Adaptive Polynomials for the Vibration Analysis of an L-Type Beam Structure with a Free End

Abstract

Vibration analysis using the component mode method has been less popular than before, since computers are powerful enough to solve complicated structures by a single large finite model. However, many structural engineers designing local structures on a ship still need simple tools to check anticipated vibration problems during their design work. Since most of local structures on a ship are simple enough to consist of several substructures, the component mode method could be of use as long as good, natural mode functions can be provided so that reasonable natural frequencies can be yielded. In this study, since mode polynomials based on static deflection of cantilever beams fail to work to cover the various configurations of L-type beams with a free end, two alternatives are suggested. One is based on more flexible mode functions—we call them adaptive polynomials. The other is a purely mathematical approach, which makes realistic mode functions unnecessary. Suggested alternatives yield very good numerical results.

Keywords

• L-type beam structure
• adaptive polynomials
• pure mathematical functions