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Extended Mode Analysis

PERMAS-DEVX Extended Mode Analysis

This module provides additional methods for dynamic eigenvalue analysis:

  • Dynamic condensation
  • Complex mode analysis
  • Eigenfrequencies over rotational speed for rotating structures

Dynamic Condensation

Two methods are available for dynamic condensation:

  • Craig-Bampton method (CB condensation),
  • Mixed-Boundary Craig Bampton method(MBCB condensation).

Craig Bampton method

The Craig-Bampton method uses fixed-interface vibration modes and the static deflections due to unit displacements of the interface degrees of freedom for the dynamic reduction of substructures (CB condensation). Like for the Guyan’s reduction, an explicit and an iterative scheme is available in order to achieve good performance (see also page 47).

The functionality may be summarized as follows:

  • Structural dynamics
  • Acoustics
  • Coupled fluid-structure acoustics

Two condensation options are available for coupled fluid-structure acoustics (see also page 79):

  • Dry Interface
    • Solution of a coupled eigenvalue problem on subcomponent level, i.e. isolation of the acoustic component. External modes are coupled modes.
    • Global solution may be a mechanical vibration analysis.
  • Wet Interface
    • Separate computation of mechanical and acoustic modes on subcomponent level.
    • Global solution is a coupled vibration analysis.
    • Condensation of the fluid-structure interface can also be made.

Mixed-Boundary Craig Bampton method

The method allows for free (or mixed) boundary conditions to derive the vibration modes (MBCB condensation). The corresponding static deflections are derived using inertia relief. This method is advantageous when the condensation is used for structures with free boundaries, because the condensation method can represent the boundary conditions. In such cases, less number of required modes and a higher accuracy can be expected from the Mixed-Boundary Craig-Bampton method compared to the classical Craig-Bampton method.
The above mentioned “dry” condensation of parts with enclosed fluids also works with the Mixed-Boundary Craig-Bampton method.

Complex Mode Analysis

This includes the calculation of complex eigenvalues and eigenvectors in modal coordinates. This method is based on a previous solution of the real eigenvalue task.
The results of this analysis are as follows:

  • Frequency
  • Complex eigenvalues
  • Complex eigenfrequencies (damping coefficient and circular frequency)
  • Equivalent viscous damping ratio
  • Complex mode shapes with physical and modal representation. The modal displacements of the complex modes represent the modal participation of the underlying real modes.

A suitable post-processor (like MEDINA) can be used to visualize and animate complex mode shapes.

Eigenfrequencies of Rotating Systems

For rotational systems it is often required to generate a so-called Campbell diagram, which relates the eigenfrequencies to the rotational speed. The values of such a diagram can be generated automatically in one single run. From these values all frequencies of interest can be selected for a subsequent frequency response analysis.

For rotating structures, any number of rotational speeds is defined in a separate input. A reference rotational velocity is used in the static pre-run. From this pre-run, additional matrices are built for the reference rotational velocity. The specified rotational velocities are used to scale the additional matrices during dynamic response analysis. This procedure makes the generation of Campbell diagrams very efficient and the response analysis of rotating structures is facilitated.