics
  • Mechanical Engineering

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