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Free vibration of spring-mounted beams
Published in Institute of Physics Publishing
2019
Volume: 1264
   
Issue: 1
Abstract
In the present work, free vibration characteristics of a spring-mounted beam is studied. The objective is to determine the natural frequencies and mode shapes of this beam. Towards this end, a novel semi-analytical method is developed. The methodology is based on Green's function of Euler-Bernoulli beam together with a Rayleigh-Ritz method. A minimal set of basis functions for the Rayleigh-Ritz method is found, by generating the beam mode shapes for extreme values (zero and infinity) of the connecting spring stiffnesses. Thus, for a beam with n intermediate spring connections, 2n beam modes are generated as basis functions. The Green's function approach is used to extract the beam mode shapes for the extreme values of the connecting spring stiffnesses. The results from the proposed formulation are compared with those from a finite element (FE) simulation. For most cases, the results obtained by the two methods are in excellent agreement. Guidelines for further improvement of the accuracy of the present results have been proposed. Detailed parametric studies on the effect of spring stiffness value and their location have been performed. © Published under licence by IOP Publishing Ltd.
About the journal
JournalJournal of Physics: Conference Series
PublisherInstitute of Physics Publishing
ISSN17426588
Open AccessYes
Concepts (14)
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    Functions
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    Green's function
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    Natural frequencies
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    Structural dynamics
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    Variational techniques
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    Finite element simulations
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    FREE VIBRATION CHARACTERISTIC
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    GREEN'S FUNCTION APPROACHES
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    Mode shapes
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    Natural frequencies and modes
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    RAYLEIGH-RITZ
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    RAYLEIGH-RITZ METHODS
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    Semi-analytical methods
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    Stiffness