I am trying to model the free vibration of a simply supported beam with an axial loading to see the variation of eigenfrequencies when varying the axial loads.
In order to consider the stiffening effect of the axial load in the solution of the eigenvalue problem (free vibration) you need to use the tangent stiffness matrix in the eigensystem. In order to do that in Abaqus you need to generate two analysis steps, the first step is for the axial load and MUST have the NLGEOM option activated (this activates the geometrical nonlinear formulation), the second step is the frequency extraction step. The inp file should look something like this like this:
*STEP, NAME=axialload, NLGEOM=YES
*STATIC, DIRECT
Data line to define direct time incrementation
*BOUNDARY
Data lines to prescribe zero-valued or nonzero boundary conditions
*CLOAD and/or *DLOAD
Data lines to specify loads
*TEMPERATURE and/or *FIELD
Data lines to specify values of predefined fields
*END STEP
*STEP, NAME=frequencies
*FREQUENCY, EIGENSOLVER=LANCZOS
Data line to control eigenvalue extraction
....
*END STEP
I agree with Martin Saravia but instead of his suggested step two, I would like to suggest performing a "Natural frequency analysis" where you could find under the Linear perturbation procedure type.
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