Abstract
The aim of this study is to investigate the curved rods subjected to dynamic loads with variable geometric properties along the axis theoretically. The transient analysis of the planar rods under the various in-plane dynamic loads has been analyzed in the Laplace domain. The obtained canonical form of the first order ordinary differential equations has been solved by Complementary Functions Method (CFM) in the transformed domain. The fifth-order Runge–Kutta method has been applied to the solution of the obtained equations. The materials of the structural elements are assumed to be homogeneous, isotropic, and elastic. The solutions obtained are transformed to the time domain using the modified Durbin's inverse numerical Laplace transformed method. For the suggested models, a computer program is coded in Fortran for the dynamic analysis of the planar curved structural elements. Verification of the computer program is performed by comparing the results of the present methods with the other numerical methods available in the literature. The procedures have been proved to be highly accurate and efficient compared to various other numerical methods.
Keywords
Two-Point Boundary Value Problems Complementary Functions Method (CFM) Inverse Laplace Transforms Planar Arches
References
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- Bayhan,S. (1993). Analysis of planner curved rods by stiffness matrix and transfer matrix method. MSc. Thesis, University of Cukurova, Adana.
- Bozkurt, M. (1995). The analysis of cylindrical vaults, circular and helicoidal structural systems by the complementary functions method-mathematica applications. MSc. Thesis, University of Cukurova, Adana.
- Yıldırım, V., İnce, N., and Kıral, E. (1997) “ Static Analysis of compound planar frames with members of linear and circular axes by stiffness matrix method. Journal of Engineering and Environmental Sciences, pp.137-148
- Çalım, F.F. (2003). Dynamic analysis of viscoelastic, anisotropic curved spatial rod systems. PhD. Thesis, University of Cukurova, Adana.
- Kıraç, M. (2007). Dynamic analysis of straight composite rods. MSc. Thesis, University of Mustafa Kemal, Hatay.
- Aktan, H. (2008). In-Plane dynamic analysis of circular beams. MSc. Thesis, Istanbul Technical University, Istanbul.
- Çoban, M. (2008). Out-Of-Plane dynamic analysis of curved beams using mixed finite element method. MSc. Thesis, Istanbul Technical University, Istanbul.
- Akkurt, F.G. (2011). Dynamic analysis of straight and circular rods on elastic foundation. MSc. Thesis, University of Mustafa Kemal, Hatay.
- Karaca, N. (2014). Static and dynamic analysis of planar rods by the transfer and stiffness matrix methods. MSc. Thesis, University of Mustafa Kemal, Hatay.
- Ecer, S., (2015) “Longitudinal vibration analysis of straight bars using mixed finite element method. MSc. Thesis, Istanbul Technical University, Istanbul.
- Durbin, F. (1974). Numerical inversion of laplace transforms: An efficient improvement to Dubner and Abate’s Method. The Computer Journal, vol.17, no.4 pp. 371 – 376. Doi: 10.1093/comjnl/17.4.371
- Temel, B., Çalim, F.F. And Tütüncü, N. (2004). Quasi-Static and dynamic response of viscoelastic helical rods. Journal of Sound and Vibration, 271:921 - 935. Doi: 10.1016/S0022-460X(03)00760-0
- ANSYS, Inc Release 15.0 (2013), Canonsburg, PA
Abstract
References
- Haktanır, V. (1990). Investigation of the static, dynamic and buckling behavior of cylindrical helical rods by transfer matrix method. PhD. Thesis, University of Cukurova, Adana.
- Bayhan,S. (1993). Analysis of planner curved rods by stiffness matrix and transfer matrix method. MSc. Thesis, University of Cukurova, Adana.
- Bozkurt, M. (1995). The analysis of cylindrical vaults, circular and helicoidal structural systems by the complementary functions method-mathematica applications. MSc. Thesis, University of Cukurova, Adana.
- Yıldırım, V., İnce, N., and Kıral, E. (1997) “ Static Analysis of compound planar frames with members of linear and circular axes by stiffness matrix method. Journal of Engineering and Environmental Sciences, pp.137-148
- Çalım, F.F. (2003). Dynamic analysis of viscoelastic, anisotropic curved spatial rod systems. PhD. Thesis, University of Cukurova, Adana.
- Kıraç, M. (2007). Dynamic analysis of straight composite rods. MSc. Thesis, University of Mustafa Kemal, Hatay.
- Aktan, H. (2008). In-Plane dynamic analysis of circular beams. MSc. Thesis, Istanbul Technical University, Istanbul.
- Çoban, M. (2008). Out-Of-Plane dynamic analysis of curved beams using mixed finite element method. MSc. Thesis, Istanbul Technical University, Istanbul.
- Akkurt, F.G. (2011). Dynamic analysis of straight and circular rods on elastic foundation. MSc. Thesis, University of Mustafa Kemal, Hatay.
- Karaca, N. (2014). Static and dynamic analysis of planar rods by the transfer and stiffness matrix methods. MSc. Thesis, University of Mustafa Kemal, Hatay.
- Ecer, S., (2015) “Longitudinal vibration analysis of straight bars using mixed finite element method. MSc. Thesis, Istanbul Technical University, Istanbul.
- Durbin, F. (1974). Numerical inversion of laplace transforms: An efficient improvement to Dubner and Abate’s Method. The Computer Journal, vol.17, no.4 pp. 371 – 376. Doi: 10.1093/comjnl/17.4.371
- Temel, B., Çalim, F.F. And Tütüncü, N. (2004). Quasi-Static and dynamic response of viscoelastic helical rods. Journal of Sound and Vibration, 271:921 - 935. Doi: 10.1016/S0022-460X(03)00760-0
- ANSYS, Inc Release 15.0 (2013), Canonsburg, PA
Details
| Subjects | Mechanical Engineering |
|---|---|
| Journal Section | Research Article |
| Authors | |
| Publication Date | July 10, 2017 |
| Published in Issue | Year 2017 Volume: 1 Issue: 3 |