VM-WB-MECH-003

VM-WB-MECH-003
Modal Analysis of Annular Plate

Overview

Reference:	Blevins, R. J. (1979). Formula for Natural Frequency and Mode Shape. Van Nostrand Reinhold Company Inc. (Table 11-2, Case 4, p. 247).
Solver(s)	Ansys Mechanical
Analysis Type(s):	Free Vibration Analysis
Element Type(s):	Solid

Test Case

An assembly of three annular plates has cylindrical support (fixed in the radial, tangential, and axial directions) applied on the cylindrical surface of the hole. Sizing control with element size of 0.5" is applied to the cylindrical surface of the hole.

Find the first six modes of natural frequencies.

Material Properties

Geometric Properties

E = 2.9008e7 psi

ν = 0.3

ρ = 0.28383 lbm/in³

Inner diameter of inner plate = 20"

Inner diameter of middle plate = 28"

Inner diameter of outer plate = 34"

Outer diameter of outer plate = 40"

Thickness of all plates = 1"

Analysis Assumptions and Modeling Notes for Ansys Mechanical

The following figure shows the finite element model in Ansys Mechanical:

Figure 3: Ansys Mechanical Schematic

Results Comparison for Ansys Mechanical

Results	Target	Mechanical	Error (%)
1st Frequency Mode (Hz)	310.911	310.2	-0.23
2nd Frequency Mode (Hz)	318.086	315.6	-0.78
3rd Frequency Mode (Hz)	318.086	315.65	-0.77
4th Frequency Mode (Hz)	351.569	346.85	-1.34
5th Frequency Mode (Hz)	351.569	347.14	-1.26
6th Frequency Mode (Hz)	442.451	437.3	-1.16