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Vibration modeling using the finite element method is extremely powerful. However, with comforting

contour plots, one can be easily deceived into thinking that a superior result has been achieved.

Nevertheless, the quality of the result directly depends upon how accurately the model represents the

actual physical problem being investigated. This involves three things: sufficient understanding of the

actual vibration problem, sufficient knowledge of vibration theory including FEA, and hands-on

experience in running an FEA software package. In particular, modelers have to understand the

limitations of the theories applied and the numerical methods used. For example, the FEA can predict

global characteristics such as natural frequencies of vibration and mode shapes more accurately than

localized features such as stresses. This is an intrinsic nature of finite element methods. Without knowing

this, modelers might incorrectly use an unnecessarily fine mesh for mode shape analysis while applying

coarse meshes to evaluate stress.

TABLE 7.2 Material Properties

Density 7800 kg/m3

Young’s modulus 2.1 £ 1011 Pa

Poisson coefficient 0.29

TABLE 7.3 The First 10 Natural Frequencies

No. Frequency (Hz)

1 46.46

2 67.73

3 81.57

4 105.5

5 166.2

6 204.6

7 205.1

8 212.0

9 213.4

10 222.8

Vibration Modeling and Software Tools 7-21

© 2005 by Taylor & Francis Group, LLC

FIGURE 7.5 The fifth mode shape (166.2 Hz) of the gearbox housing. (Courtesy of Pacific Rim Engineered

Products, Surrey, British Columbia.)

FIGURE 7.4 The first mode shape (46.5 Hz) of the gearbox housing. (Courtesy of Pacific Rim Engineered Products,

Surrey, British Columbia.)

7-22 Vibration and Shock Handbook

© 2005 by Taylor & Francis Group, LLC

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