Dynamic FE Analysis

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Dynamic FE Analysis
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Why?

• Modal analysis
• Determines a structures vibration
  characteristics natural frequencies and mode
  shapes

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Why?

• Transient analysis
• Used when loading in time dependent e.g. slamming
  loads, rotating machinery

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Modal Analysis
If there is no damping and no applied loading,
the equation of motion in matrix form reduces to
where
Where
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Modal Analysis
which may be solved using a finite element
approach to obtain the dry natural frequencies,
wi (where i 1, 2, 3), and principal mode
shapes. For the wet modes, where the
fluid-structure interaction is included, the
equation becomes
where
Where MS represents the ship displacement
MA is the ship added mass, representing
the inertia properties of the
surrounding water.
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Modal Analysis
Note that
where
Where k is structural stiffness m
is structural mass
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Geometry and Meshing

• Same considerations as a static analysis
• include details to sufficiently represent model
  geometry
• fine mesh required to resolve complex shapes
• Both Youngs Modulus and Density required
• Linear elements and material properties only.
  Nonlinearities are ignored

where
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Analysis Type
Analysis Type is modal Solution gt Analysis Type
gt New Analysis gt Modal
where
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Analysis Options
Solution gt Analysis Type gt Analysis Options
where
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Analysis Options

• Mode extraction options
• Block Lanczos generally recommended
• Number of nodes - specify number of nodes to be
  extracted
• Mode expansion options
• Expanding modes allows the user to view modes in
  post processor usually expand same number as
  extracted
• Default settings are usually sufficient

where
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Loading
Only displacement constraints are valid in modal
analysis If no displacement constraints rigid
body motions will be calculated (zero frequency)
where
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Post Processing
Post Processor gt Results Summary
where
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Post Processing
Read results for subset Post Processor gt Read
Results Then plot the deformed shape
where
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Post Processing
Results may be animated Utility menu gt Plot
Ctrls gt Animate gt Mode Shape
where
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Transient Analysis
A transient analysis is more involved than a
static or harmonic analysis. It requires a good
understanding of the dynamic behavior of a
structure. Therefore, a modal analysis of the
structure should be initially performed to
provide information about the structure's dynamic
behavior.
where
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Transient Analysis

• The Full Method
• This is the easiest method to use.
• All types of non-linearities are allowed.
• It is however very CPU intensive to go this route
  as full system matrices are used.

where
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Transient Analysis

• The Reduced Method
• This method reduces the system matrices to only
  consider the Master Degrees of Freedom (MDOFs).
• Because of the reduced size of the matrices, the
  calculations are much quicker.
• However, this method handles only linear
  problems.

where
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Transient Analysis

• The Mode Superposition Method
• This method requires a preliminary modal
  analysis, as factored mode shapes are summed to
  calculate the structure's response.
• It is the quickest of the three methods, but it
  requires a good deal of understanding of the
  problem at hand.

where
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Load Time History
Time step, dt 1/20f Where f is the smallest
modal frequency to be captured
where
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Transient Analysis Options
Analysis Type is modal Solution gt Analysis Type
gt New Analysis gt Modal
where
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Transient Analysis Options
Option for method type
where
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Transient Analysis Options
Define degrees of freedom for consideration Solut
ion gt Master DOFs gt User Selected gt Define
where
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Define Loads Solve
Define time step Solution gt Load Step Opts gt
Time/Frequenc gt Time - Time Step .. Write Load
Step File Solution gt Load Step Opts gt Write LS
File Solve Solution gt Solve gt From LS Files

where
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Post Processing
Timehist Postpro gt Results Summary Able to plot
results vs. frequency and time Note also able
to include damping term
where