Dynamic analysis of cantilever beam and its experimental validation

Abstract

Beam is an inclined or horizontal structural member casing a distance among one or additional supports, and carrying vertical loads across (transverse to) its longitudinal axis, as a purlin, girder or rafter. In Euler – Bernoulli beam theory, shear deformations and rotation effects are neglected, and plane sections remain plane and normal to the longitudinal axis. In the Timoshenko beam theory, plane sections still remain plane but are no longer normal to the longitudinal axis. In this paper, we will be formulating the equations of motion of a free cantilever beam. The natural frequency of continuous beam system will be found out at different variables of beam using ANSYS 14.0. The results will be compared further using experimentation by free vibration of a cantilever beam. Using those results, we will be able to compare the parameters in Euler-Bernoulli and Timoshenko beam. Free vibration takes place when a system oscillates under the action of forces integral in the system itself due to initial deflection, and under the absence of externally applied forces. The system will vibrate at one or more of its natural frequencies, which are properties of the system dynamics, established by its stiffness and mass distribution. The comparative displacement alignment of the vibrating system for a particular natural frequency is known as the Eigen function in continuous system. The mode shape of the lowest natural frequency (i.e. the fundamental natural frequency) is termed as the fundamental (or the first) mode frequency. The displacements at some points may be zero which are called the nodal points. Generally nth mode has (n-1) nodes excluding the end points. The mode shape varies for different boundary conditions of a beam.