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2019 | OriginalPaper | Chapter

15. Free Flexural Vibrations of Axially Loaded Timoshenko Beams with Internal Viscous Damping Using Dynamic Stiffness Formulation and Differential Transformation

Authors : Baran Bozyigit, Yusuf Yesilce, Hikmet Huseyin Catal

Published in: Seismic Isolation, Structural Health Monitoring, and Performance Based Seismic Design in Earthquake Engineering

Publisher: Springer International Publishing

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Abstract

The effects of axial compressive load and internal viscous damping on the free vibration characteristics of Timoshenko beams are carried out using the dynamic stiffness formulation and the differential transformation method. The governing equations of motion are derived using the Hamilton’s principle. After the analytical solution of the equation of motion has been obtained, the dynamic stiffness method (DSM) is used and the dynamic stiffness matrix of the axially loaded Timoshenko beam with internal viscous damping is constructed to calculate natural frequencies. Moreover, an efficient mathematical technique called the differential transform method (DTM) is used to solve the governing differential equations of motion. The calculated natural frequencies of Timoshenko beams with various combinations of boundary conditions using the DSM and DTM are presented and compared with the analytical results where a very good agreement is observed.

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Title: Free Flexural Vibrations of Axially Loaded Timoshenko Beams with Internal Viscous Damping Using Dynamic Stiffness Formulation and Differential Transformation
Authors: Baran Bozyigit
Yusuf Yesilce
Hikmet Huseyin Catal
Publisher: Springer International Publishing
Book: Seismic Isolation, Structural Health Monitoring, and Performance Based Seismic Design in Earthquake Engineering
Print ISBN: 978-3-319-93156-2

Electronic ISBN: 978-3-319-93157-9

Copyright Year: 2019
DOI: https://doi.org/10.1007/978-3-319-93157-9_15

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