Mechanical Vibrations - UNESP · Mechanical Vibrations Prof. Paulo J. Paupitz Gonçalves....
Transcript of Mechanical Vibrations - UNESP · Mechanical Vibrations Prof. Paulo J. Paupitz Gonçalves....
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Mechanical Vibrations
Prof. Paulo J. Paupitz Gonçalves
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Harmonically Excited Vibration
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Harmonically Excited Vibration
The solution of nonhomogeneous ordinary differential equation can be written as a sum of the solutions for the homogeneous and particular ODE
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Harmonically Excited Vibration
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Response of an Undamped System Under Harmonic Force
The homogeneous solution of this equation is given by
and the particular solution
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Particular Solution
where X is an constant that denotes the maximum amplitude of
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Particular Solution
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Particular Solution
Case 1. When :
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Particular Solution
Case 2. When :
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General Solution
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General Solution
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Particular Solution
Case 3. When :
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Particular Solution
Case 3. When :
Apply L'hospital's rule
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Particular Solution
Case 3. When :
The response at resonance becomes
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Response of a Damped System Under Harmonic Force
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Response of a Damped System Under Harmonic Force
We are interested in the Particular Solution
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Response of a Damped System Under Harmonic Force
Using
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Response of a Damped System Under Harmonic Force
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Response of a Damped System Under Harmonic Force
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Response of a Damped System Under Harmonic Force
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Response of a Damped System Under Harmonic Force
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Response of a Damped System Under Harmonic Force
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Response of a Damped System Under the Harmonic Motion of the Base
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Response of a Damped System Under the Harmonic Motion of the Base
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Displacement Transmissibility
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Transmissibility
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Transmitted Force
The transmitted to the base or support due to the reactions from the spring and the dashpot
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Transmitted Force
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Response of a Damped System Under Rotating Unbalance
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Response of a Damped System Under Rotating Unbalance
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Response of a Damped System Under Rotating Unbalance