# 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:

PRELOAD_NLSTAT_MFRF.fem

## Model Description

The operational loading involves three steps (or subcases).

**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)

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

**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.