Driving Point Residue algorithm

The driving point residue (DPR) algorithm searches for the most efficient DOF in exiting the different modes. In the FRF model, the residue r_{ij,k} between the locations i and j for mode k is computed as:

r_{ij,k} = a_k \nu_{ik} \nu_{jk}

where:

• a_k is a scaling factor.

• \nu_{ik} \nu_{jk} are the modal vector components in both locations.

If the structure is proportionally damped, then the modal vectors of the structure are real, while the residues are imaginary. Therefore, the scaling factor a_k is also imaginary and defined as:

a_k = \frac{1}{2j\omega_{dk}m_k}

The magnitude of the driving point residue is:

|r_{ik}| = \frac{\nu_{ik}^2}{2\omega_{dk}}

where the modal mass m_k is equal to one to scale the modes.

To capture the structural acceleration response, the DPR is computed as:

|r_{ik}| = \frac{a_{ik}^2}{2}\cdot\omega_{dk}.

For each node of the exciter input, the solver calculates the DPR for all selected modes. For each node, the algorithm defines minimum, maximum, average, and weighted average residue values. The weighted average DPR is defined as the average DPR multiplied by the minimum DPR. This weighted value is low, even if the DPR is high on average, except for one mode. Using the computed values, the algorithm defines how well the modes of interest are excited by the different nodes from the exciter group.

The DPR algorithm helps to identify the DOFs with a relatively high average value across the modes so that all modes are excited from these DOFs. It also helps to identify the DOFs with a sufficiently high minimum value, to excite the weakest mode.

Learn more

Pre-test solution process

Correlation solution process

Look up more details

Modal Analysis

Converting complex modes to real modes

Accounting for repeated modes

Modal Scale Factor (MSF)

Modal Assurance Criteria (MAC)

Coordinate MAC (COMAC)

Cross-orthogonality (X-Ortho)

Frequency Response Assurance Criterion (FRAC)

Min-MAC algorithm

MODMAC algorithm

Normal Mode Indicator Function (NMIF) algorithm

Scientific literature references for correlation

Quick links

Command reference

Pre/Post video examples

Bulk Entry Descriptions

Simcenter 3D tutorials

Browse Simcenter 3D help by product area

Driving Point Residue algorithm, Simcenter 3D 2021.1 Series

© 2020 Siemens

window.mainLanguage="en_US"

window.delivId=""

window.projectId=""

MathJax.Hub.Config({ TeX: { extensions: ["autoload-all.js"] }, tex2jax: { displayMath: [ ] }, "SVG": { scale: 125 } });