In-Plane Free Vibration Frequencies of Stepped Circular Beams

Yıl 2019, Cilt: 1 Sayı: 1, 1 - 7, 15.01.2019

Timuçin Alp Aslan Beytullah Temel Ahmad Reshad Noori

Öz

 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.

Anahtar Kelimeler

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

In-Plane Free Vibration Frequencies of Stepped Circular Beams

Öz

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.

Anahtar Kelimeler

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

Kaynakça

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