Analytic solutions for vibration characteristics of a multi-beam structure

作者：Lee Kyung Taek^*

来源：International Journal of Mechanical Sciences, 2010, 52(7): 952-969.

DOI：10.1016/j.ijmecsci.2010.03.012

• Beam
• Tip body
• Characteristic equation
• Pure-axial (PA) vibration
• Coupled bending-torsional (CBT) vibration
• Coupled axial-bending (CAB) vibration

The first purpose of this paper is to mathematically analyze the vibration characteristics of four parallel and uniform beams that are joined by a tip body at their free ends. This beam structure is often found in many mechanical structures such as robots, space constructions, and optical pickup actuators in optical disc drives (ODDS). To analyze the vibration characteristics of this beam structure, this paper considers the motions in all six directions that are coupled to each other. Mathematical expansion using the energy conservation law applied to this beam structure yields four characteristic equations, which are related to a pure-axial (PA) vibration, a coupled bending-torsional (CBT) vibration, and two coupled axial-bending (CAB) vibrations. In addition, the correctness of the equations is verified by showing that the natural frequencies from these equations match those from a finite element (FE) analysis. <br xmlns:set="http://exslt.org/sets">The second purpose of this paper is to contribute to the performance improvement of an optical pickup actuator for ODDs by analyzing key parameters of the characteristic equations. This is one of the few papers that analytically derives solutions for the natural frequencies and modes of optical pickup actuators in all six directions. From the perspective of practical usefulness for the design of optical pickup actuators, this paper describes how to reduce rotation in the two CAB beam vibrations by investigating the relationship between design parameters and rotating properties.

• 出版日期2010-7