Vibration Analysis

1
Vibration Analysis

• Chapter Five

2
Chapter Overview

• In this chapter, performing free vibration
  analyses in Simulation will be covered. In
  Simulation, performing a free vibration analysis
  is similar to a linear static analysis.
• It is assumed that the user has already covered
  Chapter 4 Linear Static Structural Analysis prior
  to this section.
• The following will be covered
• Free Vibration Analysis Procedure
• Free Vibration with Pre-Stress Analysis Procedure
• The capabilities described in this section are
  generally applicable to ANSYS DesignSpace Entra
  licenses and above.
• Some options discussed in this chapter may
  require more advanced licenses, but these are
  noted accordingly.
• Harmonic and nonlinear static structural analyses
  are not discussed here but in their respective
  chapters.

3
Basics of Free Vibration Analysis

• For a free vibration analysis, the natural
  circular frequencies wi and mode shapes fi are
  calculated fromThis results in certain
  assumptions related to the analysis
• K and M are constant
• Linear elastic material behavior is assumed
• Small deflection theory is used, and no
  nonlinearities included
• C is not present, so damping is not included
• F is not present, so no excitation of the
  structure is assumed
• The structure can be unconstrained (rigid-body
  modes present) or partially/fully constrained,
  depending on the physical structure
• Mode shapes f are relative values, not absolute
• It is important to remember these assumptions
  related to performing free vibration analyses in
  Simulation.

4
A. Free Vibration Analysis Procedure

• The free vibration analysis procedure is very
  similar to performing a linear static analysis,
  so not all steps will be covered in detail. The
  steps in yellow italics are specific to free
  vibration analyses.
• Attach Geometry
• Assign Material Properties
• Define Contact Regions (if applicable)
• Define Mesh Controls (optional)
• Include Supports (if applicable)
• Request Frequency Finder Results
• Set Frequency Finder Options
• Solve the Model
• Review Results

5
Geometry and Point Mass

• Similar to linear static analyses, any type of
  geometry supported by Simulation may be used
• Solid bodies
• Surface bodies (with appropriate thickness
  defined)
• Line bodies (with appropriate cross-sections
  defined)
• For line bodies, only mode shapes and
  displacement results are available.
• The Point Mass feature can be used
• Input for the Point Mass was described earlier in
  Chapter 4.
• The Point Mass adds mass only in a free vibration
  analysis. It is connected to selected surfaces
  as if no stiffness is present, so the effect is
  to add only mass (not stiffness) to a structure.
• Useful for including the effect of distributed
  weight on selected surfaces. Because of this,
  the Point Mass will decrease the natural
  frequency in free vibration analyses.

6
Material Properties

• For material properties, Youngs Modulus,
  Poissons Ratio, and Mass Density are required
• Since no loading is assumed, no other material
  properties will be used, if defined

7
Contact Regions

• Contact regions are available in free vibration
  analyses. However, since this is a purely linear
  analysis, contact behavior will differ for the
  nonlinear contact types
• There are two important things to remember when
  using contact in a free vibration analysis
• The two nonlinear contact behaviors rough and
  frictionless will behave in a linear fashion,
  so they will internally behave as bonded or no
  separation instead.
• If a gap is present, the nonlinear contact
  behaviors will be free (i.e., as if no contact is
  present). Bonded and no separation contact will
  depend on the pinball region size.
• The pinball region is automatically determined by
  default

8
Contact Regions

• For ANSYS Professional licenses and above,
  additional contact options can be used in free
  vibration analyses
• For rough and frictionless contact, the
  Interface Treatment can be changed to Adjusted
  to Touch, which will make the contact surfaces
  behave as bonded and no separation, respectively.
  (Even if a gap is present, the parts will behave
  as if they are initially touching if this option
  is set.)
• The size of the Pinball Region may be changed
  as well as viewed to ensure that bonded and no
  separation contact is established, even if a gap
  is present.
• Please refer to Chapters 3 and 4 for discussions
  on the pinball region and how to define its size
• For ANSYS Structural licenses and above,
  frictional contact will behave similar to bonded
  contact if surfaces are touching but act as free
  (no contact) if contact is open.
• It is not recommended to use frictional contact
  in a free vibration analysis since it is
  nonlinear.

9
Loads and Supports

• Structural and thermal loads not used in free
  vibration
• See Section B later in this chapter for a
  discussion on free vibration with pre-stress
  analysis. In this situation, loads are
  considered but only for their pre-stress effects.
• Supports can be used in free vibration analyses
• If no or partial supports are present, rigid-body
  modes can be detected and evaluated. These modes
  will be at 0 or near 0 Hz. Unlike static
  structural analyses, free vibration analyses do
  not require that rigid-body motion be prevented.
• The boundary conditions are important, as they
  affect the mode shapes and frequencies of the
  part. Carefully consider how the model is
  constrained.
• The compression only support is a nonlinear
  support and should not be used in the analysis.
• If present, the compression only support will
  generally behave similar to a frictionless
  support.

10
Requesting Results

• Most of the options for free vibration analyses
  are similar to that of static analysis. However,
  Simulation knows to perform a free vibration
  analysis when the Frequency Finder tool is
  selected under the Solutions Branch
• The Frequency Finder tool adds another branch to
  the Solutions branch
• The Details View of the Frequency Finder allows
  the user to specify the Max Modes to Find. The
  default is 6 modes (max is 200). Increasing the
  number of modes to retrieve will increase the
  solution time.
• The search may be limited to a specific frequency
  range of interest by selecting Yes on Limit
  Search to Range.
• By default, frequencies beginning from 0 Hz
  (rigid-body modes) will be calculated if a search
  range is not set.

11
Requesting Results

• Under the Frequency Finder branch are the
  requests requested
• When toggling Max Modes to Find under the
  Frequency Finder branch, more mode shapes will
  automatically be added. The user does not need
  to request mode shapes from the Context toolbar.
• If stress, strain, or directional displacements
  are to be requested, this can be done by adding
  the result from the Context toolbar.
• For each stress, strain, or displacement result
  added, the user can specify which mode this
  corresponds to from the Details view, under
  Mode.

If relative stress or strain results are needed,
be sure to add results under the Frequency Finder
branch, not the Solution branch. Recall that mode
shapes are relative values since no excitation is
present. Hence, stresses and strains are also
relative.
12
Solution Options

• The solution branch provides details on the type
  of analysis being performed
• For a free vibration analysis, none of the
  options in the Details view of the Solution
  branch usually need to be changed.
• In the majority of cases, Solver Type should be
  left on the default option of Program
  Controlled.
• If the model is a very large one of solid
  elements, and only a few modes are to be
  requested, the Solver Type, when changed to
  Iterative, may be more efficient.
• The Analysis Type will display Free
  Vibration.

13
Solving the Model

• After setting up the model, one can solve the
  free vibration analysis just like any other
  analysis by selecting the Solve button.
• A free vibration analysis is generally more
  computationally expensive than a static analysis
  on the same model because of the equations
  solved.
• If a Solution Information branchis requested
  under the Solutionbranch, detailed solution
  output, including the amount of memory used and
  solution progress, willbe available in the
  Worksheet tab.
• If stress or strain results or morefrequencies/mo
  des are requestedafter a solution is performed,
  a newsolution is required.

14
Reviewing Results

• After solution, mode shapes can be reviewed
• Because there is no excitation applied to the
  structure, the mode shapes are relative values
  associated with free vibration
• Mode shapes (displacements), stresses, and
  strains represent relative, not absolute
  quantities
• The frequency is listed in the Details view of
  any result being viewed.
• The animation button on the Results Context
  toolbar can be used to help visualize the mode
  shapes better.

15
Reviewing Results

• The Worksheet tab of the Frequency Finder branch
  summarizes all frequencies in tabular form
• By reviewing the frequencies and mode shapes, one
  can geta better understanding of the possible
  dynamic response ofthe structure under different
  excitation directions

16
B. Workshop 5.1 Free Vibration

• Workshop 5.1 Free Vibration Analysis
• Goal
• Investigate the vibration characteristics of two
  motor cover designs manufactured from 18 gauge
  steel.

17
C. Free Vibration with Pre-Stress

• In some cases, one may want to consider prestress
  effects when performing a free vibration
  analysis.
• The stress state of a structure under constant
  (static) loads may affect its natural
  frequencies. This can be important, especially
  for structures thin in one or two dimensions.
• Consider a guitar string being tuned as the
  axial load is increased (from tightening), the
  lateral frequencies increase. This is an example
  of the stress stiffening effect.

18
Free Vibration with Pre-Stress

• In free vibration with pre-stress analyses,
  internally, two iterations are automatically
  performed
• A linear static analysis is initially performed
• Based on the stress state from the static
  analysis, a stress stiffness matrix S is
  calculated
• The free vibration with pre-stress analysis is
  then solved, including the S term

19
Procedure w/ Pre-Stress Effects

• To perform a free vibration with pre-stress
  analysis (a.k.a. prestressed modal analysis), it
  is the same as running a regular free vibration
  analysis with the following exceptions
• A load (structural and/or thermal) must be
  applied to determine what the initial stress
  state of the structure is.
• Results for the linear static structural analysis
  may also be requested under the Solution branch,
  not the Frequency Finder branch
• A stress or strain result requested under the
  Frequency Finder branch will be relative
  stress/strain values for a particular mode
• A stress or strain (or displacement) result
  requested under the Solution branch will be
  absolute stress/strain/displacement values for
  the statically applied load

20
Example w/ Pre-Stress Effects

• Consider a simple comparison of a thin plate
  fixed at one end
• Two analyses will be run free vibration and
  free vibration with pre-stress effects to
  compare the differences between the two.

21
Example w/ Pre-Stress Effects

• Notice that the only difference of running a free
  vibration analysis with or without pre-stress is
  the existence of a load
• If a Frequency Finder tool is present and a load
  is present, Simulation knows that a Free
  Vibration with Pre-Stress analysis will be
  performed.
• If results such as displacement, stress, or
  strains are requested directly underneath the
  Solution branch, the results from the linear
  static analysis can be reported.

22
Example w/ Pre-Stress Effects

• In this example, with the applied force, a
  tensile stress state is produced, thus increasing
  the natural frequencies, as illustrated below

23
D. Workshop 5.2 Prestressed Modal

• Workshop 5.2 Prestressed Modal Analysis
• Goal simulate the modal response of the tension
  link (shown below) in both a stressed and
  unstressed state.

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