Lateral Natural Frequency of a Cantilever Beam. By Dr. Chuan-Chiang Chen Tuskegee University Mechanical Engineering Dept. email@example.com Copyright 2006 Expected completion time for this tutorial is 50 minutes Companion Tutorial for Vibrations/Mechanical Design Course
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By Dr. Chuan-Chiang Chen
Mechanical Engineering Dept.
Expected completion time for this tutorial is 50 minutes
Companion Tutorial for Vibrations/Mechanical Design Course
Reference Text: Mechanical Vibrations, 2nd edition, by S. S. Rao
The educational goal is to provide undergraduate engineering students with understanding of a specific engineering topic and FE theory, along with an ability to apply commercial FE software to typical engineering problems. The educational goal will be accomplished through four educational objectives based upon Bloom’s Taxonomy and ABET Criteria 3 as follows:
1. Engineering Topics (Comprehension: 3a, 3k). Understand the fundamental basis of engineering topics through the use of finite element computer models.
2. FE Theory (Comprehension; 3a). Understand the fundamental basis of FE Theory.
3. FE Modeling Practice (Application; 3a, 3e, 3k). Be able to implement a suitable finite element model and construct a correct computer model using commercial FE software.
4. FE Solution Interpretation and Verification (Comprehension and Evaluation; 3a, 3e) Be able to interpret and evaluate finite element solution quality, including the importance of verification .
W(x, t): Deflection : Mass Density A: Cross Sectional Area
L: length E: Young Modulus I: Second Moment of Inertia
xAnalytical Analysis of a cantilever beam
The natural Frequency can be found by plugging the numerical values into the equation.
=0.2875 lb/in3 A=0.81 in2
L=50” E=30x106 psi I=0.05468 in4
The FEA can provide insight in determining the natural frequency and mode shapes of a uniform cross sectional cantilever beam. The FEA method provides another analysis tool for the engineer to develop reliable designs that can avoid the severe vibrations due to the excitation close to the resonant frequency.
What do we do to improve the accuracy of the area measurement?
Sol. Time: 5 sec.
Max. Stress: 27.8 ksi
Sol. Time: 10 sec.
Max. Stress: 27.6 ksi
Sol. Time: 2 sec.
Max. Stress: 25.8 ksi