Research Article
Apr 1967
Vibration of Nonuniform Simply-Supported Beams
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VIEW THE REPLYPublication: Journal of the Engineering Mechanics Division
Volume 93, Issue 2
Abstract
The natural frequencies and corresponding mode shapes for nonuniform simply-supported beams are investigated. The deflections are approximated by a Fourier series and in addition to this normal procedure, the mass and moment of inertia functions are also approximated by Fourier expansions. These are then used in writing out the Lagrangian which can be reduced from a triple series product to a double series product. The end result is an infinite number of homogeneous linear simultaneous algebraic equations in the Fourier deflection coefficients. A finite number of equations are used in approximating the frequencies and mode shapes. Examples show good agreement between these approximations and those obtained by more exact methods.
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Published In
Journal of the Engineering Mechanics Division
Volume 93 • Issue 2 • April 1967
Pages: 1 - 16
Copyright
© 1967 American Society of Civil Engineers.
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Published in print: Apr 1967
Published online: Feb 3, 2021
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Authors
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Arthur C. Heidebrecht, AM.ASCE
Asst. Prof. of Civ. Engrg. and Engrg. Mechanics, McMaster Univ., Hamilton, Ont., Canada.
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Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.