The Transition Curve from Plate-Like to Beam-Like Behaviors in the Free Vibration of a Beam with both ends fixed and Variable Varied Mechanical Properties

Abstract

This research studied and analyzed free vibration of a thin-plate beam with both ends fixed.The aspect ratio of the beam were assigned values of 0.25 to 20 while the thickness of the beam wasfixed at 5 millimeters. Analysis of the beam was performed by using the finite element method of theANSYS program. In the analysis, mechanical properties of the beam were varied to determine thenatural frequencies and mode shapes. Results of the analysis were then used to study the influence ofmechanical properties on natural frequency and mode shape by using the Multivariate Ratio ofPolynomial Fit. The results of this study several that mode shape and the transition cure may be usedto differentiate between the plate-like and the beam-like behaviors of the beam. The relationshipbetween the natural frequency and the aspect ratio gives the transition curve of plate-like behavior andbeam-like behaviors. Since the mechanical properties of the beam material is directly related with thenatural frequency, the relationship between the frequency, the geometric ratio and the mechanicalproperties were established.