VM-WB-MECH-010

VM-WB-MECH-010
Modal Analysis of a Rectangular Plate

Overview

Reference:

Blevins, R.D. Formulas for Natural Frequency and Mode Shape. Van Nostrand Reinhold Company Inc. (Table 11-4, Case 11, p. 256).

Solver(s):Ansys Mechanical
Analysis Type(s):Free Vibration Analysis
Element Type(s):Shell

Test Case

A rectangular plate is simply supported on both the smaller edges and fixed on one of the longer edges as shown below. Sizing mesh control with element size of 6.5 mm is applied on all the edges to get accurate results.

Find the first five modes of natural frequency.

Figure 10: Schematic

Schematic

Material PropertiesGeometric PropertiesLoading
E = 2e11 Pa
ν = 0.3
ρ = 7850 kg/m3
Length = 0.25 m
Width = 0.1 m
Thickness = 0.005 m

Results Comparison

ResultsTargetMechanicalError (%)
1st Frequency Mode (Hz)595.7590.03-0.952
2nd Frequency Mode (Hz)1129.551118.4-0.987
3rd Frequency Mode (Hz)2051.792038.1-0.667
4th Frequency Mode (Hz)2906.732879.3-0.944
5th Frequency Mode (Hz)3366.483350-0.490