VM-LSDYNA-SOLVE-032

VM-LSDYNA-SOLVE-032
Fundamental Frequency of a Simply-Supported Beam

Overview

Reference: Thompson, W.T. (1965). Vibration theory and applications (2nd Printing). Prentice-Hall. p.18, example 1.5-1.
Analysis Type(s): Modal Analysis
Element Type(s): Beam

Test Case

Determine the fundamental frequency f of a simply supported beam of 80 in (𝓁) and uniform cross-section of 4 in2 (A).

This test case also appears in the Workbench Verification Manual. See VM-WB-MECH-043.

Figure 117: Problem Sketch

Problem Sketch

Material PropertiesGeometric PropertiesLoading

E = 3x107 psi

γ = 0

ρ = 7.33 x 10-4 lbf-s²/in

𝓁 = 80 in

A = 4 in2

h = 2 in

I = 1.3333 in4

—

Analysis Assumptions and Modeling Notes

When setting boundary conditions, keyword BOUNDARY_SPC_SET is used to restrict the nodes at the ends of the beam (nodes 19 and 50) from moving in the X, Y, and Z directions.

In LS-DYNA, a beam-type model (using the SECTION_BEAM keyword) is used by selecting the section type, with a value for ELFORM of 1 (using the Hughes-Liu formulation with cross-section integration) and a value for QR/IRID of 2 (2 x 2 Gauss quadrature). To find the fundamental frequency, a total of six modes will be considered by changing the value of NEIG in CONTROL_IMPLICIT_EIGENVALUE. In Figure 119, the resulting mesh is shown.

Figure 118: Problem setup

Problem setup

Figure 119: Mesh model

Mesh model

Results Comparison

The LS-DYNA results are nearly identical to the theoretical results.

ResultsTarget LS-DYNASolverError (%)
Fundamental frequency (Hz)28.76628.670.335