VM-WB-MECH-073

VM-WB-MECH-073
Modal Analysis of a Cyclic Symmetric Annular Plate

Overview

Reference:

Blevins, R. D. (1979). Formulas for Natural Frequency and Mode Shape (pp. 246-247, 286-287). New York, NY: Van Nostrand Reinhold Publishing Inc.

Solver(s): Ansys Mechanical
Analysis Type(s): Mode-Frequency Analysis
Element Type(s): Solid

Test Case

The fundamental natural frequency of an annular plate is determined using a mode-frequency analysis. The lower bound is calculated from the natural frequency of the annular plates that are free on the inner radius and fixed on the outer. The bounds for the plate frequency are compared to the theoretical results.

Figure 98: Problem Sketch

Problem Sketch

Analysis

According to Blevins, the lower bound for the fundamental natural frequency of the annular plate is found using the formula presented in Table 11-2 of the reference:

(1)

where:

λ2 = 4.80

Material PropertiesGeometric PropertiesLoading
E = 7.1 x 105 kg/cm2
ν = 0.3
ρ = 2.79 x 10 -9 kg/cm2
γ = 1.415 x 10-6 kg-sec2/cm3
Outside Radius (a) = 50 cm
Inside Radius (b) = 18.5 cm
Thickness (h) = 0.5 cm
Sector Angle = 30°
 

Analysis Assumptions and Modeling Notes for Ansys Mechanical

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

Figure 99: Ansys Mechanical Schematic

Ansys Mechanical Schematic
Ansys Mechanical Schematic

Results Comparison for Ansys Mechanical

ResultsTargetMechanicalError (%)
Frequency (Hz)23.3823.075-1.306