Dynamic > F-01 (Simple 2D Frame Vibration)

Objective

To verify the behavior of beam element vibration

Problem Description

A right-angle frame [Ref 1] vibrates under its own weight as shown below.

Material properties: E = 2e11 Pa, ν = 0.29, ρ = 7860 Kg/m3

Section properties: square section 100 x 100 mm

F-01 (Simple 2D Frame Vibration)1

Finite Element Model

50 beam elements

Model type: 2D Frame (shear deformation considered)

Results

The mode frequencies are given by [Ref 1]

Unit: mode frequency - Hz

First Four Mode Shapes:

F-01 (Simple 2D Frame Vibration)2

Mode Shape 1

F-01 (Simple 2D Frame Vibration)3

Mode Shape 2

F-01 (Simple 2D Frame Vibration)4

Mode Shape 3

F-01 (Simple 2D Frame Vibration)5

Mode Shape 4

Comments

The vibration frequencies given by ENERCALC 3D are very close to the referenced values.

Reference

[1]. Cook, Malkus, Plesha, Witt, “Concept and Applications of Finite Element Analysis” 4th Edition, pp436, John Wiley & Sons, Inc., 2002