Validation Case: Modal Analysis of a Cantilever Beam

This article is part of the series of FEA validation cases performed using OnScale Solve.

In this case, modal analysis is performed on a cantilever beam which is fixed at one end and free at the other. The aim of this FEA analysis is to find the first 5 natural frequencies of the beam.

The FEA model and the resulting comparison of the simulation results against the analytical calculations validates the use of following conditions for modal analysis in Solve: 

• Restraint

Geometry:

Download the geometry here used for this analysis: 

• Geometry Dimensions
  • Cross Sectional Area: 0.04 m by 0.04 m
  • Length of Part (l): 1 m

Material:

• Steel
  • Density (ρ) = 7700 kg/m3
  • Young’s Modulus (E) = 480 GPa
  • Poisson’s Ratio (ν) = 1e-6

Physics:

• Restraint (Fixture) 
  • Face1 ( ABCD)

Meshing

OnScale Solve generated the mesh automatically and the meshing statistics, at the time of writing this document, are as follows:

Mesh Quality: Medium

Analysis

The analysis type can be selected in the Simulator section.

Mechanical Analysis Type: Modal

Definition: Modes

Number of Modes: 5

Reference Solution:

The natural frequency (in cycles per second) of a cantilever beam is given by:

where K_n is the constant where n refers to the mode of vibration, g is the gravitational acceleration, E is the Young’s Modulus, I is the area moment of inertia, w is the weight of the beam and l is the length of the beam.  

For this case these values are as follows:

g = 9.81 m/s²

E = 480 GPa

I = 2.1333e-7 m⁴

w = 120.8592 kgm/s²

l = 1 m                                        

The mode vibration constants for the first five modes are given by:

Results Comparison

The table below compares the values obtained using the analytical methods described above and the FEA analysis performed using OnScale Solve.