TY - JOUR

T1 - Energy expressions and free vibration analysis of a rotating uniform timoshenko beam featuring bendingg-torsion coupling

AU - Kaya, Metin O.

AU - Ozgumus, Ozge Ozdemir

PY - 2010/5

Y1 - 2010/5

N2 - In this study; free vibration analysis of a uniform, rotating, cantilever Timoshenko beam featuring coupling between flapwise bending and torsional vibrations is performed. At the beginning of the study, kinetic and potential energy expressions of a rotating Timoshenko beam having single cross-sectional symmetry are derived by using several explanatory tables and figures. In the following section, Hamiltongs principle is applied to the derived energy expressions to obtain the governing differential equations of motion. The parameters for the hub radius, rotational speed, rotary inertia, shear deformation, slenderness ratio and bendingg-torsion coupling are incorporated into the equations of motion. In the solution part, an efficient mathematical technique, called the differential transform method, is used to solve the governing differential equations of motion. Using the computer package Mathematica, the mode shapes are plotted and the effects of the incorporated parameters on the natural frequencies are investigated. The calculated results are tabulated in several tables and plotted in several graphs. In order to validate the calculated results, the beam is also modeled in the finite-element program ABAQUS. Moreover, two illustrative examples, chosen from open literature, are solved for further validation. Consequently, it is observed that there is a good agreement between the results.

AB - In this study; free vibration analysis of a uniform, rotating, cantilever Timoshenko beam featuring coupling between flapwise bending and torsional vibrations is performed. At the beginning of the study, kinetic and potential energy expressions of a rotating Timoshenko beam having single cross-sectional symmetry are derived by using several explanatory tables and figures. In the following section, Hamiltongs principle is applied to the derived energy expressions to obtain the governing differential equations of motion. The parameters for the hub radius, rotational speed, rotary inertia, shear deformation, slenderness ratio and bendingg-torsion coupling are incorporated into the equations of motion. In the solution part, an efficient mathematical technique, called the differential transform method, is used to solve the governing differential equations of motion. Using the computer package Mathematica, the mode shapes are plotted and the effects of the incorporated parameters on the natural frequencies are investigated. The calculated results are tabulated in several tables and plotted in several graphs. In order to validate the calculated results, the beam is also modeled in the finite-element program ABAQUS. Moreover, two illustrative examples, chosen from open literature, are solved for further validation. Consequently, it is observed that there is a good agreement between the results.

KW - Bendingg-torsion coupling

KW - Differential transform method

KW - Differential transformation.

KW - Rotating coupled Timoshenko beam

UR - http://www.scopus.com/inward/record.url?scp=77952264201&partnerID=8YFLogxK

U2 - 10.1177/1077546309104876

DO - 10.1177/1077546309104876

M3 - Article

AN - SCOPUS:77952264201

SN - 1077-5463

VL - 16

SP - 915

EP - 934

JO - JVC/Journal of Vibration and Control

JF - JVC/Journal of Vibration and Control

IS - 6

ER -