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Math. Comput. Appl. 2004, 9(2), 257-264; doi:10.3390/mca9020257

Free Vibration Analysis of Elastic Beams Using Harmonic Differential Quadraure (HDQ)

Firat University, Civil Engineering Dept, Elazi, Turkey
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Published: 1 August 2004
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Abstract

Harmonic differential quadrature method is developed for the free vibration analysis of linear elastic beams. In the method of differential quadrature, partial space derivatives of a function appearing in a differential equation are approximated by means of a polynomial expressed as the weighted linear sum of the function values at a preselected grid of discrete points. The weighting coefficients are treated as the unknowns. Applying this concept to the governing differential equation of beam gives a set of linear simultaneous equations, which are solved for the unknown weighting coefftcients by accounting for the boundary conditions. Beams of different support combinations such as clamped, simply supported, guided, and free are selected to demonstrate the accuracy of the method. Flexural vibration case is taken into consideration. First two frequencies are obtained in the applications. Numerical results are presented to illustrate the method and demonstrate its efficiency.
Keywords: Harmonic Differential Quadrature; Beams; Free Vibration; Numerical Analysis Harmonic Differential Quadrature; Beams; Free Vibration; Numerical Analysis
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Civalek, Ö.; Ülker, M. Free Vibration Analysis of Elastic Beams Using Harmonic Differential Quadraure (HDQ). Math. Comput. Appl. 2004, 9, 257-264.

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