M.Sc Thesis


M.Sc StudentOr Yogev
SubjectExperimental and Analytical Investigation of Dynamic
Lateral Torsional Post-Buckling of an Elastic
Beam-Mass System Using the Theory of a
Cosserat Point
DepartmentDepartment of Mechanical Engineering
Supervisors Full Professors Rubin Miles
Full Professors Bucher Izhak
Full Professors Flashner Henryk


Abstract

            The purpose of this research was to investigate the phenomena of  dynamic lateral torsional post-buckling of a beam-mass system. The thesis is divided into two parts: an experimental part and an analytical part.                  

            The experimental system was designed to cause dynamic lateral torsional buckling to occur at frequencies distinct from those of small deformation free vibrations.  A thin beam was clamped to the shaft of a motor at one of its ends and a mass was attached to its other end.  The amplitude and frequency of the rotation of the motor shaft were controlled.  At low excitation frequencies and amplitudes the beam-mass system remained in the stiff bending plane.  At large enough excitation amplitudes and/or frequencies the shear force that the mass exerted on the beam was sufficient to cause the beam to buckle out-of its stiff bending plane.  The resulting periodic motion occurred at different excitation amplitudes and frequencies and it was observed to be quite stable. The main parameters that were measured were the beam's deformation and the torsional angle of the mass.

            In the theoretical part of this research, the Cosserat beam element was used to model the experimental results. An analytical expression for the tangent stiffness of the algebraic equations associated with the Newmark approximation was developed for the iterative solution using the Newton-Raphson method.  Simulations of these equations were able to predict the dynamic buckling phenomena and also the fact that two distinct modes of vibration can occur at the same excitation amplitude and frequency.