Deflection of Uniform Bar with Free Ends Mechanical Vibration
Strength and Mechanics of Materials
Accelerometers About and Application
The following are equations which predict the deflection and mode patterns for beams. They are based on simple beam theory and are accurate for beams having a length to depth ratio of the order of ten or more.
The characteristics numbers for the first three modes of this beam are: 4.73, 7.853 and 10.996.
Where: | |
y | = Deflection [in] |
= The characteristic number for the n^{th }mode and is the root of the equation | |
n | = Mode number |
Frequencies of higher modes for this beam are given below, in which w is the weight per unit length of the beam and g = 386 in/sec^{2}.
Uniform Bar With Free Ends | |||
Illustration | Amplitude Profile | Mode | Natural Circular Frequency |
2 Nodes |
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3 Nodes |
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4 Nodes |
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5 Nodes |