Free Vibration Characteristic of a Rotating Cantilever Beam With Tip Mass

Abstract

In many cases, vibration is a serious problem, undesirable, wasting energy and creating unwanted sound. Transfer Matrix Method for Multibody Systems (MSTMM) is one of the sophisticated methods that can be used efficiently to (1) Model large systems with a large number of subsystems and rigid-flexible structures, and (2) Calculate the vibration characteristics and dynamic responses of the multibody systems. The size of matrices in MSTMM remains small regardless of the number of elements in the model. Having smaller matrix sizes helps to have less computational expense leading to a faster answer. Based on the MSTMM advantages, vibration characteristic of a rotating cantilever beam with an attached tip mass is modeled and simulated in the present paper while the beam undergoes flapwise vibration. This system can be thought of as an extremely simplified model of a helicopter rotor blade or a blade of an auto-cooling fan. The overall transfer equation in the MSTMM context only involves boundary state vectors, whereas the state vectors at all other connection points do not appear. The state vectors at the boundary include the displacements, rotation angles, bending moments and shear forces. These are partly known and partly unknown. The eigenvalue problem is solved by using Frobenius method of solution in power series. Recursive eigenvalue search algorithm is used to determine the system frequencies. Numerical examples are performed to validate with those published in the literature and produced by Workbench ANSYS.