A General Approach on the Mechanical Analysis of Nonuniform Beams With Nonhomogeneous Elastic Boundary Conditions

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Abstract

The dynamic and static response of a nonuniform beam with nonhomogeneous elastic boundary conditions is studied by generalizing the method of Mindlin-Goodman and utilizing the exact solutions of general elastically restrained non-uniform beams given by Lee and Kuo. A general form of change of dependent variable is introduced and the shifting functions expressed in terms of the four fundamental solutions of the system, instead of the fifth degree polynomials taken by Mindlin-Goodman, are selected. The physical meanings of these shifting polynomial functions are explored. Finally, the limiting cases are discussed and examples are given to illustrate the analysis.

Original languageEnglish
Pages (from-to)164-169
Number of pages6
JournalJournal of Vibration and Acoustics, Transactions of the ASME
Volume120
Issue number1
DOIs
Publication statusPublished - 1998 Jan 1

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polynomials
Polynomials
Boundary conditions
boundary conditions
dependent variables
dynamic response

All Science Journal Classification (ASJC) codes

  • Acoustics and Ultrasonics
  • Mechanics of Materials
  • Mechanical Engineering

Cite this

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abstract = "The dynamic and static response of a nonuniform beam with nonhomogeneous elastic boundary conditions is studied by generalizing the method of Mindlin-Goodman and utilizing the exact solutions of general elastically restrained non-uniform beams given by Lee and Kuo. A general form of change of dependent variable is introduced and the shifting functions expressed in terms of the four fundamental solutions of the system, instead of the fifth degree polynomials taken by Mindlin-Goodman, are selected. The physical meanings of these shifting polynomial functions are explored. Finally, the limiting cases are discussed and examples are given to illustrate the analysis.",
author = "Sen-Yung Lee and Chen, {Terry Yuan-Fang} and Wang, {Wen Rong}",
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AB - The dynamic and static response of a nonuniform beam with nonhomogeneous elastic boundary conditions is studied by generalizing the method of Mindlin-Goodman and utilizing the exact solutions of general elastically restrained non-uniform beams given by Lee and Kuo. A general form of change of dependent variable is introduced and the shifting functions expressed in terms of the four fundamental solutions of the system, instead of the fifth degree polynomials taken by Mindlin-Goodman, are selected. The physical meanings of these shifting polynomial functions are explored. Finally, the limiting cases are discussed and examples are given to illustrate the analysis.

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