Dynamic Analysis of a Cantilever Beam with an Offset Mass

Abstract

This thesis investigates the dynamic characteristics of a cantilever beam with an offset mass. Starting with a linear system consisting of a cantilever beam with a tip mass, Hamilton's principle is utilized to derive the equation of motion for the system, then similar method is applied to a cantilever beam with an offset mass. The equation of motion and boundary conditions are nondimensionalized to simplify the situation. The theoretical trend of natural frequency is also derived to show the effects of mass ratio, offset ratio and moment of inertia. Experimental results are derived using a system consisting of a base, a 3D-printed beam and several attachments. After comparing with theoretical data, several factors including damping ratio, moment of inertia and Poisson's ratio are taken into consideration. Both damping ratio and moment of inertia have very little effect and Poisson's ratio has opposite influence on the results. Explanation for the deviation lies on the isotropy of 3D-printed beam, which also puts forward a question on the qualification of using 3D-printed structures for dynamical analysis.