Work Reading
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Consider the harmonic shaking force P0cosΩt acting on a damped sping-mass system. The differential equation of motion with an external force exciting the system is
mΫ + cϓ + KY = P0cosΩt
The solution of this equation consists of a complementary function plus a particular function. The complementary solution is the free vibrations. Thesewill die out because of tthe damping. The particular solution can be taken in the form
Y = Y0 cos(Ωt - Θ)
The maximum displacement Y0 can be expressed in terms of the maximum impressed force, P0 as follows:
Y0 = P0 / [(K - m 2)2 + C2Ω2]1/2
Dividing the numerator and denominator of the above equation by K and substituting leads to the following:
Y0 = (P0 / K) / {[1 - (Ω / Ωn)2]2 + [2(c/cc)(Ω/Ωn]2}1/1
Let Yst = P0/K, where Yst is the deflection of the system due to the maximum dunamic input load acting as a static load. For additional simplification, let
YΩ = (Ω / Ωn) and Rc = (c/cc)
This leads to the general amplification (not transmissibility) equation:
A = Y0/Yst = 1 / [(1 - RΩ2)2 + (2RcRΩ)2]1/2
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QUOTE (Pheylan @ Nov 16 2009, 12:33 AM) <{POST_SNAPBACK}>Looks like a lot of general substitution to me.
Curiously the math is not as big a hang up as the complete lack of definition of terms. -
QUOTE (Andrew @ Nov 16 2009, 09:13 AM) <{POST_SNAPBACK}>Curiously the math is not as big a hang up as the complete lack of definition of terms.
And that is the point where math becomes physics. -
QUOTE (Governor @ Nov 16 2009, 10:21 AM) <{POST_SNAPBACK}>And that is the point where math becomes physics.
Yst is the deflection of the system due to the maximum dynamic input load acting as a static load.
How does a dynamic input load act as a static load? Is this simply another way of referencing the instantaneous load at the maximum input load?
This book is assuming an awful lot about my working knowledge of spring systems. While trying to teach me about spring systems.
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