Nodal position control of bending mode of three- dimensional beam structures based on visualization of eigenmode formation

In a conceptual design phase of noise and vibration performance, CAE (Computer Aided Engineering) is frequently introduced to design appropriate properties of individual members. One of the most commonly used computational methods for conceptual design is the eigenvalue analysis of finite element (FE) models. However, since this method ignores formation process of natural vibration, structural engineers cannot adequately comprehend the mechanisms of eigenmode formation in a sense of the superposition of waves. This paper proposes a design method for nodal position control of a mode shape based on three-dimensional wave analysis. First, a ray trace method is introduced to comprehend the eigenmode formations by means of superposition of transmitted and reflected waves in a general three-dimensional beam structure. Summations of computed wave vectors coincide with modal vectors of the structure. The method was then used to discuss the formation of bending mode shape of a three-dimensional beam structure of block geometry. Finally, it is shown that nodal position of bending mode shape of interest can be controlled based on phase changes of bending propagative waves.