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 |
| Input Files: | Link to Input Files Download Page |
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.
| Material Properties | Geometric Properties | Loading |
|---|---|---|
|
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.
