AE301WingVibration19SupplementLogrithmicDecrement - m n 4...

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1.9. Supplement on Logarithmic Decrement Theory 1. With the solution of the free vibration, the oscillation is when B 2 is imaginary Converting to a real term for oscillations, Using the Euler formula, the exponentials can be written as sines and cosines 2. The square bracket term is the oscillating behavior that does not decay. The amplitude decay causes the y oscillation to decay The amplitude decay function is verified by generating q(t) from the y(t) data. If q(t) appears as an undamped solution, then the amplitude decay solution is verified. 3. Following the trigonometric functions for the oscillation, a peak amplitude is observed at integer-multiple cycles, b 2 t = m 2 , where m=[0,1,2,3,. ..] .
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Then at a particular peak, numbered by j , and at another distinct peak, numbered by
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Unformatted text preview: m+n 4. The m+n defines a peak that, in the undamped oscillation, q or Q, is congruent with m . The square bracket terms, Q(m) and Q(m+n) are equal. Then a ratio of any two distinct peaks is This requires the measurement of amplitudes, integer cycles apart. As shown below, the ratio of amplitude measurements gives the damping ratio. 5. For small damping , the natural frequency term out-weighs the damping term (now the m symbol here is mass and n is for the natural frequency subscript) Then the key to calculating damping are 1. the calculation of critical damping from mass and natural frequency or 2. the computation of amplitude reduction from oscillation peaks. You can find peaks using the MATLAB code and the mouse selection method....
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This note was uploaded on 02/07/2011 for the course AE/ME 301 taught by Professor Lafleur during the Spring '11 term at Clarkson University .

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AE301WingVibration19SupplementLogrithmicDecrement - m n 4...

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