Vibration Transmission from a Machine with Three Degree of Freedoms to Beam Structures by Dynamic Stiffness Method

Abstract

The dynamic stiffness method (DSM) is proposed for vibration transmission from a machine with three degree of freedoms (DOFs) to its supporting beam structures. The machine is idealized as a rigid mass with three major degrees of freedom, namely, heave, roll, and pitch. It implies that the moments of inertia and torques due to unbalanced parts can be taken into consideration. The three types of vibration within beam structures, i.e., bending, longitudinal, and torsional motions, are formulated in terms of dynamic stiffness matrices. The finite element techniques can be applied similarly to assemble the developed dynamic stiffness matrices of both the machine and its supporting beam structures. A beam-like raft carrying a machine is designed to illustrate the accuracy of the proposed method in numerical simulation, where the differences brought by three-DOF modeling in vibration transmission analysis are discussed as well. This work would provide a novel and easy-to-use alternative to the existing mobility method and finite element method due to low discretization requirements, high efficiency, and high accuracy.