Page 292 - Finite Element Modeling and Simulations with ANSYS Workbench

Structural Vibration and Dynamics 277

FIGURE 8.13
Car crash analysis using the FEA. (From LS-Dyna website, http://www.dynaexamples.com/)

TABLE 8.2
Units in Dynamic Analysis
Choice I Choice II
t (time) s s
L (length) m mm
m (mass) kg Mg
a (accel.) m/s 2 mm/s 2
f (force) N N
ρ (density) kg/m 3 Mg/mm 3

symmetry can still be applied in creating the FEA model of a symmetric
structure.
• Mechanism or rigid body motion means ω = 0. Can use this to check FEA models
to see if they are properly connected and/or supported.
• Input for FEA: Loading F(t) or F(ω) can be very complex and data can be enormous
in real engineering applications (e.g., the load data for a car) and thus they often
need to be filtered first before being used as input for FEA.
• Selecting a proper unit system is very important in vibration or dynamic analysis.
Two choices of the units are listed in Table 8.2. Make sure they are consistent in
the FEA models.

8.7 Case Studies with ANSYS Workbench

Problem Description: Musical instruments such as acoustic guitars create sound by
means of vibration and resonance. The body of an acoustic guitar acts as a resonating
chamber when the strings are set into oscillation at their natural frequencies. The fol-
lowing figure gives the dimensions of a simplified acoustic guitar model. The guitar has
a wall thickness of 3 mm, and is made of Douglas fir wood (E = 13.1 GPa, Poison’s ratio
ν = 0.3, Density = 470 Kg/m ). Assuming the back surface of the guitar is fixed, find the
3
first ten natural frequencies and plot the first five vibration modes of the guitar. Suppose
a harmonic pressure loading of magnitude 1 MPa is applied to a side wall of the guitar.
Plot the frequency response of the z displacement (along the surface normal direction) of
the front surface.