# OS-E: 0305 Preloaded Modal Frequency Response Analysis

A Preloaded Modal Frequency Response Analysis of folding blade shaft which is mounted on the bolted flange.

## Model Files

Refer to Access the Model Files to download the required model file(s).

The model file used in this example includes:

## Model Description

In the first subcase a pre-tensioning force of 3.5E3 Newton’s is applied on 3 bolts that are connected to the flange. In the second subcase a Clamping pressure of 1E4 MPA is applied on the flange and 1MPA is applied on the folding blades. In the third subcase a tip load is applied on the flat surface of the blade.
Case 1
Nonlinear Static Analysis
Bolt Pretension
Case 2
Nonlinear Static Analysis
Pressure Load with CNTNLSUB and STATSUB(PRETENS)
Case 3
Modal Frequency Response Analysis
In Modal Frequency Response Analysis, the modal solution is performed using AMSES.
FE Model
Bolts
CBEAM
CHEXA
CTETRA
The linear material properties are:
MAT1
Young’s Modulus
2.1E5
Poisson's Ratio
0.3
Initial Density
7.8E-9

## Results

The displacement results on the bolts for subcase 1 and read the .PRET file and review the results. In Figure 2, observe the displacement results snapshot from all the 3 subcases.

In subcase 3, the preloading is captured by a geometric stiffness matrix ${K}_{G}$ which is based on the stresses of the preloading nonlinear static subcase 2. In prestressed analysis, this geometric stiffness matrix is augmented with the original stiffness matrix $K$ of the (unloaded) structure.

In this model since there is contact, the contact status can be carried over from the preloading subcase 2 to the preloaded subcase 3.
For comparison study, when this example model is run with and without STATSUB (Pre-Load) in subcase 3, notice the different in the frequencies of the eigenvector in the .out files. In the Modal Frequency Response Analysis without Preload you have rigid body modes as the contact between the bolts and the flange has not been established.
Also, when you plot the MFREQ results at frequency 300Hz, notice the difference between the mode shape.