טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentTomer Ganon
SubjectDynamic Analysis and Buckling of a Rotating Variable Cross
Section Beam
DepartmentDepartment of Civil and Environmental Engineering
Supervisor Full Professor Eisenberger Moshe


Abstract

This thesis presents dynamic and buckling analysis of a general variable rotating beam. The beam is assumed to be off-clamped i.e. the axis of rotation does not pass through the beam's clamped end. As a result of the rotation, compression centrifugal force can be generated. The work also includes the solution for a rotating beam clamped at the axis of rotation with a tensile centrifugal force. A Timoshenko beam model was selected for the analysis. The plane of the cross section does not remain perpendicular to the beam axis during vibration. On the other hand the out of plane deformations of the cross section, i.e. the warping, was neglected.

The equations of motion of the problem are composed of six coupled differential equations. The first equation describes the axial behavior, the next four are for the bending and shear of the beam, in the two directions, and the sixth equation is for the torsion response.

The natural frequencies, mode shapes, and critical rotational speed that will cause buckling were developed using the exact element method combing the dynamic stiffness matrix. The method produces exact results for the beam (up to the accuracy of the machine) without the need to divide it to several secondary elements. The beam element has a general variable shape. The dynamic stiffness matrix is derived from the shape function using the finite elements technique. The exact shape function of the element is achieved by an infinite polynomial (till the desired accuracy).

In order to demonstrate the solution procedure numerous beams with different sizes, variable or uniform cross sections, and different combinations of boundary conditions were analyzed. Also an investigation of the Coriolis Effect influence on the beam response was carried out. The beam was analyzed for a number of rotation speeds and compared with the results of previous research findings. Many new results are presented.