# 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

Before you begin, copy the file(s) used in this example to
your working directory.

## Model Description

The operational loading involves three steps (or subcases).

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 1 MPa 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
- With STATSUB (PRELOAD)

In Modal Frequency Response Analysis, the modal solution is performed using
AMSES.

**FE Model**- Bolts
- CBEAM
- Flange and Blade
- 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.