In-Plane Free Vibration Frequencies of Stepped Circular Beams

Year 2019, Volume: 1 Issue: 1, 1 - 7, 15.01.2019

Timuçin Alp Aslan , Beytullah Temel , Ahmad Reshad Noori

Abstract

 In this study, in-plane natural frequencies of stepped circular beams are presented. The material of the beam is considered to be isotropic, homogeneous and elastic. The effects of shear deformation and rotary inertia are considered in the necessary assumptions and formulations. The obtained canonical form of governing equations is solved numerically by the complementary functions method (CFM) in the Laplace domain. To obtain the natural frequencies of the considered structures the Laplace parameter is replaced with the parameter of free vibration. The 5^th order Runge Kutta (RK5) algorithm is applied to solve the initial-value problem based on the CFM. To examine the in-plane free vibration of Timoshenko beams with stepped circular cross-section a program is coded in FORTRAN. In order to demonstrate the accuracy of the current scheme, present results are compared with those of literature.  The accuracy and efficiency of the presented results are observed.

Keywords

Free vibration; Stepped beams with circular Cross-section; Laplace transform.

In-Plane Free Vibration Frequencies of Stepped Circular Beams

Abstract

ABSTRACT: In this study, in-plane natural
frequencies of stepped circular beams are presented. The material of the beam
is considered to be isotropic, homogeneous and elastic. The effects of shear
deformation and rotary inertia are considered in the necessary assumptions and
formulations. The obtained canonical form of governing equations is solved
numerically by the complementary functions method (CFM) in the Laplace domain.
To obtain the natural frequencies of the considered structures the Laplace
parameter is replaced with the parameter of free vibration. The 5^th
order Runge Kutta (RK5) algorithm is applied to solve the initial-value problem
based on the CFM. To examine the in-plane free vibration of Timoshenko beams
with stepped circular cross-section a program is coded in FORTRAN. In order to
demonstrate the accuracy of the current scheme, present results are compared
with those of literature.  The accuracy
and efficiency of the presented results are observed.

Keywords

Free vibration; Stepped beams with circular Cross-section; Laplace transform.

References

• [1] Aktan H, 2008.In-Plane dynamic analysis of circular beams. MSc. Thesis, Istanbul Technical University, Istanbul.
• [2] Çoban M, 2008.Out-Of-plane dynamic analysis of curved beams using mixed finite element method. MSc. Thesis, Istanbul Technical University, Istanbul.
• [3] Tong X, Mrad N, Tabarrok B, 1998. In-Plane vibration of circular arches with variable cross-sections. J. Sound Vib. 212 (1) 121-140.
• [4] Huang C S, Tseng Y P, and Lin C J, 1998. In-plane transient responses of arch with variable curvature using dynamic stiffness method. J. Eng. Mech. 124:826-835.
• [5] Wu J S, and Chiang L K, 2004. A new approach for free vibration analysis of arches with effects of shear deformation and rotary inertia considered. J. Sound and Vib. 277 49-71.
• [6] Tüfekci E, and Arpacı A, 1998. Exact solution of in-plane vibrations of circular arches with account taken of axial extension, transverse shear and rotatory inertia effects. J. Sound and Vibration, 209(5), 845-856 .
• [7] Tüfekci E, Özdemirci Ö, 2006. Exact solution of free in-plane vibration of a stepped circular arch. Journal of Sound and Vibration, 295, 725-738.
• [8] Lee W Y, Lee Y J, 2016. Free vibration analysis using the transfer-matrix method on a tapered beam. Computers and Structures 164 (2016) 75–82.
• [9] Temel B, Aslan T A, and Noori A R., 2017. An efficient dynamic analysis of planar arches. European Mechanical Science, vol. 1(3), pp. 82-88.
• [10] Noori A R, Temel B, and Aslan, T A, Transient analysis of in-plane loaded elastic stepped circular arches. International Conference on Advances and Innovations in Engineering (ICAIE), 2017 May 10-12, p.721-728.
• [11] Aslan T A, Noori A R, Temel B, Forced vibration of out of plane loaded stepped circular rods. International Conference on Civil and Enviromental Engireening, May 8-10, 2017 , Nevsehir, Turkey, 2062-2074.
• [12] Noori A R, Aslan T A, Temel B, Damped transient response of in-plane and out-of-plane loaded stepped curved rods. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 40 1-24, 2018.
• [13] Chapra S C, and Canale, R P, 1998.Numerical Methods for Engineers With Programming and software Applications. McGraw-Hill Books.
• [14] ANSYS Swanson Analysis System, Inc., 201 Johnson Road, Houston, PA15342-1300, USA.